Building a Quantum Engineering Undergraduate Program

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Building a Quantum EngineeringUndergraduate Program

Abraham Asfaw, Alexandre Blais, Kenneth R. Brown, Jonathan Candelaria, Christopher Cantwell,Lincoln D. Carr, Joshua Combes, Dripto M. Debroy, John M. Donohue, Sophia E. Economou, Emily

Edwards, Michael F. J. Fox, Steven M. Girvin, Alan Ho, Hilary M. Hurst, Zubin Jacob, Blake R.Johnson, Ezekiel Johnston-Halperin, Robert Joynt, Eliot Kapit, Judith Klein-Seetharaman, Martin

Laforest, H. J. Lewandowski, Theresa W. Lynn, Corey Rae H. McRae, Celia Merzbacher, SpyridonMichalakis, Prineha Narang, William D. Oliver, Jens Palsberg, David P. Pappas, Michael G. Raymer,

David J. Reilly, Mark Saffman, Thomas A. Searles, Jeffrey H. Shapiro, and Chandralekha Singh

(Received, revised, accepted dates of manuscript.) This work waspartially supported by the U.S. National Science Foundation undergrant EEC-2110432. S. Girvin, T. A. Searles, and S. E. Economouwere supported by the U.S. Department of Energy, Office of Science,National Quantum Information Science Research Centers, Co-designCenter for Quantum Advantage (C2QA) under contract number DE-SC0012704. M. Raymer acknowledges support from the NSF Engi-neering Research Center for Quantum Networks (CQN), led by theUniversity of Arizona under NSF grant number 1941583. E. Johnston-Halperin acknowledges support from NSF C-ACCEL 2040581. H. J.Lewandowski acknowledges support from NSF QLCI OMA–2016244.L. D. Carr, H. M. Hurst, E. Kapit, and T. Lynn acknowledge supportfrom NSF QLCI-CG OMA-1936835. C.R.H. McRae and D.P. Pappaswere supported by NIST NQI and QIS efforts, as well as the U.S.Department of Energy, Office of Science, National Quantum Infor-mation Science Research Centers, Superconducting Quantum Materi-als and Systems Center (SQMS) under the contract No. DE-AC02-07CH11359. A. Blais was supported by the Canada First ResearchExcellence Fund. S. Michalakis was supported by Caltech’s Institutefor Quantum Information and Matter (IQIM), a National Science Foun-dation (NSF) Physics Frontiers Center (NSF Grant PHY-1733907). M.Saffman was supported by NSF QLCI-HQAN Award 2016136. Thisarticle was presented in part at the Quantum Undergraduate Education& Scientific Training (QUEST) Workshop and at the SPIE Photonicsfor Quantum Symposium. (All authors contributed equally to thiswork; authorship is listed alphabetically by last name.) (Correspondingauthor: Lincoln D. Carr, [email protected])

A. Asfaw and B. R. Johnson are with IBM Quantum, IBM T. J.Watson Research Center, Yorktown Heights, NY, U.S.A.

A. Blais is with Institut Quantique and Departement de Physique,Universite de Sherbrooke, Sherbrooke J1K 2R1 QC, Canada andCanadian Institute for Advanced Research, Toronto M5G 1M1 ON,Canada

K. R. Brown and D. Debroy are with the Duke Quantum Center,Department of Physics, Department of Electrical and Computer Engi-neering, and Department of Chemistry, Duke University, Durham, NC27708, U.S.A.

J. Candelaria is with SystemX Program and Department of ElectricalEngineering, Stanford University, Stanford, CA 94305, U.S.A.

C. Cantwell is with Department of Physics and Astronomy, Univer-sity of Southern California, Los Angeles, California 90089, U.S.A.

L. D. Carr and E. Kapit are with the Quantum Engineering Programand Department of Physics, Colorado School of Mines, Golden, CO80401, U.S.A.

J. Combes is with the Department of Electrical, Computer and En-ergy Engineering, University of Colorado Boulder, Boulder, Colorado80309, U.S.A.

J. M Donohue is with the Institute for Quantum Computing, Uni-versity of Waterloo, Waterloo, ON N2L 3G1 Canada

S. E. Economou is with the Department of Physics, Virginia Tech,Blacksburg, Virginia 24061, U.S.A.

E. Edwards is with the IQUIST, University of Illinois Urbana-Champaign, Urbana, IL 61801, U.S.A.

M. F. J. Fox and H. Lewandowski are with JILA, National Instituteof Standards and Technology and the University of Colorado, Boulder,CO 80309, U.S.A. and Department of Physics, University of ColoradoBoulder, Boulder, CO 80309, U.S.A.

M. F. J. Fox is with the Department of Physics, Imperial CollegeLondon, Prince Consort Road, London, SW7 2AZ, UK

S. Girvin and D. Debroy are with the Yale Quantum Institute andDepartment of Physics, Yale University, New Haven, CT 06520, U.S.A.

A. Ho is with Google Research, Venice, CA 90291, U.S.A.H. M. Hurst is with the Department of Physics & Astronomy, San

Jose State University, San Jose, California 95192, U.S.A.Z. Jacob is with the School of Electrical and Computer Engineering,

Purdue University, West Lafayatte, Indiana - 47907, U.S.A.E. Johnston-Halperin is with the Department of Physics, The Ohio

State University, Columbus, OH 43210, U.S.A.R. Joynt and M. Saffman are with the Department of Physics,

University of Wisconsin-Madison, 1150 University Avenue, Madison,WI 53706, U.S.A.

J. Kelin-Seetharaman is with the Quantitative Biosciences andEngineering Program and Department of Chemistry, Colorado Schoolof Mines, Golden, CO 80401, U.S.A.

M. Laforest is with ISARA Corporation, Waterloo, Ontario N2L0A9, Canada

T. W. Lynn is with the Department of Physics, Harvey MuddCollege, Claremont, CA 91711, U.S.A.

C. R. H. McRae is with the Department of Physics, University ofColorado Boulder, Boulder, CO 80309, U.S.A., and National Instituteof Standards and Technology Boulder, Boulder, CO 80305, U.S.A.

C. Merzbacher is with SRI International, Boulder, CO 80302S. Michalakais is with the Institute for Quantum Information and

Matter, California Institute of Technology, Pasadena, CA 91125,U.S.A.

P. Narang is with the John A. Paulson School of Engineeringand Applied Sciences, Harvard University, Cambridge, Massachusetts02138, U.S.A.

W. D. Oliver is with the Department of Electrical Engineering andComputer Science and Lincoln Laboratory, Massachusetts Institute ofTechnology, Cambridge, MA 02139, U.S.A.

J. Palsberg is with the Department of Computer Science, Universityof California – Los Angeles, Los Angeles, California 90095, U.S.A.

D. P. Pappas is with the National Institute of Standards and Tech-nology, Boulder, CO 80303, U.S.A.

M G. Raymer is with the Department of Physics and Oregon Centerfor Optical, Molecular and Quantum Science, University of Oregon,Eugene, OR 97403, U.S.A.

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Abstract—The rapidly growing quantum informationscience and engineering (QISE) industry will require bothquantum-aware and quantum-proficient engineers at thebachelor’s level. We provide a roadmap for building aquantum engineering education program to satisfy thisneed. For quantum-aware engineers, we describe how todesign a first quantum engineering course accessible toall STEM students. For the education and training ofquantum-proficient engineers, we detail both a quantumengineering minor accessible to all STEM majors, anda quantum track directly integrated into individual engi-neering majors. We propose that such programs typicallyrequire only three or four newly developed courses thatcomplement existing engineering and science classes avail-able on most larger campuses. We describe a conceptualquantum information science course for implementationat any post-secondary institution, including communitycolleges and military schools. QISE presents extraordi-nary opportunities to work towards rectifying issues ofinclusivity and equity that continue to be pervasive withinengineering. We present a plan to do so and describe howquantum engineering education presents an excellent setof education research opportunities. Finally, we outlinea hands-on training plan on quantum hardware, a keycomponent of any quantum engineering program, with avariety of technologies including optics, atoms and ions,cryogenic and solid-state technologies, nanofabrication, andcontrol and readout electronics. Our recommendations pro-vide a flexible framework that can be tailored for academicinstitutions ranging from teaching and undergraduate-focused two- and four-year colleges to research-intensiveuniversities.

CONTENTS

I Introduction to Quantum Engineering 3

II Undergraduate Quantum Engineering inContext 4

II-A Technology, Industry, and Oppor-tunity . . . . . . . . . . . . . . . . 4

II-B The Quantum Education Landscape 5

III Building a First QISE Course for STEMStudents 6

III-A Module 0: Linear Algebra forQISE (E) . . . . . . . . . . . . . . 7

III-B Module 1: Classical informationtheory (E) . . . . . . . . . . . . . 8

D. J. Reilly is with the ARC Centre of Excellence for EngineeredQuantum Systems, School of Physics, The University of Sydney,Sydney, NSW 2006, Australia and Microsoft Quantum Sydney, TheUniversity of Sydney, Sydney, NSW 2006, Australia

T. A. Searles is with the IBM-HBCU Quantum Center, Departmentof Physics & Astronomy, Howard University, Washington, DC 20059,U.S.A.

J. H. Shapiro is with the Department of Electrical Engineering andComputer Science, Massachusetts Institute of Technology, Cambridge,MA 02139, U.S.A.

C. Singh is with the Department of Physics and Astronomy, Uni-versity of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

III-C Module 2: One and two quantumbits (E) . . . . . . . . . . . . . . . 8

III-D Module 3: Two-qubit gates andentanglement (E) . . . . . . . . . 8

III-E Module 4: Quantum algorithms(E/A) . . . . . . . . . . . . . . . . 8

III-F Module 5: NISQ devices and al-gorithms (E/A) . . . . . . . . . . . 8

III-G Module 6: Quantum error correc-tion (E/A) . . . . . . . . . . . . . 8

III-H Module 7: Quantum communica-tion and encryption (E) . . . . . . 8

III-I Module 8: Hamiltonians and timeevolution (A) . . . . . . . . . . . . 8

III-J Module 9: Dynamics with time-varying Hamiltonians (A) . . . . . 9

III-K Module 10: Open quantum sys-tems (A) . . . . . . . . . . . . . . 9

III-L Module 11: Physical quantum bits(E/A) . . . . . . . . . . . . . . . . 9

III-M Module 12: Quantum SensingModalities (E/A) . . . . . . . . . . 9

IV Creating a Complete Undergraduate Quan-tum Engineering Program 9

IV-A QISE Education Research . . . . . 9IV-B Freshman-Level Concepts-

Focused QISE courses: Quantum101 . . . . . . . . . . . . . . . . . 10

IV-C Considerations in Creating QISECourses . . . . . . . . . . . . . . . 12

IV-D The Quantum Engineering Minor . 12IV-E The Quantum Engineering Track

within Engineering Majors . . . . 14IV-F The Future Quantum Engineering

Major . . . . . . . . . . . . . . . . 14

V Promoting Diversity in Quantum Engineer-ing Undergraduate Programs 14

V-A Recommendations for Course andProgram Design . . . . . . . . . . 15

V-B Opportunities at Minority ServingInstitutions . . . . . . . . . . . . 16

V-C Transfer Pathways from Two-Yearand Four-Year Institutions . . . . . 17

V-D Industry’s Role in Promoting Di-versity in Undergraduate QuantumEngineering . . . . . . . . . . . . 17

V-E Summary of Diversity, Equity, andInclusion Recommendations . . . 17

VI Hands-on Training on Quantum Hardware 18VI-A Optics . . . . . . . . . . . . . . . 19VI-B Atoms and Ions . . . . . . . . . . 19

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VI-C Cryogenic and Solid State . . . . 19VI-D Nanofabrication . . . . . . . . . . 20VI-E The Quantum-Classical Interface . 20VI-F Tools and Involvement from Industry 20

VII Summary and Key Recommendations 21

References 22

I. INTRODUCTION TO QUANTUM ENGINEERING

Quantum information science combines our under-standing of nature at its most fundamental level—quantum mechanics —with information theory. Froman applications standpoint, advancements in this fieldnow rely on incorporating an engineering approach tobetter design, integrate, and scale quantum technologies.For example, the landmark quantum advantage resultachieved in 2019 [1], in which a quantum computer meta computational benchmark not achievable on the sametime scale with present classical computing resources,made heavy use of a range of engineering disciplinesto construct a machine capable of quantum speed-up.This is one example of the many recent advances inquantum information science (QIS) spanning algorithms,architectures, and qubit technologies, including atomsand ions, semiconductors, superconductors, as well assupporting hardware in integrated optics, and microwaveand RF control and readout [2], [3], [4], [5]. This newchapter of discovery and innovation is centered on noveldevices that employ non-classical states, superposition,and entanglement to create technological advantage overclassical systems. In addition, devices based on theseaspects of quantum physics could serve as a foundationaltechnology, similar to the role of semiconductors in the20th century. In doing so, QIS is predicted to open upotherwise impossible vistas in communication, computa-tion, and sensing. Future engineers are needed to addressgrand challenges such as scalability and identifyingunique real-world opportunities for quantum systems,and indeed industry positions reflect this need [6], [7].Given this expectation, incorporating quantum infor-mation into formal engineering curricula will preparestudents to work at the forefront of current scienceand technology, and drive future growth across multipleengineering sectors.

