Lecture 6, March 29, 2018 - Quantum Device Lab

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Last week:

Brief revisit of the dispersive limit Parametric amplifiers Qubit spectroscopy

Qubit-Qubit coupling in circuit QED 2-qubit gates by virtual photon interaction The controlled NOT gate

This week:

Qubit-Qubit coupling in circuit QED Characterizing 2-qubit gates Creating entangled states

State transfer and remote entanglement State of the art Challenges

29-Mar-18Andreas Wallraff, Quantum Device Lab 207

Lecture 6, March 29, 2018

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Reading: BooksHaroche, S. & Raimond, J.-M.; Exploring the Quantum: Atoms, Cavities, and Photons, Oxford University Press, New York, USA, (2006)


Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information, Cambridge University Press (2000)

Gerry, C. & Knight, P. L. Introductory Quantum Optics, Cambridge University Press (2005)

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Reading: Papers, Reviews, Other Material


Read (some of) the research papers mentioned on the slides.

• First read abstract and discussion/summary• Try to understand essence of the paper reading

it once, not caring for the details• Don’t be put off by not understanding

everything immediately• Read a different paper to get another authors

view of the same subject• Research you will do in the lab (Semester

Thesis, Master Thesis) aims at going beyond (all of) the papers that you read in preparation.

E.g.:A. Blais, et al., PRA 69, 062320 (2004)

Quantum Machines: Measurement and Control of Engineered Quantum Systems: Lecture Notes of the Les Houches Summer School: Volume 96, July 2011chapters: (link on QIP II web site)• 3 Circuit QED: superconducting qubits coupled to

microwave photons S. M. Girvin Department of Physics, Yale University

• 4 Quantum logic gates in superconducting qubitsJ. M. Martinis Department of Physics, University of California, Santa Barbara, CA 93111, USA

• 6 Readout of superconducting qubitsD. Esteve Quantronics Group Service de Physique de l’Etat Condensé/IRAMIS/DSM (CNRS URA 2464) CEA Saclay

ETH Zurich, TU Delft, (Imperial College), RWTH Aachen IDEA league summer school series.Lectures slides, videos, homework sets: http://www.qei.ethz.ch/education/IDEA-School.htmlhttp://qischoolsidea.wikispaces.com/home

http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780199681181.001.0001/acprof-9780199681181

http://www.qei.ethz.ch/education/IDEA-School.html

http://qischoolsidea.wikispaces.com/home

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for Implementing a quantum computer in the standard (circuit approach) to quantum information processing (QIP):

#1. A scalable physical system with well-characterized qubits.#2. The ability to initialize the state of the qubits.#3. Long (relative) decoherence times, much longer than the gate-operation time.#4. A universal set of quantum gates.#5. A qubit-specific measurement capability.

plus two criteria requiring the possibility to transmit information:

#6. The ability to interconvert stationary and mobile (or flying) qubits.#7. The ability to faithfully transmit mobile qubits between specified locations.


The DiVincenzo Criteria

David P. DiVincenzo, The Physical Implementation of Quantum Computation, arXiv:quant-ph/0002077 (2000)

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4 Qubit Device with Nearest Neighbor Resonator-Mediated Coupling

Salathé et al., PRX 5, 021027 (2015)

four qubitsfour resonators→ mediate couplingtwo readout linesfour microwave drive linesfour flux bias lines

→ tune qubit transition

1 mm29-Mar-18Andreas Wallraff, Quantum Device Lab 211

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Universal Two-Qubit Non-Adiabatic Controlled Phase Gate (11-20)

proposal: F. W. Strauch et al., Phys. Rev. Lett. 91, 167005 (2003).first implementation: L. DiCarlo et al., Nature 460, 240 (2010).

Interaction mediated by virtual photon exchange

through resonator

Tune levels into resonance using magnetic field

Full 2π rotation induces phase factor -1


Make use of qubit states beyond 0, 1

|qubit A, qubit B>

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Universal Two-Qubit Controlled Phase Gate

proposal: F. W. Strauch et al., Phys. Rev. Lett. 91, 167005 (2003).first implementation: L. DiCarlo et al., Nature 460, 240 (2010).

