SIMULATION ON / OF QUANTUM COMPUTERS AND … Europe_April_2018_michielsen.pdf · simulation on / of quantum computers and quantum annealers qubits europe 2018, d-wave users conference

SIMULATION ON / OF QUANTUM COMPUTERS AND QUANTUM ANNEALERSQUBITS EUROPE 2018, D-WAVE USERS CONFERENCE APRIL 10-12, 2018 I KRISTEL MICHIELSEN

Kristel Michielsen

INTEREST IN QUANTUM COMPUTING

12 April 2018

from the perspective of a supercomputer centre is …

Page 2

… to go beyond classical digital computing FOR & WITH the users

Kristel Michielsen

CHALLENGES AND OPPORTUNITIES

12 April 2018 Page 3

with various hard computational challenges

Optimization

Science & Industry:Diverse user group

Machine learning

Quantum simulations

Diverse collection of qubit devices for quantum annealing and quantum computation à new computing technology

UCSB/Google

IBM

D-Wave

Rigetti Computing

JARA-IQI

Intel

KIT

Kristel Michielsen12 April 2018 Page 4

© Kristel Michielsen, Thomas Lippert – Forschungszentrum Jülich(http://www.fz-juelich.de/ias/jsc/EN/Research/ModellingSimulation/QIP/QTRL/_node.html)

Experimentalqubit devices

IBMGoogleRigettiComputing

D-Wavequantum annealer

QUANTUMTECHNOLOGYREADINESSLEVELS

Kristel Michielsen

HOW TO EVALUATE QUANTUM COMPUTING

We need profound test models and benchmarks to compare quantum computing / annealing devices with trustworthy simulations on digital supercomputers !

• Quantum Gate Based Systems• Quantum Annealers• Quantum Simulators

12 April 2018

as a new compute technology?

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QUANTUM COMPUTER IN THE MATHEMATICAL WORLDGate-based quantum computer: pen-and-paper (PaP) version

Test models /

Simulation

Kristel Michielsen

QUANTUM COMPUTER & QUANTUM ALGORITHM

• Quantum computer• System with 1 qubit ≡ system with 1 spin-1/2 particle

|𝜓⟩ = 𝑎&|0⟩ + 𝑎)|1⟩; 𝑎& - + 𝑎) - = 1 𝑎&, 𝑎) ∈ ℂ

• System with 𝑁 qubits ≡ system with 𝑁 spin-1/2 particles

|𝜓⟩ = 𝑎 0⋯00 |0⟩34) ⋯ |0⟩)|0⟩& + ⋯+ 𝑎 1⋯11 |1⟩34) ⋯ |1⟩)|1⟩&

à |𝜓⟩ can be represented as a vector of length 23, containing all complex amplitudes 𝑎• Quantum algorithm = sequence of elementary operations (gates) that change the state |𝜓⟩ of the quantum processor


Kristel Michielsen

SOME GATES

• X-gate (= NOT gate)

X|0⟩ = |1⟩; X|1⟩ = |0⟩ → X = 0 11 0

• Hadamard (H) gate

H|0⟩ =|0⟩ + |1⟩

2�; H|1⟩ =

|0⟩ − |1⟩2�

→ H =12�+1 +1+1 −1

• CNOT (CControl-Target = CCT) gateC&)|0)0&⟩ = |0)0&⟩;C&)|0)1&⟩ = |1)1&⟩;C&)|1)0&⟩ = |1)0&⟩;C&)|1)1&⟩ = |0)1&⟩

→ C&)

0)0&0)1&1)0&1)1&

=1 00 0

0 00 1

0 00 1

1 00 0

0)0&0)1&1)0&1)1&


X

H

+

Kristel Michielsen

WHERE DOES THE POWER OF THE PEN-AND-PAPER QC (PaP-QC) COME FROM?• An operation of a PaP-QC amounts to multiplying the wave function with a unitary matrix• It is believed, without any empirical evidence, that Nature knows how to do such an

operation in 1 step ó many-world interpretation?

• It follows that the PaP-QC is a superb parallel computer that multiplies a 23×23matrix and a 23vector in 1 step

• In theory: exponential speed-up (order of 1 instead of 2-3 operations) for algorithms that can exploit this parallelism (hard to find!), e.g. Shor’s number factoring algorithm

• In practice: measurement of the outcome might destroy the parallelism


Kristel Michielsen

MEASUREMENT

• PaP-QC outputs |𝜓′⟩ = 𝑈|𝜓⟩

à all 23 complex amplitudes 𝑎<; 𝑗 = 0,⋯ , 234) are known

à all probabilities 𝑎<-; 𝑗 = 0,⋯ , 234) can be calculated

• Measurement with a real gate-based QC device• In each measurement, every qubit is read-out returning a value 0 OR 1 for each qubità Each measurement returns one of the 23 basis states

à Many measurements are required to determine 𝑎<-; 𝑗 = 0,⋯ , 234) How many?