So, what is this new field of quantum engineeringand what are the implications for education programs?As defined by the U.S. National Quantum Initiative Act,quantum information science is “the use of the laws ofquantum physics for the storage, transmission, manipu-lation, computing, or measurement of information” [8].Building on this definition, we define quantum engineer-ing as the application of engineering methods and prin-ciples to quantum information systems and problems.

This includes the work of both quantum-aware engineersand quantum-proficient engineers– and is necessarilyredefining the field to be quantum information scienceand engineering (QISE).

Increasing the engineering talent flow into QISE couldvastly accelerate the development of quantum tech-nologies, some of which might be harnessed to tacklesome of the world’s most pressing problems, such asmore efficient nitrogen fixation [9], making artificiallight-harvesting photosynthetic complexes for clean en-ergy [10], and addressing the rapidly approaching endof Moore’s law and subsequent limitation on computingresources [11]. It is also a major opportunity to broadenparticipation in terms of diversity, equity, and inclusion.In this regard, it has been argued that modifications andinnovations in the engineering portion of that pipeline,as well across the physical and computational sciences—perhaps spanning kindergarten to Ph.D. with many on-ramps and opportunities along the way—will be vitalfor developing the workforce necessary to capitalize onthe promise of QISE. There is a pressing educationalgap between, on the one hand, excitement generatedboth by the popular media and the increased interestin introducing QISE in secondary school, and on theother hand, quantum-related graduate programs focusedmainly on PhDs, with a few MS programs as well. Thisundergraduate gap can be addressed in the near term,and closing it will likely have substantial impact on thequantum workforce. Finally, many engineers tradition-ally do not pursue a PhD, but rather a Bachelor’s or atmost a Master’s. Specializing in quantum engineeringwill offer a similar educational pathway to professionallife as other traditional engineering disciplines withspecializations, such as bioengineering. Thus, withinthe context of emerging quantum education activities atthe K-12, Masters, and workforce upskilling levels, thisarticle focuses its attention on the existing gap in thequantum engineering pipeline at the undergraduate level.

Within undergraduate programs, quantum mechan-ics has long been taught in physics departments, butQISE is cross-disciplinary and demands a workforce thatdraws from formal education programs in departmentsincluding applied mathematics, chemistry, computer sci-ence, electrical engineering, materials engineering, andmolecular engineering, to name a few. Well-establishedPh.D. programs and undergraduate physics programsmust now be complemented by new efforts that broadenthe population of quantum-proficient and quantum-awarescientists and engineers. This need is supported by thecurrent demand for traditional engineering skills in quan-tum industry, which is well documented [12]. Thus, oneof the tensions in discussing new formal education pro-grams in QISE surrounds sufficiently training studentsin quantum engineering, while not overly diluting their

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broader engineering degree so that students retain a solidfoundation for many decades of continued learning andprofessional experience. We need to prepare T-shapedengineers, who have deep core knowledge and skills insome engineering discipline, while also having breadthso that they are agile and adaptable for interdisciplinaryinnovation in a quickly changing technological and sci-entific landscape [13].

This article lays out a detailed initial road-map forengineering schools and departments to drive quantumengineering education forward. We focus on undergrad-uate quantum engineers and the recommendations areintended to be tailored for different academic contextsfrom teaching and undergraduate-focused four-year col-leges and universities to research-intensive universities—there is no one-size-fits-all solution. In Sec. II, weprovide a brief description of the technological, educa-tional, and logistical context for quantum engineering,which also helps define the field. To facilitate quantum-awareness among budding engineers, in Sec. III wepresent different pathways to build a first course inQISE accessible to any STEM major. To train quantum-proficient engineers, in Sec. IV we describe how to createa more complete undergraduate quantum engineeringprogram. This includes QISE education research; a com-plete quantum engineering minor with three existingworking examples; a quantum track within an engi-neering major with one current working example; andsome remarks on a potential future quantum engineeringmajor, which we believe is premature at this stage. Thenin Sec. V, we discuss how QISE presents an extraordi-nary opportunity to have a major impact on equity andinclusion in engineering as a whole, and provide specificrecommendations to do so. In Sec. VI, we walk throughthe most common quantum technologies and sketchhands-on training programs in each of them, which canbe adapted to different academic environments. Finally,in Sec. VII we summarize our recommendations.

The roadmap will also prove useful to other sciencedepartments creating their own QISE programs or part-nering with engineering programs to do so. Additionally,a key recommendation of this paper centers aroundan introductory “Quantum 101” course with minimalmath content, like Anthropology 101 or Psychology 101,which we feel should be implemented at as many univer-sities and colleges as possible to provide both an entrypoint to the field and a route towards promoting quantumawareness among the general population. Communitycolleges especially have returning older students as wellas many high school students taking classes, and canincluding a general QISE course could have an out-size impact. Since a significant fraction of engineeringstudents are transfers from two-year colleges [14], thisfurther justifies the design and wide-spread adoption of

a ”Quantum 101 course.” We include Quantum 101 inSec. IV as both broader impact and a recruiting tool forquantum engineering.

II. UNDERGRADUATE QUANTUM ENGINEERING INCONTEXT

A. Technology, Industry, and Opportunity

The modern information age rests in large part on afoundation of semiconductor materials and devices that,at a fundamental level, require a quantum mechanicaldescription. For example, semiconductor devices are thedriving force behind modern computing, sensing, andnetworking technologies. In addition, an understandingof quantum mechanical band structure has led to thedevelopment of transistors, lasers, and photodetectors,which transmit and receive the glut of data carried bythe internet’s fiber-optic backbone. Today, the continuedminiaturization of semiconductor devices is approachingthe end of Moore’s law. As the transistor size stan-dard approaches the semiconductor atomic lattice scale,quantum effects begin to limit rather than enable furtherprogress. But, as has happened before in engineering,these limitations have spurred progress as we seek toturn a bug into a feature, and develop new quantum-enhanced, rather than quantum-limited, technologies.

Quantum computers, whose non-classical propertiesseem to evade the bounds of the extended Church-Turinghypothesis, could provide breakthrough capabilities inoptimization [15] and machine learning [16], [17]. Theyalso have the unrivaled ability to efficiently simulatequantum systems [18], [19] since they are quantumsystems themselves, and thus will find uses in chemistry,molecular biology, materials science, and drug discovery,to name a few applications. Quantum communicationwill enable quantum computers to be connected in aquantum internet [20], [21], which will open up a hostof possibilities, such as quantum secret sharing. Quan-tum sensing will open up new measurement modalitiesand sensitivities, such as Quantum Positioning Systems(QPS) capable of autonomous navigation (GPS-free)with accuracy down to the centimeter level.

Many of the predicted technology implications andcorresponding investment can be traced back to quantumkey distribution (QKD), which was proposed by Bennettand Brassard in 1984 [22]. This application allows twocommunicating parties to establish a secret key forsecure communication in the presence of an all-powerfuleavesdropper. QKD’s potential importance was magni-fied enormously in 1994, when Peter Shor publisheda quantum-computer algorithm [23] for breaking theRivest-Shamir-Adelman (RSA) public-key infrastructureon which internet commerce currently depends. Thepossible vulnerability of RSA soon spurred research—

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both theoretical and experimental—in quantum commu-nication and quantum computing that went far beyondQKD and algorithmic attacks on cryptographic protocolslike RSA.

Currently, one of the largest areas of activity in QISEis associated with quantum computers [24] and thecreation of quantum networks [25]. There are alreadyover 300 quantum simulators, or specialized “analog”quantum computers worldwide, built on over 10 dis-tinct physical architectures [19]. More general “digital”quantum computers already report achieving a quantumadvantage [1], [26], [24], that is, meeting computationalbenchmarks not possible on a reasonable time scalewith present classical computing resources. There isalso ample activity related to the future of quantumsensing [27], [28], [29], [30]. Quantum sensing hasbeen applied in magnetometry [31] and ultra-preciseclocks [32], among other areas. There may also be newuntapped possibilities for improved classical informationtransmission using quantum communication [33], [34],[35], [36]. Moreover, quantum communication and sens-ing principles have led to proposals for improving theangular resolution of astronomical imagers [37], [38] andthe sensitivity of microwave radars [39], [40], [41], [42],and additional such advances are anticipated.

Due to advances in QISE coupled to its potentialscientific and societal impacts, quantum research hascorrespondingly expanded beyond academia and gov-ernment laboratories into industry. As of Fall 2019there were already more than 87 quantum-related com-panies, spanning sensors, networking and communica-tions, computing hardware, algorithms and applications,and facilitating technology, and this industry continuesto expand [12]. Recent research by Fox, Zwickl, andLewandowski [12] points out that although researchersin this field are often Ph.D. physicists, as quantumindustry products are moved out of development and intoproduction, the need for engineers will increase. Thiswork goes on to summarize the skill set valued by em-ployers in the quantum industry: coding, statistical meth-ods for data analysis, laboratory experience, electronicsknowledge, problem-solving, materials properties, andquantum algorithms. Inasmuch as nearly all quantumcomputation, communication, and sensing developmentswill involve a great deal of classical engineering, havingsome level of quantum awareness will be sufficientfor many engineering graduates [43]. Examples includemicrowave engineers who will work on interconnectionswithin superconducting quantum computers, photonicsengineers who will work on the fiber links for quantumnetworks, and control engineers who will work on thevarious control systems required by quantum computingtechnologies. This quantum awareness could potentiallybe achieved with a single course or a two-semester se-

quence, see Secs.III and IV-B, or with an undergraduateminor or track, see Secs. IV-D-IV-E.

B. The Quantum Education Landscape

The rapid growth of QISE as an academic disci-pline and viable career path for graduates has led to agrowing number of formal quantum education efforts atall academic levels. Outreach efforts to a broad rangeof nonspecialist audiences have also been developedin limited contexts recent years, and we expect thateducation and outreach efforts will continue to expand.To supplement this paper’s emphasis on undergraduatequantum engineering education, we discuss how under-graduate quantum engineering would fit into the widerquantum education landscape, with a focus on the U.S.national landscape, and how those relationships, alongwith lessons learned in other activities, could informthe development of undergraduate quantum engineeringprograms and courses.