C-Phase gate:

Universal two-qubit gate. Used together with single-qubitgates to create any quantum operation.

|qubit A, qubit B>

Qubits in states 01, 10 and 00 do not interact

and thus acquire no phase shift


Make use of qubit states beyond 0, 1

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2011

Two-excitation manifold

Two-Excitation Manifold of System

Strauch et al., PRL (2003): proposed using interactions with higher levels for computation in phase qubitsslide adapted from L. DiCarlo (TUD)

• Spectroscopy of higher excited states

• Avoided crossing (160 MHz)

11 02↔

Flux bias on right transmon (a.u.)


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Flux bias right transmon (a.u.)

01

10

11

2-excitationmanifold

1-excitationmanifold

ζ

2001 10f f+

11 1e1 11 iϕ→

01 e10 10iϕ→

10 1e0 01 iϕ→

0

2 ( )ft

a at

f t dtϕ π δ= − ∫

Adiabatic Controlled Phase Gate

slide credit: L. DiCarlo (TUD)

0

11 10 01 2 ( )ft

t

t dtϕ ϕ ϕ π ζ= + − ∫


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1 0 0 00 1 0 00 0 1 00 0 0 1

U

−

B

Adjust timing of flux pulse so that only quantum amplitude of acquires a minus sign:

11

01

10

11

1 0 0 00 0 00 0 00 0

ˆ

0

i

i

i

eU

ee

ϕ

ϕ

ϕ

B

00 1001 11

00

10

01

11

Implementing the C-Phase Gate with One Flux Pulse

slide credit: L. DiCarlo (TUD)

How to verify the operation of this gate?


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Process Tomography: C-Phase Gate

Nielsen, M. A. & Chuang, I. L. Cambridge University Press (2000)

arbitrary quantum process

decomposed into operator basis positive semi definite Hermitian matrix characteristic for the process

Measured χ-matrix: Re[χ] (|Im[χ]|<0.04)Controlled phase gate

χ


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Re[χ] (|Im[χ]|<0.08)

Process Tomography of a C-NOT Gate

Nielsen, M. A. & Chuang, I. L. Cambridge University Press (2000)

Measured χ-matrix:Controlled-NOT gate

=


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Creating 3 Qubit Entanglement: GHZ State

This data: J. Heinsoo et al., ETHZF = 88%: DiCarlo et al. Nature 467, (2010)F = 62%: Neeley et al. Nature 467, (2010)F = 96%: Barends et al. Nature 508, (2014)

Fid(𝜎𝜎,𝜌𝜌) = Tr 𝜌𝜌𝜎𝜎 𝜌𝜌†2

= 88.9% (MLE)

Real Imaginary

Measured (color) and ideal (wireframe) density matrix:Protocol

GHZ class states, e.g. |000>+|111> created using:

• single qubit gates• C-PHASE gates


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GHZ-like State with 4 Qubits

This data: J. Heinsoo et al., ETHZF = 86.3%: Barends et al. Nature, 2014, 508

Real Imaginary

Fid(𝜎𝜎,𝜌𝜌) = Tr 𝜌𝜌𝜎𝜎 𝜌𝜌†2

= 74.8% (MLE)

Measured (color) and ideal (wireframe) density matrix:Protocol


|| 15-Mar-18Andreas Wallraff, Quantum Device Lab 225

Conversion and Transmission of Quantum Information in Networks

A. Fowler et al., Phys. Rev. Lett., 104, 180503 (2010)L.-M. Duan and C. Monroe, Rev. Mod. Phys. 82, 1209 (2010)Reiserer and G. Rempe, Rev. Mod. Phys. 87, 1379 (2015)

Universal quantum node: Send Receive Store Process

Direct quantum channel: Coherent link Deterministic, ideally

Applications: Creating distributed entanglement Distributed quantum computing Quantum error correction across

different nodes using surface code

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A Challenge Addressed in Many Physical Systems

P. Kurpiers et al., arXiv:1712.08593 (2017) Cirac et al., Phys. Rev. Lett. 78, 3221 (1997)

Over 15 years of experiments: Remote entanglement realized in a wide variety of

quantum systems Protocols: Single or two-photon interference + detection Measurement-induced Direct transfer with (shaped) photons Most/all probabilistic or heralded, typically with

entanglement generation rates < 100 Hz

Recently also in Superconducting Circuits: Three deterministic protocols with SC circuits Following protocol proposed by Cirac et al. realized

with shaped photons/radiation fields


Atomic Ensembles

Trapped Ions

Single atom Bose-Einstein condensateVibrational States of DiamondSingle atom

Nitrogen Vacancy

Superconducting Circuits

Quantum Dot

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Cavity QED with Superconducting Circuits as a Quantum Node