At the graduate level, a growing number of insti-tutions have already launched or are developing mas-ter’s degree programs, offering bachelor’s degree hold-ers in several STEM fields the specialized educationand professional training to help them transition intothe quantum workforce—or in some cases into Ph.D.programs in QISE. These programs face many chal-lenges that undergraduate quantum engineering will alsoencounter, such as the need to accommodate a varietyof incoming technical backgrounds and prior exposurelevels to quantum science; the need to recruit and supporta diverse student population in order to promote equityand a broad range of creative perspectives in the fieldas a whole; and the need to train teaching assistantsand faculty from a wide range of departments to teachinterdisciplinary QISE courses.

Outside higher education, numerous K-12 and publicoutreach programs in quantum information already existor are under development, but the reach of such programsremains limited and impact is relatively unknown. Inan effort to begin establishing content frameworks forbroadly introducing QISE into K-12 classrooms, muse-ums and other learning environments, an NSF-sponsoredworkshop in 2020 drafted a set of nine Key Conceptsfor Future QIS Learners [44] that can be adapted forengineering contexts. The National Q-12 Education Part-nership and the Q2Work program are collaborating withteachers to expand these concepts for different ages andsubjects and supporting the development of K-12 andpublic education initiatives [45]. To increase quantumliteracy among educators and community stakeholders,and to develop curricula, the NSF supports teacher work-shops that are piloting lesson design and implementationas well as convergence accelerators QuSTEAM and the

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National Quantum Literacy Network [46]. Complement-ing these efforts are numerous summer camps, after-school programs, and online courses for students inter-ested in QISE. These programs can provide inspirationand even a pipeline for students as they consider a futurein quantum engineering.

K-12 formal quantum education is in its infancyand will require significant resources for full-scale im-plementation. This includes integrating quantum train-ing into teacher professional development programs,researching and developing effective curricular models,and promoting long-term public awareness and engage-ment. Additionally, coordination with state and localeducation stakeholders is necessary for broad implemen-tation.

As programs begin to scale up over the comingdecades, they will begin to create a new population ofstudents who enter college already primed with an inter-est in QISE and fuel the quantum information revolution,much as classical computer classes and opportunitiesfueled the classical information revolution starting in the1980s.

The pressing need for quantum-proficient andquantum-aware engineers in the workforce, the growingset of graduate programs tailored to interests and ambi-tions in the field, and the expanding set of outreach andeducation opportunities for K-12 students currently leavea clear gap in the trajectories available to many quantum-interested students during their undergraduate years. Itis essential that academia support and develop coursesthat address this gap at diverse types of institutions—including community colleges, undergraduate colleges,and large and small research intensive universities—andpromote a wide range of pathways into the field.

For instance, because a large fraction of engineeringstudents nationwide transfer from two-year colleges [47],community colleges and four-year institutions need topartner to remove barriers for students to make thistransition in quantum engineering, just as in other STEMmajors, tracks, and minors. To further support students asthey move through their education, institutions could tiethe development of quantum engineering programs to K-12 activities that connect with secondary school studentsand educators. Those having experience in K-12 andoutreach programs have indicated that initial exposuresshould be varied to engage a broad range of potentialfuture quantum engineers. For some students, quantumgames [48] could be an excellent opportunity to piqueinterest, build intuition, motivate more future rigorousstudy, and even deepen understanding through repeatedpractice in different learning contexts. For others, ex-amples of practical applications, interdisciplinarity, andsocietal impact embedded within courses could be morecompelling. Professionals working in K-12 and outreach

efforts indicate that demystifying the field rather thanemphasizing its exotic attributes may lower the barrierfor entry, and potentially attract a larger, more diversestudent population, as students become aware that QISEis more than an intellectual exercise and offers bothexisting technological applications and stable and wide-ranging job opportunities. Future quantum engineeringprograms at the undergraduate level can perhaps im-prove retention by providing regular examples of existingcareer trajectories and facilitating mentoring relation-ships [49]. Anecdotal experience suggests that deliberateattention to these areas could be more critical in quantumengineering than in a more established field, where manystudents have career models available in the form ofrelatives and other community members.

Finally, a key component of QISE education is con-tinuing education, called upskilling in the industrialcontext. As mentioned, a few universities already providea master’s program or graduate professional certificatein quantum engineering geared towards students withan existing undergraduate degree in STEM. Others offeronline learning and certification for existing profession-als. A growing number of online continuing educationplatforms such as EdX, Coursera, etc., are offeringformal quantum courses for the general public [50], [51].Informally, there have been a rapidly growing numberof university courses placed on YouTube for publicviewing. However, these programs and courses appear tobe insufficient, or are too narrow in scope, to meet therapidly increasing need for quantum proficiency acrossmultiple disciplines. Given that the fields that contributeto QISE are not gender, racially, or ethnically diverse,upskilling programs are also unlikely to result in anincrease in diversity across the technical workforce.

This all presents an opportunity for universities build-ing their quantum engineering profile and programs.Introductory undergraduate courses such as those de-scribed in Sec. IV-B and Sec. III can be leveragedas part of a university’s MOOC program for existingworkforce training. Over and above upskilling, currentlythe workforce needs [6], [7] are such that a large numberof new BS/BE recipients will need to have quantumengineering education already in place. In the followingsections, we lay out a plan for accomplishing this goal.

III. BUILDING A FIRST QISE COURSE FOR STEMSTUDENTS

Designing introductory courses in QISE is challengingbecause the field is in rapid technological flux andbecause we need courses that are accessible to studentsfrom a wide variety of disciplines having varied mathe-matical and scientific preparation levels. In this sense, thechallenge is similar to that faced by computer science inthe early days. In addition, local faculty expertise varies

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at different colleges and universities. An introductorycourse might be designed for first year college students,graduate students, or anyone in between. As a result,we have chosen to present our recommendations foran introductory QISE course as a set of modules fromwhich a course can be built and then tailored to meet theindividual needs of the students, program, and faculty;some of these modules, such as the introduction to thegate model, can be made accessible to students at anylevel (labeled with an E) below, whereas others likequantum noise are likely more appropriate for advancedstudents (labeled with A).

This course is designed overall for engineering or atleast STEM students as it has significant mathematicalcontent; in Sec. IV-B we suggest a separate Quantum101 course which is accessible to non-STEM students.We strongly recommend that a first QISE course asdescribed in this section assume only a backgroundin high school and freshman physics. In contrast, theQuantum 101 course in Sec. IV-B assumes no physicsbackground at all. However, even for engineering stu-dents one may want to avoid continuous variable systemsin introductory courses, even unentangled, single-particleones. Studying them in depth typically requires quite alot of pre-requisite specialized mathematical knowledge,although some QISE educators have explored otherapproaches [52]. Some studies suggest the discrete-variable or “spin-first” approach to quantum mechanicsprovides more opportunities for students to understandthe underlying concepts independently from the complexmathematical calculations often associated with quantummechanics [53]. Appropriate to a college-level class, weassume students will have taken a linear algebra coursebeforehand, and recommend spending the first week onreview of the basics of linear algebra as a refresher.Alternatively, one could choose not to rely on linearalgebra as a pre-requisite and teach the required conceptsas part of the course (at the expense of covering lessground in QISE) – see Sec. III-A. We envision eachmodule taking 1-3 weeks of a standard semester course,depending on depth and the educational level of thestudents.

The goal of our recommendation is to be able toeasily combine modules to create an introductory courseat any level based on the goals of the program. Touse a few of the authors of this paper as examples,Girvin has taught an introductory quantum computingcourse aimed at first-year students onward that roughlyfollowed the sequence of modules 1-2-3-4-6; Kapittaught an advanced course aimed at preparing seniorsand graduate students for further specialized courses andresearch, which proceeded as 2-3-8-9-10-4; Blais taughtsimilar level students with the sequence 2-3-7-4-6-11;Economou teaches two courses, one purely on quantum

software, roughly following 1-2-3-7-4-6, and one fo-cused on physical platforms and their control, following8-9-10-11; and Lynn has taught an introductory courseaimed at sophomores onward but sometimes taken byfirst-year students and even advanced high-school stu-dents, which followed the rough sequence 2-3-11-4-6-7,interspersing ideas from 1. Carr has used module 0 asan add-on to a variety of STEM classes with quantumcontent when students have little to no knowledge oflinear algebra. The choice of modules would also beinformed by the selection of more advanced courses theprogram offers beyond this introduction. For example,a program that offers a dedicated quantum algorithmsclass might de-emphasize much of module 4 in theintroductory course, and a program that offers microwaveengineering courses would certainly want to includemodule 9. Such a course could be titled, “Introductionto Quantum Engineering.”

Comprehensive learning goals may vary somewhatfrom course to course and should be set for any imple-mentation of the modules. The Key Concepts for FutureQuantum Information Science Learners [44] presents aset of essential QISE ideas, but learning goals basedon this must be developed. It is an open engineeringeducation research question as to what learning goalswould be appropriate in the context of undergraduatequantum information engineering. Finally, we note thatalthough we have not included a survey of pre-quantuminformation era quantum mechanics, sometimes called“Quantum 1.0”, explicitly in our modules, it is impliedin many of our topics as an appropriate background to“Quantum 2.0”, i.e., QISE. Alternately, Quantum 1.0 canbe included as a separate module on extant pre-QISEtechnologies such as lasers, MRIs, atomic clocks fornavigation, the photoelectric effect in motion sensors,etc., for example as a non-mathematical Module 0 inplace of linear algebra.

The modules below and other course recommenda-tions are focused more on quantum computing, with lesscontent covering quantum communication and quantumsensing. We support and encourage the development ofadditional modules in these critical QISE pillars, whichwill be essential for providing a complete curriculum.

A. Module 0: Linear Algebra for QISE (E)Vector spaces (superposition, concept of a ba-

sis), linear transformations, matrix multiplication, non-commutativity, diagonalization, inversion, Hermitian andunitary operators, trace and partial trace, outer and ten-sor products, scaling up to larger matrices numerically.These concepts can be introduced in the context of thesingle qubit, i.e. 2×2 matrices, and their tensor products.As linear algebra is a strong prerequisite for most QISE,students can either take it as a separate course or it can

8

be included here as a focused unit. The alternate optionis a non-mathematical quantum concepts course as inSec. IV-B.

B. Module 1: Classical information theory (E)

Basics of bits, gates, communication, randomness andstatistics, error correction, parity and data compression.Discusses the basics of computation itself, shows thatthe number of distinct programs mapping n input bitsto m output bits is doubly exponential N = 2m2n andintroduces the notion of a universal classical gate set thatcan reproduce any of this enormous number of programs.Vector spaces could be introduced at this point, as inMermin’s book [54], where classical bits are representedas vectors and gates as matrices. This eases the transitionto qubits.

C. Module 2: One and two quantum bits (E)

Quantum bits, superposition states, measurements andthe Born rule. Single-qubit Hilbert space: linear op-erators, Dirac notation, orthonormal bases and basischanges, qubit rotations, and the Bloch sphere. Expec-tation values and variance of measurement results. Thisintroduces students to the basics of quantum theory inthe concrete context of the analytically solvable problemof 1 or 2 qubits. It helps students understand multi-qubitHilbert space and operators, leading to tensor productspaces and the combinatorial complexity explosion.

D. Module 3: Two-qubit gates and entanglement (E)

The CNOT gate and the circuit model of computa-tion. Bell states and non-classical correlations. A typicalexample would be the spin singlet or Bell states, inwhich information is encoded in the global system whileno information is contained in the constituent qubits.Quantum dense coding and monogamy of entanglement.The no-cloning theorem and state teleportation. Uni-versal quantum gate sets. This shows students how tobuild quantum computation from basic elements (gates)and some of the surprising outcomes. Depending onthe programmatic emphasis, this module could focus onentanglement more generally, for instance, in single-ionoptical atomic clocks, cold molecular ion spectroscopy,quantum communications, random key generation, etc.

E. Module 4: Quantum algorithms (E/A)

Early examples of quantum advantage in computation:the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon’salgorithms. Phase kick back from controlled unitaries.Oracle algorithms. Grover’s algorithm, phase estimation,and the quantum Fourier transform. In discussing Shor’salgorithm, one may want to focus on the QFT and the

period-finding algorithm more than factoring itself, sincethe factoring application depends on number theoreticresults which are less relevant to quantum algorithmsmore broadly. Students will gain an understanding ofthe breadth of quantum algorithm development.

F. Module 5: NISQ devices and algorithms (E/A)

Noisy intermediate scale quantum devices. Heuristicalgorithms, including the Variational Quantum Eigen-solver (VQE), the Quantum Approximate OptimizationAlgorithm (QAOA), and possibly machine learning al-gorithms. Error mitigation. Use of online software andcloud-accessible hardware. Students will understand howto program actual quantum hardware and learn someminimal quantum software skills.

G. Module 6: Quantum error correction (E/A)

Quantum computers are analog and errors are contin-uous, but measured errors are discrete. Error models:coherent errors, incoherent errors as coherent errorsin a larger Hilbert space, correlated errors. Repetitioncode for dephasing or bit-flip errors. Shor code. Con-catenation, code capacity threshold vs. fault-tolerancethreshold. Error correction is one of the most essentialtopics in QISE and students need a careful introductionto clarify the contrast with much easier error correctionmethods on classical computers.

H. Module 7: Quantum communication and encryption(E)

Inability to perfectly distinguish non-orthogonal statesand no-cloning theorem. The BB84 quantum key distri-bution protocol. Entanglement-based quantum key dis-tribution protocol (E91). Entanglement swapping andquantum repeater networks. Error correction in commu-nication and entanglement distillation. This module canbuild on module 3, and is the intro to the power of QISEfor communications.

I. Module 8: Hamiltonians and time evolution (A)

Eigenstates and eigenenergies of a Hamiltonian. TheSchrodinger equation and time evolution. Expectationvalues; motion and transitions as interference phenom-ena. The harmonic oscillator and general N -level sys-tems. Basic properties of systems with multiple identicalparticles. This module is especially useful for buildinga knowledge of quantum and classical control systems,since quantum gates are based on the underlying dynam-ics.

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J. Module 9: Dynamics with time-varying Hamiltonians(A)

Dynamics and control of two-level systems subject toAC fields. Quantum mechanics in a rotating frame, andthe rotating wave approximation. Rabi oscillations. Con-trol of harmonic systems with an auxiliary anharmonicelement. The quantum adiabatic theorem. This modulenaturally builds on module 8, or can be expanded andsubstituted in place of it. AC fields such as microwavesare key to classical control of quantum systems.

K. Module 10: Open quantum systems (A)

The density matrix formulation of quantum me-chanics. Entangling and non-entangling noise. Fermi’sGolden Rule. Models for a bath. Reduced density matri-ces. Physical noise mechanisms. Quantifying coherencethrough estimates of relaxation and dephasing times. Anessential concept in QISE is the fragility of quantumstates. This module can provide underlying knowledgeto comprehend the severity of the decoherence problem.

L. Module 11: Physical quantum bits (E/A)

Broad overview of candidate systems for quantumcomputing. Superconducting qubits, trapped ions, spinqubits. At a more advanced level, one can also presentphotonic systems, neutral atoms and topological qubits.One could also formulate this module as a more in-depthexploration of a single class of qubits.

M. Module 12: Quantum Sensing Modalities (E/A)

Quantum-enhanced resolution in optical interferom-etry: classical operation versus N00N-state (entangled)operation. Heisenberg uncertainty principle for the quan-tum harmonic oscillator: coherent states and squeezedstates. This will demonstrate to students the basic prin-ciples of quantum-enhanced accuracy in optical interfer-ometry, including coherent-state operation with standard-quantum-limit scaling versus squeezed-state operationwith Heisenberg scaling.

IV. CREATING A COMPLETE UNDERGRADUATEQUANTUM ENGINEERING PROGRAM

The purpose of this section is to identify theissues associated with quantum engineering programdevelopment and to outline possible approaches thatcan be tailored to individual institutions, includingcourse development and a minor or track. In addition toresource constraints and opportunities particular to eacheducational institution, it is useful to keep in mind theneeds of the QISE industry as it stands today and inthe near future. This is shown in Fig. 1. Higher levelsof specialization are at the top, while lower levels of

specialization, but also more jobs, are at the bottom.Positions near the very top are most likely to be filledby PhD graduates, while MS graduates will be at themiddle and lower levels, and BS/BE graduates willform the base. Undergraduate program developmentmust concern itself with filling all three of these niches.In the following, we discuss STEM education researchin QISE, developing concepts-focused and advancedundergraduate courses, and practical plans for minorsand tracks, closing the section with a few comments ona future quantum engineering major.

A. QISE Education ResearchThere are several pedagogical challenges associated

with developing a quantum engineering program. Wemust contemplate the content of individual courses anddegree programs. We must also bridge the gap betweenwhat we think we are teaching and what students areactually learning. Methods to do so include evidence-based active-engagement pedagogies and curricula. Thisbridge should ideally be research-validated in the contextof STEM education, as well as be effective for studentsfrom diverse backgrounds and prior preparations. The in-terdisciplinary nature of QISE education implies that thediversity in students’ prior preparation and backgroundis likely to be greater in QISE-focused courses. Thisfact makes it even more critical to use STEM educationresearch-validated curricula and pedagogies that focuson helping all students, not just the best-prepared, tolearn. As the quantum engineering education roadmapcontained in this article develops new programs andcourses from scratch, we have the unusual opportunity todo things well from the ground up, rather than improvingexisting courses as e.g. in quantum physics educationresearch [55], [56], [57], [58], [59], [60], [61], [62].

Development and implementation of these types ofpedagogies and curricula entails thinking carefully aboutthe learning objectives and goals of each course andaligning these with instructional design and assessment(e.g., is a pen and paper exam able to assess students’proficiency in aligning an optical system?) It also en-tails having a good understanding of students’ priorknowledge and skills that can be built on, the com-mon difficulties students have after traditional lecture-based instruction [63], [64], and consideration of howto leverage the diverse prior preparation of studentseffectively. For example, education research has studiedstudents working in small groups on collaborative groupproblem solving, tutorials and clicker questions [65],[66], [67], [68], [69], [70], [71], [72] using approaches inwhich individual accountability has been integrated withpositive interdependence, e.g., through grade incentives.These methods have been shown to improve learning

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Increasinglevels ofquantum

education

Increasingnumber of

positions

Non-quantum engineer employed in quantum company

electronic, software, process, mechanical, cryo, fab, chemical, optical, materials, sales

Quantum aware engineer

works at the interface of quantum and classical

Quantum proficient engineer

deep technical understanding

Specialists

R&D of new devices or theory

Fig. 1. Representation of the relative number of anticipated positions for various sectors of the quantum job market and the requisite level ofquantum education for each.

outcomes for all students. Furthermore, it is critical tocontemplate how different courses build on each otherin a degree program in order to maximize their benefitfor students who take those courses simultaneously orsequentially.

Explicit effort should be made to ensure an equitableand inclusive learning environment, as discussed in Sec-tion V, so that students from diverse demographics andbackgrounds have an opportunity to excel. Moreover,validated assessment tools need to be designed to mea-sure growth in students’ knowledge and skills, as wellas development in their motivational beliefs about quan-tum. Assessing and improving the motivational beliefsof students from different demographic groups aboutQISE (e.g., their QISE-related self-efficacy or sense ofbelonging in classes) is especially important to ensurethat students from underrepresented groups also havehigh self-efficacy and sense of belonging, since thesebeliefs can impact student outcome, as well as theirshort and long-term retention within the field. Along withissues of diversity, equity, and inclusion, considerationof social, societal, ethical and sustainability issues ofQISE would be beneficial, in line with directions inengineering education worldwide [73], [74], [75].

Finally, although there has been some education re-search on the effectiveness of QISE courses, more needsto be done as new programs are developed. This researchneeds to examine not just theory courses, but also hands-

on experimental experiences and lab courses, as manyof the desired skills are best learned in these environ-ments [76]. Hands-on learning is covered in Sec. VI.

B. Freshman-Level Concepts-Focused QISE courses:Quantum 101

Many in the community assert that offering QISEcourses at the freshman or sophomore level, withoutnecessarily requiring linear algebra, is desirable in orderto stimulate students’ interest through concepts andapplications, and to help resolve structural inequities inSTEM pedagogy and improve diversity, see e.g. Fig. 2.For instance, such a course can be offered in communitycollege and military school settings, and as a “Quantum101” option for students who have a general interestin learning the quantum information perspective. De-pending on the setting, the modules above would needadjustment or supplemented to effectively provide anentry point into QISE.

By learning concepts and applications first, withoutthe need for advanced mathematical formalism, studentsmay gain appreciation for the topic and intuition for theconnections between concepts and applications. More-over, avoiding advanced mathematical prerequisites orco-requisites lowers the barrier to entry for students whocome to the field with less mathematical preparation,or relatively late in their education. A similar approachis common in computer science and math departments,

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First Quantum course

prerequisitesMinimal/None

Content: Qinfo focus

Linear Algebra+Calc.

Content: Qinfo focus Content: Gen. Qtheory

no yes

Fig. 2. Several possibilities exist for first quantum courses for students outside physics departments. The fundamental decision is whetherprerequisites are required or not. The general consensus in the community is without prerequisites the course should be focused on quantuminformation topics, labeled here as “Qinfo focus”. For areas of engineering that require a quantum education, departments have a decision tomake. The first option is to have students take a specialized quantum information course, resulting in quantum aware engineers. The secondoption is to give students a holistic quantum education, which will better prepare students for more advanced quantum courses and applicationsof quantum theory encountered in industrial settings, resulting in quantum proficient engineers – see also Fig. 1.

where programming concepts, or proof concepts courses,are often required entry points for a major or minor. Suchcourses also function as recruiting tools due to their wideaccessibility.

This approach in addition allows the connection be-tween end-use applications and discussion of poten-tial career pathways, which may appeal to technology-oriented students. Therefore, such courses may broadenthe on-ramp for quantum engineers and help to recruitand retain a more diverse, more equitable, and moreinclusive cohort of students into the discipline.

A potential concern with a QISE course that doesnot require sophisticated math is that it would requiresacrificing rigor or accuracy. Surprisingly, that does nothave to be the case, and there now exists a formalismthat can explain quantum states, the concept of su-perposition, entanglement, and unitary transformations,as well as quantum algorithms rigorously without theneed for linear algebra [77], [78], [79], [50]. The onlyrequirement is knowledge of basic arithmetic. Throughthis method, which some of us have used for outreachto high school students, in courses at the freshman level,and for courses drawing broadly on all STEM studentswith no quantum background, students can predict theoutcome of quantum circuits. This is a nice complementto using online cloud processors or simulators, especiallythe drag-and-drop option that IBM offers to build circuits(which does not require text-based programming skills),as they can verify the results of their calculations usingthe online interface [79]. At this time, more research isneeded to understand these approaches and their overallefficacy as courses and as bridges into more advancedmaterial.