A. Blais, et al. , PRA 69, 062320 (2004)A. Wallraff et al., Nature (London) 431, 162 (2004)

With superconducting circuits:


Josephson Junction (JJ): • 2 superconducting

materials separated by an insulator

• Non-linear inductor• Anharmoic resonator

JJ resonator

Cavity QED setup for coherent control:

Our architecture achieves:• Strong coupling in solid state system• Easy to fabricate and integrate various

elements• High level of control over individual system

parameters

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Remote Integration


P. Kurpiers et al., arXiv:1712.08593 (2017)

Readout circuit Purcell filter; allows to increase

interaction rate without loss of lifetime Transmission reveals state of qubit Amplified for FPGA measurement

Transfer circuit Interaction with transmon creates

entanglement Photon emission

Nominally identical mirror circuit Time reversed dynamics Photon absorption Deterministic remote interaction

JJ resonator:Artificial Atom


Chip Design

Walter et al., Phys. Rev. Applied 7, 054020 (2017)

Qubit: Transmon qubit drive line

Readout elements (bottom): λ/4 readout resonator λ/4 Purcell filter

Optional reset, photon-detection and photon-transfer elements (top): λ/4 readout resonator λ/4 Purcell filter

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Remote Realization


chip A chip B

chip A chip B

Sample mounts Left: chip A Right: chip B Center: parametric amplifiers

Individual magnetic shields coaxial link (0.4 m) – circulator –

coaxial link (0.4 m) – HEMT

paramps


Tunable Atom-Resonator Interaction

M. Pechal et al. Phys. Rev. X 4, 041010 (2014)S. Zeytinoglu et al., Phys. Rev. A 91, 043846 (2015)P. Kurpiers et al., arXiv:1712.08593 (2017)

Atom coupled to resonator -> JC-type Hamiltonian

𝐻𝐻𝐽𝐽𝐽𝐽 = 𝜔𝜔𝑟𝑟 𝑎𝑎†𝑎𝑎 + 𝜔𝜔𝑡𝑡𝑏𝑏†𝑏𝑏 +𝛼𝛼2𝑏𝑏†𝑏𝑏†𝑏𝑏𝑏𝑏 + 𝑔𝑔(𝑎𝑎†𝑏𝑏 + 𝑔𝑔𝑏𝑏†𝑎𝑎)

Microwave drive at |𝑓𝑓, 0⟩ ↔ |𝑔𝑔, 1⟩ with Amplitude Ω and phase φ in rotating frame

𝐻𝐻eff = 𝑔𝑔 𝑡𝑡 |𝑔𝑔, 1⟩⟨𝑓𝑓, 0| + ℎ. 𝑐𝑐

With 𝑔𝑔 𝑡𝑡 ∝ 𝑔𝑔Ω 𝑡𝑡 𝑒𝑒i𝜙𝜙

Tunable interaction between atom and resonator! Excitation in resonator coupled to transmission line at rate κ |𝑔𝑔, 1⟩ population controls emission probability of single photon Generates a symmetric photon on-demand. Time-reversed interaction 𝑔𝑔 𝜏𝜏 − 𝑡𝑡 absorbs incident photon Allows deterministic remote quantum state transfer

Qutrit statetransitions

Resonator statetransitions

Coupled interactionDriven

interaction


Time-Reversal Symmetric Photon EmissionCavity QED Strong coupling Detuned dressed state level

diagram

|𝑔𝑔, 1⟩ population … … controls emission of shaped

photon Amplitude and phase controled

by drive 𝑔𝑔 𝑡𝑡 All-microwave process Single photon emission enforced

by trapping in dark state 𝑔𝑔, 0 Stark-shift and Rabi-rate

calibration is essentialP. Magnard et al., arXiv:1801.07689 (2018)

M. Pechal et al. Phys. Rev. X 4, 041010 (2014)J. I. Cirac et al., Phys. Rev. Lett. 78, 3221 (1997)

𝐻𝐻eff = 𝑔𝑔 𝑡𝑡 |𝑔𝑔, 1⟩⟨𝑓𝑓, 0| + ℎ. 𝑐𝑐𝑔𝑔 𝑡𝑡 ∝ 𝑔𝑔Ω 𝑡𝑡 𝑒𝑒i𝜙𝜙

time-symmetric photon with envelope

𝜅𝜅eff2 cosh(𝜅𝜅eff 𝑡𝑡/2)