Finding space for such a concepts course in an engi-

neering degree is a difficult task, but one that may be anessential entry point to the field at many institutions. Inprograms where linear algebra is not a significant barrierfor the student body, a first course as described in SectionIII can provide an efficient grounding in the concepts ofquantum information, couched in the same mathematicallanguage typically used within the field. A one-semesterintroduction at this level enables students to engage witha variety of further literature and instructional resourcesavailable in the field, and can even provide enoughquantum awareness to prepare engineering graduates forentry-level employment in quantum industry. In contrast,students in many programs do find linear algebra to bea significant barrier to enrollment in a first quantumcourse. In that case, a QIS concepts course can give stu-dents a solid understanding of the fundamental conceptsand applications, as well as the motivation to pursuefurther studies. Students who go on may then need totake more courses overall to arrive at a given level ofliteracy in the field, but this tradeoff can be more thanworthwhile in exposing more students to the possibilitiesof QISE.

There are three major institutional uses for this kindof course. First, it can be taught in community colleges,military schools, and universities that do not have theresources to create a more advanced QISE curriculum,let alone QISE degrees, to provide quantum awareness totheir students. Second, it is valuable to universities thatdo not yet have advanced QISE courses and degrees, asa stepping stone toward building quantum engineeringprograms. Third, it can ease entry into more advancedand demanding courses, and provide intuition into QISEconcepts without conflating them with the mathematicalformalism itself.

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C. Considerations in Creating QISE CoursesTo develop a robust quantum workforce, it is necessary

to educate students about more than simply qubit modal-ities, quantum circuits, and quantum algorithms. For ex-ample, many nascent offerings at universities lack educa-tion in quantum sensing, quantum communications, thetheory of quantum hardware, and lab courses on quantumhardware. Rather, the majority of offerings presentlyfocus on quantum information and quantum algorithms.Yet, this does not at all reflect the breadth of needs inindustry or academia [12]. Indeed, the primary difficultyin quantum hardware and quantum technologies (sens-ing, communications, computing) is understanding thehardware itself, which is also changing. For example,while developing commercial quantum algorithms is oneof the grand challenges of the coming decade, buildingquantum computers that can run these algorithms reliablyat scale is equally important. Additionally, developinginterconnects for quantum networks of either sensors ordevices remains a challenge. As such, within a majorityof vertically integrated quantum companies, the quantumalgorithms team is but a fraction of the total headcountand likely composed of PhD-level employees for theforeseeable future. Thus, overemphasizing algorithms atthe expense of hardware at the undergraduate level willlikely miss many employment opportunities.

In contrast, the quantum engineer requires a broadknowledge of different technologies, including atomsand ions, semiconductors, superconductors, integratedoptics, as well as microwave and RF control and read-out [2], [3], [4], [5]. At the same time, the quantumengineer can pursue different areas of specialization,including communications, cryptography, and informa-tion theory; quantum computation and classical controlsystems; and quantum sensing and devices. Undergrad-uate QISE education to date remains almost entirelyhoused in physics departments focused on fundamentalscience in preparation for the physics PhD. Thus, astrong advantage of a quantum engineering program isto create BS/BE level students with a general knowledgeof quantum technologies and specializations. Advancedundergraduate quantum engineering programs shouldseek to capitalize on this opportunity at all levels byintegrating many technologies and specializations eitherinto separate topical courses, where resources are avail-able, or into broad survey courses. Ideally, any quantumengineering program would offer the opportunity to learnquantum communications and cryptography, quantumsensing and devices, and quantum simulations and com-puting.

However, one of the challenges to augmenting existingengineering programs with a minor or a track is thatthese programs are already highly constrained, in partby the Accreditation Board for Engineering and Tech-

nology (ABET), as well as the need for multiple coresubjects and the relative lack of electives. For example,a “Digital Signal Processing” track versus a “MicrowaveEngineering” track may differ in practice by only 3 or4 courses. That leaves essentially 3-4 available “slots”to make a minor or a track. Thus, it is paramount thatquantum engineering programs integrate closely withexisting engineering programs, as will be laid out indetail in Secs. IV-D-IV-E.

Another issue of concern, and also a major op-portunity, is the lack of textbooks suitable for quan-tum engineering. Quantum theory textbooks are pre-dominately written by physicists and assume a greatdeal of physics background, such as Hamiltonian andLagrangian mechanics, thermodynamics and statisticalphysics, etc. While there are some exceptions [80], [81],[82], there is a need for quantum theory textbooks fornon-physics majors that provide education in generalaspects of quantum theory. Even more seriously, to ourknowledge, no quantum engineering textbook presentlyexists for learning the diversity of quantum hardwareat the advanced undergraduate level—see the detaileddescriptions in Sec. VI. Introductory and review articlesexist at a wide spectrum of levels from graduate toprofessional QISE researchers [2], [3], [4], [5], and thereare even a few graduate-level textbooks with hardwarecomponents, such as [83]. However, much of this ma-terial is too specialized or advanced for undergraduatecourses. Morover, in some cases the state-of-the-art ischanging on a rapid time scale, which presents anotherchallenge in course design and also places a burden oninstructor capacity. For specific topics, there are someexcellent materials aimed at undergraduates, e.g., for su-perconducting devices [84]. To create a holistic hardwarecourse, the instructor is forced to cobble such materialstogether. Similar issues arise for quantum sensing andquantum characterization, verification, and validation.The latter is particularly problematic, as a major taskfor a quantum engineer at the moment is to assess theperformance of quantum hardware and improve designsor control strategies based on this assessment. Broadlyintegrating classical engineering expertise in e.g., controltheory into the quantum domain, i.e., quantum controltheory, will likely occur over many years.

D. The Quantum Engineering MinorA Quantum Engineering interdepartmental minor is

advantageous because it supplements and leverages ex-isting degree programs in engineering, computer science,mathematics, and the fundamental sciences. Althoughminors can be highly variable from institution to in-stitution, a typical minor requires six to seven courses:three are considered core to the minor, and the remain-ing courses are electives. The electives may be chosen

13

from relevant subjects within the department hosting theminor, from other departments (assuming prerequisitesrequirements are met), or from a student’s home depart-ment. This has two consequences. First, it opens morepathways for non-traditional students to study quantumtechnology. Second, it avoids overloading students withsubjects outside their college. The primary decision forthe host department(s) is to determine which QISEsubjects should constitute the three core courses and inwhich departments they are taught. Such considerationsare usually particular to each academic institution, butobvious candidates are electrical engineering, computerscience, materials engineering, chemistry, and physics.

There are a few quantum engineering minor programsin the U.S. with many more to appear shortly. We provideas an example here the quantum engineering minorsat the Colorado School of Mines, at the Universityof Colorado Boulder, and at The Virginia PolytechnicInstitute and State University (Virginia Tech), whichoffer an initial roadmap for creating a minor at publicresearch universities.

These are intended as working examples, and shouldnot be construed as the only or the best programs outthere. Different institutions may structure their degreesdifferently and may emphasize quantum computing,communications, or sensing, depending on the expertiseand interests of the local QISE faculty; likewise differenthardware platforms may be emphasized depending onavailable resources. To help ameliorate the latter, werecommend programs partnering with national labs andnearby institutions, when possible, as well as incorporateinternships in industry to maximize breadth of experi-ence in new quantum engineers.

The Colorado School of Mines quantum engineeringminor requires six courses as part of the Quantum Engi-neering Interdisciplinary Academic Program supportedby six departments including electrical and materialsengineering. The first four are linear algebra, and threeof the following courses: (i) fundamentals of quantuminformation, (ii) quantum programming, (iii) low temper-ature microwave measurement, (iv) quantum many-bodyphysics, and (v) microelectronics processing. Studentscan either take their remaining two courses from thislist to round out their quantum education, or else anytwo from the quantum engineering course catalog toincrease specialization. The catalog is extensive, butincludes existing STEM courses such as feedback con-trol systems, digital signal processing, semiconductordevice physics and design, computational materials, andmachine learning. This minor required the creation of4 new courses targeted at quantum engineers, namely(i)-(iv). Course (i) is covered in Sec. III, while (ii)-(iv)were designed with the considerations of Sec. IV-C inmind. Because Mines is a purely STEM school, many

prerequisites are not necessary to specify.The University of Colorado Boulder quantum en-

gineering minor requires six courses with three pre-requisites: programming, calculus, and linear algebra.Students are then required to take the following threecourses: (i) foundations of quantum engineering, (ii)foundations of quantum hardware, and (iii) introductionto quantum computing for the theory track, or quantumengineering lab for the experimental track. Flexibilityis built into requirement (i): two semesters of upperdivision quantum mechanics in the physics departmentcan also satisfy the requirement. The remaining threecourses are required from a large elective list which,similar to Mines, is drawn from existing STEM coursesacross campus, such as microwave and RF laboratory,control systems analysis, machine learning, and solidstate physics. Thus, similar to Mines, the quantum engi-neering minor required the creation of four new courses,some of which had already been taught in pilot form asa proof-of-principle.

The Virginia Tech QISE minor is a joint effort amongseven departments/programs across the College of Sci-ence and the College of Engineering, and it requires eightcourses. Five of them are mandatory: linear algebra, anintroductory (freshman/sophomore level) QISE coursewithout any prerequisites (see Sec. IV-B), an advancedQISE course with only a linear algebra prerequisite(modules 1-4, 6, 7) described in Sec. III, and twoprogramming courses that include classical programming(e.g., Python), quantum programming (using online hard-ware and quantum languages such as Qiskit), and useof collaborative software. The fifth course is a choicebetween one focusing on physical quantum platforms(an expanded version of modules 9-11 in Sec. III) anda more advanced theoretical quantum computing course.This allows students from diverse departments to deepentheir QISE knowledge irrespective of whether they havea quantum mechanics background. The remaining twocourses are selected out of a long list of existing electivesfrom six departments. The creation of this minor requiredthree new courses (the introductory QISE course and thetwo programming courses).

We conclude that creating a quantum engineeringminor in a STEM environment can require the additionof three or four new courses, some of which mayonly need adaptation from preexisting instruction. Thelargest barrier to the minor is hands-on training onquantum hardware, which we treat separately in Sec. VI.These examples should not be taken as an exact ordetailed plan but instead as first successful attempts thatcan be improved upon. We emphasize that it is moreimportant to teaching engineering principles and designin the context of QISE than to focus on any particularquantum technology or platform, as also reflected in the

14

diverse technologies found in Sec. VI. This is critical forproviding the depth of education and agility necessaryto support student success in future careers, whether ornot they are quantum related.

E. The Quantum Engineering Track within EngineeringMajors

A quantum engineering track within an existing engi-neering program is an alternative option to the minor. Inthe near term, it provides a means to more readily designa program without the need for interdepartmental col-laboration. Existing engineering programs already havemany subjects that are relevant to quantum engineering.Thus, a track should not be difficult to construct withinsuch an existing framework. Each engineering depart-ment would be able to offer multiple customized trackscomprising a series of courses that enables students toobtain domain-specific knowledge through both “clas-sical” and targeted quantum subjects. For example, anelectrical engineering or computer science departmentcould offer a quantum software track, an algorithmstrack, a quantum hardware track, etc. When paired withthe core courses the students have chosen to form theirdegree program, the track provides a supplemental, in-depth training in topics relevant to a future quantumworkforce, such as low-level control of quantum hard-ware, quantum programming languages and paradigms,quantum compilers, and the like, while fundamentallyretaining the structure of their bachelors degree.

A typical quantum engineering track in an engineeringprogram could involve the standard engineering coursesplus a two-semester sequence of quantum engineeringI-II, two semesters of hands-on training on quantumhardware I-II, and two specialty courses drawn from alist of standard courses available at the university suchas nanofabrication, materials science, solid state devices,machine learning, etc. For a more software-centric trackimplementation or option quantum computation and al-gorithms can take the place of quantum hardware II. Thequantum engineering I-II sequence should cover materialfrom Sec. III and indeed may draw directly on such acourse designed for the minor in Sec. IV-D. Dependingon the engineering discipline, additional requirementsmay be necessary. For example, at the U. Chicago thereis a quantum engineering track in molecular engineering,which also requires intermediate electromagnetism, anecessary component for classical control systems. Wealso think it would be a good idea to add to a quantumengineering track along these lines a first year freshman-level concepts-focused course, Quantum 101. Such acourse is also a highly useful addition and recruitingtool, see Sec. IV-B. Likewise instrumentation or labcourses offering opportunities for the quantum engineer

to develop experience on two or more technologies is animportant consideration, see Sec. VI.

F. The Future Quantum Engineering Major

The minor or track may be part of existing engineeringdepartments, or be part of an interdisciplinary programsupported by several departments, including electricalengineering, materials engineering, engineering physics,computer science, chemistry, and applied mathematics,to name one of many examples discussed here. Suchquantum engineering programs may naturally evolve tothe point of seeking a complete undergraduate degreetitled “quantum engineering.” Programs can in somecases lead to stand-alone departments, as we see inthe past with nano-engineering and other engineeringspecializations.

Whether in a program or department, the developmentof a quantum engineering major is a complex undertak-ing that may not yet be suitable for the majority of aca-demic institutions. It is foreseeable that such majors maymore commonly emerge as quantum technologies matureover the next decade and quantum engineering developsas an engineering discipline. The current ambiguity ofa quantum engineering major and what it entails couldadversely impact the employment prospects of studentsgraduating with such a quantum engineering degree. Forexample, employers would be understandably uncertainabout the preparation and training of a quantum engineer.On the other hand, a track record of hires that wereelectrical engineers or software engineers, now with aminor or a track in quantum engineering, may makeevaluating such a candidate relatively straightforward.

V. PROMOTING DIVERSITY IN QUANTUMENGINEERING UNDERGRADUATE PROGRAMS

Advances in QISE and the development of associatedtechnologies rely on expertise from multiple disciplinesincluding, but not limited to, applied mathematics, chem-istry, computer science, electrical engineering, materialscience and materials engineering, and physics. Thesedisciplines have historically struggled to be inclusiveand equitable, as reflected in persistently low num-bers of graduates identifying as coming from educa-tionally marginalized racial and ethnic groups, sexualpreferences, and genders, including women, the largestmarginalized group of all. For example, in the U.S.,the overall percentage of bachelors degrees in physicsawarded to women (20%), Hispanic students (9%) andAfrican American students (4%) has remained stub-bornly low for decades [85], with similar trends in theother fields. Not surprisingly, the existing quantum work-force in industry is correspondingly lacking in diversity.The issues of each discipline with respect to broadening

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participation and facilitating success of marginalizedstudents (e.g., for physics [49]) compound to paint ableak picture for building diverse, equitable, and inclu-sive quantum engineering undergraduate programs goingforward.

It is therefore imperative that curriculum designers,researchers, and university administrators implementingQISE programs think critically about issues of diversity,equity, and inclusion from the beginning. While the fieldand the associated undergraduate academic programs arein the early stages, we have an opportunity to effectlong-lasting change in QISE and its related disciplines,and offer equitable outcomes for students from all back-grounds. Moreover, a large percentage of engineeringstudents in the US are foreign born. A careful explorationof barriers to learning for foreign born students will behelpful toward producing the best quantum engineers.Some of these barriers interface with diversity, equity,and inclusion issues. We recognize that there is not aone-size-fits all solution and that education programsmust be tailored to different institutions, departments,and disciplines.

A. Recommendations for Course and Program DesignHere, we provide some recommendations for any

institution looking to add more QISE content to theircurriculum in a way that also intentionally promotesdiversity, equity, and inclusion. This is a world-wideissue, but the focus of this and following subsectionsof Sec. V is on the U.S. context, needs, and initiatives.

All courses and curricula should have learning out-comes for required QISE knowledge and skills [65],[66], [67], [68], [69], [70], [71], [72]. Courses shouldalso have explicit outcomes to promote a high sense ofbelonging, self-efficacy, and identity as a person who canexcel in QISE for all students, but particularly studentsfrom historically marginalized groups, e.g., women andracial/ethnic minorities [86]. Self-efficacy, or belief inone’s ability generally, is known to be a key predictorof success in STEM fields [87], [88], [89]. Outcomescan be evaluated through entry and exit surveys ofstudents in each introductory QISE class. For example,in an introductory quantum mechanics class, studentself-efficacy in performing quantum calculations andunderstanding quantum concepts should increase by theend of the course. In order to achieve these learningoutcomes, it is critical for faculty to ensure that thelearning environment in their courses and labs are eq-uitable and inclusive. To this end, faculty need to betrained in inclusive mentoring approaches, such as beinggenuinely invested in the success of the student andhaving a growth mindset about their student’s potentialto excel [90], [91], [92], [93]. There is also evidencethat brief interventions in the classroom at the beginning

of the term can make the learning environment moreequitable and inclusive [94], which can have long-termeffects on the success of students from marginalizedgroups [95], [96].

Evaluation of new courses and degree programsshould include key elements related to diversity, andbe coupled to larger longitudinal studies of climate,culture, and industry hiring (for example, this could beincluded in continuing industry surveys carried out bythe Quantum Economic Development Consortium). In alldata gathering efforts, it is critical to disaggregate quan-titative data about student outcomes by race/ethnicityand gender. Additionally, qualitative interviews are keyto understand the impact of curricular and mentoringchanges on students’ experiences and persistence todegree. Recruitment of more marginalized students isnot enough to achieve a truly diverse program andworkforce; rather, the key metric of progress should bethese students thriving in the program as well as theirdegree attainment and subsequent employment. In otherwords, equity of outcomes is a key metric of success forany program.

One concrete recommendation for increasing diversityis to restructure science and engineering programs toaccommodate QISE knowledge earlier in the curricu-lum. Departments should prioritize creation of a single“quantum awareness” introductory course as a short-term goal, see Sec. IV-B. This is critical for institutionsthat are not able to implement a full QISE program.Early introduction of QISE content, the field’s impact,and future career opportunities are especially importantfor retaining students from economically disadvantagedbackgrounds (who are often also marginalized students)because it enables them to see viable career paths towell paying jobs in the quantum industry. In addition,professional development skills should be integrated intothe curriculum early to facilitate student confidence.Students may also benefit from targeted training on howto work in diverse teams [91].

Another way to incorporate knowledge of real-worldQISE applications early on is through undergraduateresearch experiences. Perhaps more than any other in-tervention, undergraduate research has been shown toincrease student self-efficacy and persistence to degree,both in the general student population [97], [87] andfor marginalized students in particular [88]. There isalso evidence that undergraduate research experiencescan encourage marginalized students to pursue highereducation after their undergraduate degree, which wouldhelp to diversify the existing PhD pipeline [98]. Un-dergraduate research experiences can be offered in avariety of ways; for example, research could be com-pleted at the student’s home institution or in partner-ship with more well-resourced institutions in the area

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(for example, through summer programs). However, itmust also be stated that not all undergraduate researchexperiences are equal in quality and effectiveness. High-quality mentoring is essential to achieving increased self-efficacy among students. Mentors need to be preparedto provide advice not only on research, but on otherprofessional skills such as time-management and sci-entific communication [88]. Increasing social supportfor undergraduate researchers through designated cohortscan help them build community with their peers and seethemselves as engineers and scientists, something thatis often difficult for marginalized students who do notsee themselves reflected in the celebrated leaders of thefield. Finally, there is some evidence that longer researchexperiences can be better for students, because they areable to form a stronger relationship with their mentorand other students [98]. To that end, we recommendthat departments seriously consider implementing multi-year research programs for undergraduates during theacademic year, if possible. Smaller institutions mightpursue partnerships with research groups in industry orat nearby academic institutions to facilitate longer-termundergraduate research experiences. It is also importantto note that there are significant barriers for manystudents to participate in undergraduate research, whichcan be magnified for many students from marginalizedgroups. These barriers include not having the ability toparticipate during the summer due to financial or familyreasons. Thus, when developing new programs, it isimportant to consider these barriers and how to lowerthem so that more marginalized students can participate.

B. Opportunities at Minority Serving Institutions

Historically black colleges and universities (HBCUs),Hispanic serving institutions (HSIs), tribal colleges, andnative-serving institutions in the US play a significantrole in promoting racial and gender diversity in engi-neering [99]. For example, from 2001 to 2009, HBCUsconsistently produced over 45% of all black engineeringundergraduates at US institutions [100]; yet only 15of the 107 HBCUs have ABET-accredited programs asof 2021. Further, HBCUs are known to produce largepercentages (≥ 40%) of black undergraduate degrees inother QISE-related disciplines contributing to diversityin most subfields (e.g., HBCUs produced an average of25% of CS undergraduates from 2001-2009 [100]). Here,we present evidenced-based strategies for developingnew opportunities in quantum engineering at minority-serving institutions through curriculum development,increasing participation in QISE and motivating engi-neering student success at HBCUs, HSI, tribal colleges,native-serving intuitions, and community colleges in theUS.

In 1942, 20 years after the first quantum revolution,Dr. Herman Branson produced two works focused onthe training of black physics students and the need for aphysics-aware workforce in the context of World WarII [101]. He identified the need for qualified facultytrained in physics at HBCUs, and the development ofnew programs in physics at HBCUs. Today, althoughphysics majors are being produced at an all time highin the US, the AIP TEAM UP Report the Time isNow highlighted the success of HBCUs in produc-ing African-American physicists despite their persistentunder-representation in physics in US institutions over-all [49].

Similar to Branson’s findings in 1942, there is nowa need to train a new diverse, workforce in the con-text of the quantum information revolution. Establishingnew programs centered around quantum engineering atHBCUs can help achieve the overall goals of the U.S.National Quantum Initiative (NQI). Part of the largerstrategy of the NQI is prioritizing the development ofeducation and research activities through the establish-ment of collaborative research and education centersacross the U.S. Recent examples exist of both U.S.government and industry-led efforts to direct resourcesto HBCUs where the majority of black undergraduatesattain degrees in STEM [102]. Whether industry-led orsupported solely by government, new programs shouldutilize the best practices of Sec. V-A when engaging di-verse communities in the context of addressing issues ofbelonging, providing research opportunities to students,and collaborating and engaging with HBCU faculty.

Hispanic Serving Institutions (HSIs) are institutionswith at least 25% Hispanic undergraduate students. As of2014, 13% of post-secondary institutions were classifiedas HSI, but enrolled 62% of undergraduate Hispanicstudents [103]. Furthermore, the Hispanic populationis the fastest growing major racial/ethnic group in theUnited States, which suggests that the role of HSIs intraining the STEM workforce will only increase as timegoes on [99], [49]. This demographic trend indicatesthat implementing new quantum engineering programs atHSIs now could meaningfully increase the participationof Hispanic Americans in the quantum workforce in thelong-term. Some HSIs are also research-intensive insti-tutions, but many are smaller, primarily undergraduate-serving institutions [103]. There are opportunities forpartnerships between HSIs with and without engineeringprograms, enabling sharing of resources and curriculafor introductory QISE courses between the two. Industryand government initiatives similar to those for HBCUsshould also be considered for HSIs. Following thisguidance, new programs in quantum engineering canexpect to find that each subfield of QISE also benefitswith respect to their overall diversity and equity efforts.