Measurement of Qutrit Population Dynamics upon Photon Emission

prepare qutrit in |𝑓𝑓⟩ state Apply |𝑓𝑓, 0⟩ ↔ |𝑔𝑔, 1⟩ drive Truncate at time t 𝑓𝑓 population well described my master-

equation-simulation


Qutrit population at node B:

Excellent agreement with master equation simulation

𝑃𝑃𝑔𝑔=95.8 %

𝑃𝑃𝑓𝑓=0.9 %


Measurement of Qutrit Population Dynamics upon Photon Emission


Qutrit population at node B: Envelope of reflected photon:

Similar results at node A Allows to measure photon loss between A & B

Excellent agreement with master equation simulation


Characterization of Photon Loss

P. Kurpiers et al., arXiv:1712.08593 (2017)P. Kurpiers et al., EPJ Quantum Technology 4, 8 (2017)

Similar emission dynamics and performance at node A

Photon shape disturbed by reflection at node B

Compare integrated aout τ 2

emitted from node A and B Total photon loss: 23 ± 0.5 %

Origin – based on independent measurements & manufacturer data Circulator: 13% 0.4 m cable: 4% PCB: 4%


Absorption Dynamics of Qubit State Transfer

transfer



Absorption Dynamics of Qubit State Transfer

transfer transfer


Population of receiving qutrit : Envelope of reflected photon:

𝑃𝑃𝑔𝑔=28.6 %

𝑃𝑃𝑒𝑒=67.5 %

𝑃𝑃𝑓𝑓=3.9 %

Compare with & without absorption Pabs = 98.1 ± 0.1 %

Photon loss: ~ 22 % Qubit decay and dephasing: ~ 9 %Pulse truncation: ~ 1.5%

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Average state fidelity ℱavg𝑠𝑠 = 1

6∑⟨𝜙𝜙|𝜌𝜌m|𝜙𝜙⟩

= 86.0 ± 0.1 % >2/3

Transfer Process Matrix: Process fidelity ℱ𝑝𝑝 = Tr 𝜒𝜒𝜒𝜒ideal = 80.02 ± 0.07 % >1/2

MES: trace distance Tr[ 𝜒𝜒m − 𝜒𝜒sim 2] = 0.01415-Mar-18Andreas Wallraff, Quantum Device Lab 249

Quantum State Transfer: Process Tomography


transfer

QST

|𝑒𝑒⟩

i =12

( 𝑔𝑔 + i 𝑒𝑒 )

Prepare qubit A in six mutually unbiased input states |𝜙𝜙⟩

Quantum state tomography on qtB

ℱ|i⟩𝑠𝑠 = 87.9 ± 0.1 %

ℱ|e⟩𝑠𝑠 = 66.8 ± 0.1 %

Input state: Output state:


Generation of Remote Entanglement


entangle

2 qtQST

Protocol: Use entanglement scheme Perform full 2-qutrit state tomography

Result:Entanglement measure for multi-state systems (ccnr criterion) 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 1.612 ± 0.003 If ccnr>1 state must be entangled Excellent agreement with master

equation simulation Trace distance

Tr[ 𝜌𝜌m − 𝜌𝜌sim 2] = 0.024

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Density matrix of qubit pair:


Generation of Remote Entanglement


entangle

2 qtQST

Protocol: Use entanglement scheme Perform full 2-qutrit state tomography

2-qubit subspace of 2-qutrit system Bell-state 𝜓𝜓+ = ( 𝑒𝑒,𝑔𝑔 + 𝑔𝑔, 𝑒𝑒 )/√2 Fidelity ℱavg𝑠𝑠 = ⟨𝜓𝜓+|𝜌𝜌m|𝜓𝜓+⟩ = 78.9 ± 0.1 % Concurrence 𝒞𝒞 𝜌𝜌m = 0.747 ± 0.004

Master Equation Simulation: Infidelity: 1 − ℱavg𝑠𝑠 = 21.1 % from ~ 10.5 % photon loss ~ 9 % finite transmon coherence times ~ 1.5 % imperfect absorption or pulse

truncation

Pauli sets:

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Parametric Conversion mediated remote entanglement: 3D C. Axline et al., arXiv:1712.05832 (2017)

Blue-Sideband mediated remote entanglement: 3DP. Campagne-Ibarcq et al., arXiv:1712.05854 (2017).