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C. Transfer Pathways from Two-Year and Four-YearInstitutions

Many engineering programs have connections withtwo-year community colleges and four-year institutionswithout engineering programs, and these partnershipsprovide an important pathway for students to enter engi-neering professions. In 2000, as many as 40% of studentswho received a bachelor’s or master’s degree in engineer-ing attended a community college at some point [47].Several studies have shown that transfer students areequally or more successful compared to non-transferstudents in completing degrees in engineering [104],[105], [106]. Thus this student group is key to growingthe quantum workforce. New QISE programs shouldbuild connections with existing partnerships where pos-sible, for example, by helping community colleges im-plement an introduction to quantum science course (seeSecs. III and IV-B) or by offering summer internshipsfor students. Building new partnerships with communitycolleges serving a large minority population should beprioritized [47].

Near-term opportunities abound for leveraging cur-riculum development efforts in QISE to create bridgesbetween a more diverse cohort of students and careersin quantum engineering. For example, the introductorymodules discussed in Sec. III intended for everyone(E) should be accessible to students at 2- and 4-yearinstitutions with existing transfer pathways to establishedSTEM programs. This could be realized as either re-served seats in classes offered at the destination in-stitution with existing cross-registration agreements oroffering the class at the transfer school with a guaranteedtransfer credit, depending on local circumstances. If aneffort is made to emphasize applications and potentialcareer trajectories in QISE during these introductoryclasses, this approach may help build bridges fromstudents unfamiliar with the STEM landscape to degreeprograms and careers.

D. Industry’s Role in Promoting Diversity in Undergrad-uate Quantum Engineering

External stakeholders should provide powerful in-centives to promote diversity, equity, and inclusion inundergraduate quantum engineering programs, which inturn will help to diversify the future workforce. It isfirst important to recognize that increasing diversity inindustry promotes diversity in undergraduate education,and vice versa. In this section, we highlight some waysthat industry can work together with academia to expandand diversify the quantum workforce.

Students from marginalized groups are more likely toapply for a particular major if they see their peers fromthat major being hired by industry [107]. Presently, the

majority of employees at quantum technology companieshave a PhD in physics or engineering, but it is unlikelythat the PhD qualification will be needed for many of thepositions required for a thriving quantum industry [12].Industry can support the twin goals of workforce growthand diversification in several ways.

First, extra effort both by universities and industry isneeded with respect to placing marginalized student inindustry internships. This is because a strong predictorof whether a student will be hired by a company isif the student has completed an internship with thecompany, as explored e.g. in [108], [109]. If internshipsare too limited, or not available at an undergraduatelevel, alternative programs such as participating in theopen-source community (e.g. contributing to GitHubrepositories or participating in hackathons) to get real-world coding experience may also improve chances ofplacement [107].

Second, industry must strive to democratize accessto online training and resources (including quantumcomputing access) for quantum engineers, and in par-ticular focus on partnerships with MSIs, as discussedin Sec. V-B. In fact, this is already occurring in someplaces, for example through the IBM strategic partner-ship with San Jose State University [110], the IBM-HBCU Quantum Center [102], and Google’s relateddiversity and open source initiatives [111].

Lastly, industry and academic institutions need tocontinue benchmarking progress on improving diversity.For example, today in the U.S., the Quantum EconomicDevelopment Consortium already has the participationof companies to perform workforce surveys, so werecommend it expand its workforce development charterto track diversity metrics as well. The U.S. NationalScience Foundation has grant programs that can similarlyevaluate student outcomes of academic institutions, andprofessional societies such as the American Society forEngineering Education (ASEE), American Institute ofPhysics (AIP), American Physical Society (APS), theAmerican Chemical Society (ACS), etc. already playa large role in obtaining such statistics. Implementingperiodic evaluation of academic and industry diversityinitiatives is essential to ensure that programs meet theirdesired outcomes. Similar efforts can be undertaken inmany nations throughout the world.

E. Summary of Diversity, Equity, and Inclusion Recom-mendations

Our recommendations fall into three categories: cli-mate; curriculum and program evaluation; and industry.

First, regarding the climate for diversity, we recom-mend faculty and industry research mentors be giventraining in best practices for mentoring, including build-ing authenticity and trust with students and engaging in

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culturally aware communication that builds on students’strengths, since this is especially critical for the successof marginalized students [90], [91], [92], [93]. Suchtraining programs are available at many colleges anduniversities and where they are lacking can be leveragedfrom partner institutions. Departments developing QISEcourses and programs should conduct periodic climatesurveys of students and make them publicly available,to establish new best practices and continually evaluatewhat is and is not working. It is also very helpful to in-tegrate high-quality undergraduate research experiencesearly (see Sec. VI). Longer, multi-semester researchexperiences are preferable to short ones if possible [98].

Second, regarding curriculum and program evaluation,we emphasize that at minimum a quantum awarenessor concepts course be offered to introduce students tothe field early, at the freshman or sophomore level.This is particularly important for institutions that donot offer engineering degrees but which have manystudents that transfer to engineering programs. Thismay also be applicable to other QISE fields such asphysics and computer science. In program evaluation,we recommend disaggregating all data on outcomes bygender and race/ethnicity. Instructors should considerimplementing brief interventions in the classroom earlyin the semester to make the learning environment moreinclusive and equitable [94]. Course and departmentalgoals around equity should focus on equity of outcomesfor students, e.g., ensuring that marginalized studentsthrive in the program and, after completing their degree,have successful careers in QISE. A singular focus onrecruitment should be avoided [93]. We recommendprofessional development (writing and culturally awarecommunication skills) be integrated into the requiredcurriculum [91]. Quantum programs should restructurehow and when the first year of quantum science is taught.Frontloading applications could make career trajectoriesmore transparent, see Sec. IV-B. It is important to engage2-year and 4-year institutions without engineering pro-grams to open up transfer pathways [104], [105], [106].

Finally, regarding industry, we recommend that stu-dents be provided equitable access to industry educa-tional resources and internships, e.g., through formalpartnerships with minority serving institutions. It is im-portant to evaluate existing workforce needs and long-term goals and to communicate those needs to degreeprograms and curriculum designers. Industry can addi-tionally develop credentialing pathways for marginalizedstudents through internships and/or open-source educa-tional materials.

VI. HANDS-ON TRAINING ON QUANTUM HARDWARE

Hands-on learning in QISE is key to creating viablequantum engineers. Experimental research in QISE is

extremely diverse; the tools used in quantum optics labsdiffer greatly from those used in microwave-controlledsuperconducting quantum circuits, for example. How-ever, one of the chief opportunities of quantum informa-tion as a lens to view these experiments is its ability tolink them with a common language. Educational labs thatmake this connection physical, as well as mathematical,by showing that similar experimental conclusions arisefrom experiments that look completely different, willhelp to develop a cross-disciplinary skill set and allowfor a quantum workforce that can communicate acrosstraditional hardware barriers.

Assembling and selecting hands-on labs for a quantumengineering course or program will not be a one-size-fits-all solution. Each program will have constraints,including budgets and faculty expertise. While plug-and-play resources in quantum engineering are availablein some cases, many are expensive, while lower-costdo-it-yourself approaches require significant expertise.Affordable hands-on training availability may dependon cross-institution exchange of expertise. For example,the Advanced Laboratory Physics Association (ALPhA)currently provides funds and structure for faculty mem-bers to exchange hands-on training on advanced under-graduate physics lab modules [112]; support for similarefforts in quantum engineering could be transformativefor many fledgling programs.

The diversity of hardware modalities makes it im-practical to effectively cover the breadth and depth ofquantum systems that form the basis for current researchand industrial R&D. Effective training strategies shouldtherefore seek to cover a core but limited collection ofrequired knowledge, supplemented by a selected subsetof more in-depth studies of particular platforms. Thethree major areas of QISE, communication, computing,and sensing, all involve preparation, measurement, andcontrol of quantum states. Core components of hands-ontraining should therefore include an exploration of prepa-ration, measurement, and control, while highlighting howquantum approaches differ from the classical techniquesthat are routinely covered in introductory engineeringlaboratory courses. Even if specific institutional barriersrestrict hands-on lab work to a single platform, or ifmost of the interactivity comes from remote resources,adding simpler demonstrations of alternative platformswill provide students larger context through which tounderstand the field. This section will provide examplesof affordable approaches to covering these core capabil-ities.

Below we include a wide variety of platforms. It isimpossible to predict which platforms currently underinvestigation, or yet to be discovered, may end up beingthe best subject(s) for future quantum engineers. There-fore, inline with best practices in engineering education

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across engineering disciplines, it is important to trainquantum engineers in general principles and design, notto be a technician on one particular technology. For thisreason, we emphasize that programs should try to coverat least two platforms as part of the hands-on courses.

A. Optics

Quantum optics in the visible regime provides a rela-tively budget-friendly toolbox for lab activities, allowingstudents to gain hands-on experience with quantum statepreparation, manipulation, and measurement. Many ex-periments can be performed using the polarization stateof a laser beam as an analogy to a true quantum state,such as single-qubit state and channel tomography. It ispossible to use classical laser beams to simulate quantumkey distribution (QKD) in a way that has lingeringsecurity loopholes, but gives students an interactive andtactile project making explicit use of many quantum-relevant features, such as superposition and measurementdisturbance [113]. Student experiments with classicallaser beams can also provide students with an essentialtoolbox of classical skills necessary in experimentalquantum optics, such as optical fiber alignment anddetection electronics.

For experiments that require quantum states of light,such as nonlocality experiments, spontaneous parametricdown-conversion of visible or near-ultraviolet laser lightin a nonlinear optical crystal is a well-developed andaffordable approach. There are many articles describinghow to set up spontaneous parametric down-conversionsources and related accessible optical experiments inquantum state preparation and measurement for stu-dents [114], [115]. The equipment needed is also avail-able as a plug-and-play system from multiple companies,with costs currently on the order of $20k USD [116].1

Whether quantum or classically simulated, optics ex-periments clearly show how changes of the quantumstate impact measurement results. This is most sim-ply accomplished through the polarization degree offreedom, where polarizers are used for projective mea-surement and combinations of half- and quarter-waveplates can be used to rotate states and measurements toarbitrary points on the Bloch sphere. However, the sameeffects can also be shown in space using Mach-Zehnderinterferometers and time through Franson interferometry,although some effort will be required for stabilizationin these degrees of freedom. Partial coupling betweendegrees of freedom, such as a birefringent crystal thatcouples time and polarization, can be used to simulatedecoherence.

1Mention of commercial suppliers is provided for information onlyand is not an endorsement of the products of a particular company.

With quantum systems that feature single pho-tons such as those generated by spontaneous para-metric down-conversion, students may show Bellnonlocality through violations of the Clauser-Horne-Shimony-Holt inequality, non-classical photon corre-lation functions through Hanbury-Brown-Twiss inter-ferometry, Wheeler’s delayed-choice quantum eraser,photon bunching in a Hong-Ou-Mandel interferome-ter, multi-qubit state tomography, entanglement-enabledquantum key distribution in the Ekert protocol, de-termination of one- and two-photon coherence times,and more [117]. Many protocols relevant to quantuminformation, such as the bulk optical C-NOT imple-mentation and GHZ state creation, are also possibleto implement, although they require specially tailoredphoton pair sources and/or multi-pair emissions, whichmay be prohibitively expensive or alignment-sensitivefor lab courses.