15-Mar-18 256

Deterministic Remote Entanglement with Microwave Photons

Andreas Wallraff, Quantum Device Lab

Raman mediated remote entanglement: 2D P. Kurpiers, P. Magnard, T. Walter et al., arXiv:1712.08593 (2017), in print

|| 257

Metrics for Remote Entanglement

with Superconducting Circuits

P. Kurpiers et al., arXiv:1712.08593 (2017) Andreas Wallraff, Quantum Device Lab 15-Mar-18

Axlineet al.

Campangne-Ibarcq et al.

Kurpierset al.

Bell State Fidelity 61 % 73 % 79 %

Concurrence 0.51 - 0.75

Ent. Gen. Rate 10 kHz - 50 kHz

Protocol duration 6 𝜇𝜇𝜇𝜇 2.5 𝜇𝜇𝜇𝜇 0.2 𝜇𝜇𝜇𝜇

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Schemes to realize remote interaction: • measurement induced (triangles)• single- (crosses) or • two-photon (squares) interference and detection • direct transfer (pentagons)• direct transfer with shaped photons (circles)

Implementations:• probabilistic unheralded (red)• probabilistic heralded (blue)• fully deterministic (green)• deterministic delivered (yellow)


Performance Metric Summary and ProspectsProjections from simulations With straight forward improvements to qutrit

performance and reduced photon loss:

𝜅𝜅2𝜋𝜋

= 18 MHz , 12% photon loss, T1 = T2 ~ 𝟑𝟑𝟑𝟑 𝛍𝛍𝛍𝛍

ℱ𝑠𝑠𝑠𝑠𝑠𝑠 = 𝜓𝜓+ 𝜌𝜌𝑠𝑠𝑠𝑠𝑠𝑠 𝜓𝜓+ ~ 93% Further improvements expected by heralding

highest state transfer rate: Γ = 50kHz high concurrences of remote entanglement

protocol: C = 0.75 highest deterministic (un-heralded) remote

entanglement fidelity: F = 0.80

P. Kurpiers et al., arXiv:1712.08593 (2017), in print

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for Implementing a quantum computer in the standard (circuit approach) to quantum information processing (QIP):

#1. A scalable physical system with well-characterized qubits.#2. The ability to initialize the state of the qubits.#3. Long (relative) decoherence times, much longer than the gate-operation time.#4. A universal set of quantum gates.#5. A qubit-specific measurement capability.

plus two criteria requiring the possibility to transmit information:

#6. The ability to interconvert stationary and mobile (or flying) qubits.#7. The ability to faithfully transmit mobile qubits between specified locations.


The DiVincenzo Criteria

David P. DiVincenzo, The Physical Implementation of Quantum Computation, arXiv:quant-ph/0002077 (2000)

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Protocols: TeleportationL. Steffen et al., Nature 500, 319 (2013) M.. Baur et al., PRL 108, 040502 (2012)

Quantum Computing with Superconducting Circuits

Architectures: Circuit QED A. Blais et al., PRA 69, 062320 (2004)

A. Wallraff et al., Nature 431, 162 (2004)M. Sillanpaa et al., Nature 449, 438 (2007)

H. Majer et al., Nature 449, 443 (2007)M. Mariantoni et al., Science 334, 61 (2011)

R. Barends et al., Nature 508, 500 (2014)

Deutsch & Grover Algorithms, Toffoli GateL. DiCarlo et al., Nature 460, 240 (2009)L. DiCarlo et al., Nature 467, 574 (2010)A. Fedorov et al., Nature 481, 170 (2012)

Error CorrectionM. Reed et al., Nature 481, 382 (2012)

Corcoles et al., Nat. Com. 6, 6979 (2015) Ristè et al., Nat. Com. 6, 6983 (2015) Kelly et al., Nature 519, 66-69 (2015)

Adiabatic Quantum ComputationR. Barends et al., Nature, 534, 222-226 (2016)


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Quantum Simulation Applications with Superconducting Circuits

Salathe et al., PRX 5, 021027 (2015)

Solid State and Atomic Physics: Digital simulation of exchange, Heisenberg, Ising spin models

Solid State and Atomic Physics:

two-mode fermionic Hubbard models

Barends et al., Nat. Com. 6, 7654 (2015)

Photonics:Analog simulations with cavity

and/or qubit arraysHouck et al., Nat. Phys. 8, 292 (2012)