B. Atoms and Ions

Other possibilities for experiments with individualquanta can be contemplated with nitrogen vacancy cen-ter, neutral atom, or trapped ion hardware. Nitrogenvacancy centers, in particular, are well suited for sens-ing applications and demonstration kits are commer-cially available [118]. Complete demonstration kits atthe level of individual quantum operations based onthe other hardware platforms are not readily avail-able. Compact and cost effective hardware for lasercooling and magneto-optical trapping of atoms can bepurchased [119]. Besides laser cooling, this type ofhardware can be used for demonstrating quantum statecontrol by optical pumping. The extension to experi-ments with single quanta using optically trapped atomsor electromagnetically trapped ions still requires substan-tial local expertise and infrastructure. Partnerships withindustry could enable such laboratory experiences.

Ultracold atoms provide another setting where quan-tum phenomena including superposition, interference,and tunneling can be observed. The apparatus to produceBose Einstein condensates is complex, comparable to adilution refrigerator in cost, and not practical to maintainwithout locally available expertise [120]. An alternativeis cloud access to a commercial machine that can beremotely operated [121].

C. Cryogenic and Solid State

Quantum solid-state platforms such as superconduct-ing circuits and quantum dots require cryogenic opera-tion at a temperature of 4K or lower, while experimentsdeep in the quantum regime require dilution refrigeratorsto reach temperatures down to 10 mK. Such equipmentis highly specialized and expensive ($300k is the entry

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level cost for a dilution refrigerator). Thus, deploymentof dilution refrigerator experiments in an undergraduatelaboratory will rely on local expertise or grouping thecost across regional schools. Similar to trapped ionsand atoms, institutional partnerships could be essentialto bring experience with such techniques within thegrasp of students at a broader range of colleges anduniversities.

Higher-temperature alternatives include implementingother types of cryogenic systems such as the QuantumDesign Physical Property Measurement System (PPMS)2

which can cool to 1.9K and thus would facilitate labsbased on ancillary measurements such as superconduct-ing transition temperatures or basic microwave resonatortransmission data acquisition.

As an alternative that will help undergraduates gainfamiliarity with control of spins, techniques for manip-ulating and measuring them, and the terminology ofcoherence, experience with a pulsed NMR apparatus canbe valuable. Complete setups are commercially avail-able [122].

D. Nanofabrication

Nanofabrication is crucial to the creation of manytypes of quantum devices, including in photonic quantumcomputing, superconducting quantum computing, spinqubits, and ion traps. A laboratory or set of labora-tories focusing on the design and implementation ofa fabrication process for a simple device such as alumped element resonator or Josephson junction wouldgive students an understanding of the requirements ofdevice fabrication, knowledge which is much neededin many implementations of quantum computing. Part-nerships with nanofabrication facilities or groups withspecialized equipment for qubit device design wouldaugment student learning in this area.

E. The Quantum-Classical Interface

All quantum technology requires a means of passinginformation between the classical and quantum domain,for instance, in the readout and control of qubits orquantum sensing devices. The quantum-classical inter-face (QCI) is a catch-all term for the electronic andoptical sub-systems of readout and control, such as dataconverters, amplifiers, signal sources, and digital logicresponsible for generating and detecting readout andcontrol waveforms, sequencing and synchronising them,as well as the infrastructure that connects those signalpaths to the physical quantum devices that encode quan-tum information. Such infrastructure comprises cabling,

2https://qd-europe.com/at/en/product/physical-property-measurement-system-ppms/

packaging, optical fibres, chip-interconnects, resonators,and on-chip routing and multiplexing approaches thattogether, constitute IO management between the classicaland quantum worlds.

The QCI provides an important opportunity for hands-on training, making use of the classical software andhardware needed to support and enable quantum ex-periments. Laboratory courses featuring microwave en-gineering, programming of embedded systems, signalgenerators, digitizers, and related hardware can provideskills of broad applicability for experimental R&D. Itsworth noting that in the context of teaching, reasonablysophisticated electronics can be sourced for minimal costin comparison to other domains of quantum hardware.Further, such electronic sub-systems provide an idealplatform for the development of generic problem solvingskills such as trouble-shooting and debugging.

Modern communication systems and the engineeringframework for their design provide a solid foundationfor developing quantum control and readout platforms.Examples include modulation and demodulation tech-niques, non-reciprocal elements, noise mitigation andapproaches to bandwidth narrowing, for instance, usinglock-in amplifiers for detecting weak signals. With re-spect to these topics, there is much common groundbetween electronic and optical or photonic systems.Indeed, radio frequency and microwave circuits (thebasis for qubit control and readout) mix electrical andoptical concepts and terminology. An ability to map andbridge these domains is a particularly useful attribute ofthe quantum engineer.

Moreover, the challenges associated with thequantum-classical interface are likely to be majorhurdles for the scale-up of quantum computers andquantum networks. The complexity of these systemsover the next decade will rival the most sophisticatedtechnological platforms ever constructed. Beyond thechallenge of the hardware itself, quantum engineers mustalso simultaneously be able to work at various levels ofabstraction, bridge fields, and leverage long-forgottenknowledge with new research discoveries.

F. Tools and Involvement from Industry

Undergraduate engineering education has a long his-tory of using tools from industry in the classroom.For QISE education, providing the physical hardwareto university students affordably and at scale is a chal-lenge. However, within the quantum computing industry,innovations drawing from the infrastructure of classicalcomputing have led to increased access to quantumcomputing resources. While not strictly hands-on innature, these tools provide an opportunity for studentsto experience authentic quantum devices. These quan-tum computing tools can be categorized into either

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open-source software or hardware access via the cloud.Open source software packages such as QisKit [123],Cirq [124], and Katas [125] are essentially free for stu-dents and educators to use, and can be used to simulatequantum computers up to 30+ qubits on an affordableclassical computer accessible to most undergraduate stu-dents. Furthermore, higher level libraries such as Tensor-Flow Quantum [126], OpenFermion [127], and QisKitAqua [128] can increase accessibility to students whoare already familiar with machine learning or chemistrysimulations.

For hardware access, companies including AWS,Google, IBM, IonQ, and Rigetti have made availablesome of their quantum processors for use via the cloudby the public and in the classroom. For example, IBMprovides free access to their smaller systems, and Googlehas implemented batch execution of student assignmentson their cloud systems. Although computer explorationsare not a substitute for hands-on experimentation, forinstitutions that are not able to provide a laboratoryexperience, there are widely available and valuable ed-ucational tools supported by major companies in theareas of quantum computing and simulation. Companiesincluding Google, IBM, and Microsoft provide extensiveonline tutorial material as well as quantum circuit sim-ulators, among other publicly available interfaces. Forexample, IBM’s QisKit platform provides free accessto students wishing to experiment with quantum circuitdesign and in addition to simulation tools allows usersto run examples on real hardware via cloud access.

In addition to the above industry tools, internships[129] [130] not only provide hands-on opportunities,but can also provide the education and experience ofworking directly within industrial settings, which allhave very different cultures and goals compared toacademic labs.

VII. SUMMARY AND KEY RECOMMENDATIONS

The rapid expansion of quantum information scienceand engineering (QISE) outside of the research lab andin industrial applications necessitates growth of a di-verse workforce with increasing quantum knowledge andskills. Development of QISE applications including com-munication, computing, and sensing require people at alllevels from K-12 to the PhD who are trained in quantum-related science and engineering. One strong focus of newtraining is at the undergraduate level for engineers. Tofacilitate the development and implementation of newquantum engineering education opportunities, we presentan initial roadmap for those creating these new programs,including suggested courses and modules, approaches toengage students in QISE training, and ways to rethinkand create diverse, inclusive and equitable education.

Our recommendations will enable bachelor’s level en-gineers to achieve two levels of QISE training, quantumaware and quantum proficient.

Below, we outline the broad recommendations toconsider when developing new quantum engineeringeducation programs at the undergraduate level.

• Traditionally, quantum courses and programs havebeen contained within physics departments. To pre-pare engineers for jobs in the quantum industry,new programs and training should be created inengineering departments with collaborations fromscience and math departments.

• To create quantum-aware engineers, we have de-tailed, module by module, the development of afirst QISE course for STEM students that can beimplemented in many different academic environ-ments. Such a course could be adjusted for differentcontexts, with additional modules, and would besufficient for any engineer to obtain the minimumquantum expertise needed to participate in the QISEindustry.

• To create quantum-proficient engineers at a higherlevel than just being quantum aware, and at thecurrent stage of the quantum industry, we recom-mend universities and colleges develop new minorsin quantum engineering or tracks embedded intraditional majors, rather than full undergraduatedegree programs. As the quantum industry growsover the next decade, full undergraduate degrees inquantum engineering may be desired and can benatural extensions of minor and track programs.

• Minors or tracks in quantum engineering can beoffered at many colleges and universities, as wesuggest a minimum of only three or four newcourses need to be created, with additional electivesdrawing from standard STEM course offerings.

• We suggest a QISE course accessible to non-STEMstudents can be taught using very little math andinstead focus on basic concepts and applications—Quantum Information Science and Engineering 101.This course can recruit students into a minor pro-gram, onboard students into the minor, and serveas general QISE education accessible to all STEMstudents from freshman year on. The focus onapplications could make career trajectories moretransparent to students as well. We recommend thistype of course could be implemented broadly, in-cluding at community colleges and military schools,which could facilitate students’ transition to a 4-year institution.

• One important component to any minor programis hands-on experimental training, as many of thejobs in the quantum industry require this expertise.We recommend a variety of hardware platforms

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where students can get this experience. We note thatless expensive “classical” options, or partnershipswith institutions with more resources, could helpstudents at institutions with less infrastructure gainhands-on experience. Additionally, we recommendintegration of high-quality undergraduate researchexperiences early in students’ academic careers,with longer, multi-semester research experiencesbeing preferable as this will also improve diversity.

• It is important to make sure these new coursesand programs are effective at helping students toachieve the learning goals for the courses and pro-grams. Toward that end, we recommend continuedand expanded STEM education research be donefor QISE, especially the engineering context, toestablish effective practices in this new domain.

• As we begin to develop new programs, we have theopportunity to focus on creating a more diverse, in-clusive, and equitable environment for our students.We have several recommendations to help achievethese goals. Departments developing QISE coursesand programs should conduct periodic climate sur-veys of students and make the results publiclyavailable. This will help to establish effective prac-tices and provide formative feedback to improvethe programs. Aligned with this, we suggest thatcourse and program goals around equity shouldfocus on equity of outcomes for students, i.e., degreeattainment and employment, and avoid a singularfocus on recruitment [93].

Our recommendations, although ultimately reflectingonly the authors, draw heavily on community input.As QISE engineering programs develop and maturebased on ongoing education research other programs inQISE fields will benefit from lessons learned. In partic-ular, the“Quantum 101” course, if implemented, couldprovide data on how conceptual quantum science andtechnology can be taught in different settings, potentiallyproviding an opportunity to modify current curriculawithin other QISE-related departments. Currently, thereis a breadth of quantum physics education research thatcould be leveraged [55], [56], [57], [58], [59], [60], [61],[62] but more must be done in the context of engineeringfields. Additionally, because QISE is cross-disciplinary,additional QISE curricula and education research acrossa range of settings could inform course design andpedagogy within QISE fields outside of engineering.

We acknowledge the extensive thoughts and feedbackfrom the QISE community developed in a series ofdocuments in the February 2021 NSF Workshop onQuantum Engineering Education with 480 quantum in-formation scientists and engineers in attendance fromacross academia, government, industry, and nationallabs. We also acknowledge useful conversations with

Abida Mukarram on the specific needs of U.S. commu-nity colleges.

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