Raftery et al., PRX 4, 031043 (2014)

Eichleret al., PRX 5, 041044 (2015)O’Malley et al., PRX 6, 031007 (2016)

Quantum Chemistry: simulation of correlated systems using variational approach


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Quantum Optics with Superconducting CircuitsStrong Coherent CouplingChiorescu et al., Nature 431, 159 (2004)Wallraff et al., Nature 431, 162 (2004)Schuster et al., Nature 445, 515 (2007)

Parametric Amplification & SqueezingCastellanos-Beltran et al., Nat. Phys. 4, 928 (2008)Abdo et al., PRX 3, 031001 (2013)

Microwave Fock and Cat StatesHofheinz et al., Nature 454, 310 (2008)

Hofheinz et al., Nature 459, 546 (2009)Kirchmair et al., Nature 495, 205 (2013)Vlastakis et al., Science 342, 607 (2013)

Wang et al., Science 352, 1087 (2016)

Waveguide QED –Qubit Interactions in Free Space

Astafiev et al., Science 327, 840 (2010)I.-C. Hoi et al. PRL 107, 073601 (2011)

van Loo et al., Science 342, 1494 (2013)

Root n NonlinearitiesFink et al., Nature 454, 315 (2008)

Deppe et al., Nat. Phys. 4, 686 (2008)Bishop et al., Nat. Phys. 5, 105 (2009)


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Hybrid Systems with Superconducting CircuitsQuantum Dots: CNT, Gate Defined 2DEG, nanowires Delbecq et al., PRL 107, 256804 (2011)Frey et al., PRL 108, 046807 (2012)Petersson et al., Nature 490, 380 (2012)Radiation Emission: Liu et al., Science 347, 285 (2015)Stockklauser et al., PRL 115, 046802 (2015)Strong Coupling Cavity QED: Mi et al., Science 355, 156 (2017)Stockklauser et al., PRX 7, 011030 (2017)Bruhat et al., arXiv:1612.05214 (2016)

Spin Ensembles: e.g. NV centersSchuster et al., PRL 105, 140501 (2010)Kubo et al., PRL 105, 140502 (2010)

Nano-MechanicsTeufel et al., Nature 475, 359 (2011)Zhou et al., Nat. Phys. 9, 179(2013)

Polar Molecules, Rydberg, BECRabl et al, PRL 97, 033003 (2006)

Andre et al, Nat. Phys. 2, 636 (2006)Petrosyan et al, PRL 100, 170501 (2008)

Verdu et al, PRL 103, 043603 (2009)

Rydberg AtomsHoganet al., PRL 108, 063004 (2012)

zx

vz


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105 Improvement in Coherence Time in 13 Years

M. Devoret, R. Schoelkopf Science 339, 1169 (2013) 29-Mar-18Andreas Wallraff, Quantum Device Lab 283

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Towards Quantum Error Correction

DM

DT

DB

encode

P

P

Discretize, signal errors using quantum parity checks

0

0

X

X

X

X

X

X

• IBM: Corcoles et al., Nat. Com. 6, 6979 (2015), ArXiv:1410.6419

• QuTech: Ristè, Poletto, Huang et al., Nat. Com. 6, 6983 (2015), ArXiv:1411.5542

• UCSB/Google: Kelly et al., Nature 519, 66-69 (2015), ArXiv:1411.7403

Slide courtesy of L. DiCarlo

AM

AT

000 111α β+

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Industry & StartupsIBM Qhttp://research.ibm.com/ibm-q/

Google/UCSBhttp://web.physics.ucsb.edu/~martinisgroup/

D-Wave Systemshttps://www.dwavesys.com/

Microsofthttps://stationq.microsoft.com/

Rigetti Computinghttp://rigetti.com/

Intelhttps://phys.org/news/2015-09-intel-mn-quantum.html


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The Economist


Quantum leaps• An entangled web: The promise of quantum

encryption• Cue bits: Why all eyes are on quantum

computers• Here, there and everywhere: Quantum

technology is beginning to come into its own• Commercial breaks: The uses of quantum

technology• Program management: Quantum computers

will require a whole new set of softwarehttp://www.economist.com/topics/quantum-computinghttp://www.economist.com/

http://www.economist.com/topics/quantum-computing

http://www.economist.com/

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Design


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Fabrication



Control


Automation


Cryogenics

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Quantum Science and Engineering


Lecture 6, March 29, 2018 - Quantum Device Lab

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