à If each 𝑎< ≠ 0, then 23×𝑠𝑎𝑚𝑝𝑙𝑒𝑠 measurements are requiredShor algorithm: small fraction of 𝑎< ≠ 0


Kristel Michielsen

JÜLICH QUANTUM COMPUTER SIMULATOR (JUQCS)

• 𝑁 qubits à |𝜓⟩ is a superposition of 23 basis states• Represent a quantum state with 2 bytes à 𝑁 qubits requires at least 23D) bytes of memory à new world record in 2018


JUQUEEN, Jülich, Germany

K, Kobe, Japan

Sunway TaihuLight, Wuxi, China

N Memory27 256 MB39 1 TB48 0.5 PB49* 1 PB

* Could be run on Trinity, Los Alamos

CNOT operation on each subsequent pair of qubits à entangled state

For up to 48 qubits these supercomputers beat the exponential growth!

QUANTUM COMPUTER IN THE MATHEMATICAL WORLDFull dynamics of a quantum spin-1/2 system: gate-based quantum computer & quantum annealer

Test models /

Simulation

Kristel Michielsen

QUANTUM COMPUTER / ANNEALER

• Quantum computer / annealer hardware can be modeled in terms of qubits that evolve in time (dynamics) according to the time-dependent Schrödinger equation (TDSE)

𝑖ℏ𝜕𝜕𝑡|𝜓 𝑡 ⟩ = 𝐻 𝑡 |𝜓 𝑡 ⟩

• |𝜓 𝑡 ⟩: linear combination of all possible qubit states (23), describes the state of the whole quantum computer at time 𝑡

• 𝐻 𝑡 : time-dependent Hamiltonian modeling the quantum computer / annealer hardware and its control and eventually its interaction with the environment to model all kinds of errors


Kristel Michielsen

QUANTUM COMPUTER / ANNEALER

• Model for a universal quantum computer / annealer (spin-1/2 system):

𝐻 𝑡 = −J J ℎLM 𝑡 𝜎LM�

MOP,Q,R

3

LO)

− J J 𝐽L<M 𝑡�

MOP,Q,R

𝜎LM𝜎<M3

L,<O)

where:

𝜎LP =0 11 0 ;𝜎L

Q = 0 −𝑖𝑖 0 ;𝜎LR =

1 00 −1

are the Pauli matrices and

𝐽L<: exchange interactionℎL: magnetic field


Kristel Michielsen

QUANTUM COMPUTER / ANNEALER IN CONNECTION TO AN ENVIRONMENT • Quantum computer / annealer modeled as a quantum spin-1/2 system 𝑆in connection to a

heat bath (environment) modeled as a quantum spin-1/2 system 𝐵at a given temperature𝐻 = 𝐻V + 𝐻W + 𝜆𝐻VW

• # bath spins ≥ # system spins• # bath + system spins ≤ 43

à Models all kinds of errors, not just the depolarizing channel


S

B

Kristel Michielsen

QUANTUM ALGORITHMS

• Gate-based quantum computer: A quantum algorithm consists of a sequence of elementary operations (gates) that change the state |𝜓 𝑡 ⟩ of the quantum processor according to the TDSE.

• Quantum annealer: A quantum algorithm consists of the continuous time (natural) evolution of a quantum system to find the lowest-energy state of a system representing an optimization problem.


Kristel Michielsen

GATE-BASED QUANTUM COMPUTER: EXAMPLE

• Quantum network to add the content of three 4-qubit registers


W 2 4 8W 4 2

W 2W

W-2-4-8W-4-2

W-2W

1111

222

448 1

111

222

448

1 2 3 4 5 6 7 8 9

10 11 12

1 2 3 4 5 6 7 8 9

10 11 12

QFT QFT-1Phase shifts Phase shifts

(S. Bettelli, PhD Thesis, University of Trento, 2002)

Kristel Michielsen

QUANTUM ANNEALING: HOW TO SOLVE AN OPTIMIZATION PROBLEM?• Write the cost function 𝐹 = ∑ 𝑄L<𝑥L𝑥<�

L,< with 𝑥L ∈ 0,1 as Hamiltonian (energy function) of the Ising model such that its lowest-energy state represents the solution to the optimiza-tion problem (QUBO)

𝐻_ = −JℎL𝑠L

3

LO)

−J𝐽L,<𝑠L𝑠<

�

L,<

𝐽L,<: exchange interactionℎL: external magnetic field

• Add a term 𝐻` representing quantum fluctuations to induce quantum transitions between the states


Kristel Michielsen

QUANTUM ANNEALING: HOW TO SOLVE AN OPTIMIZATION PROBLEM?• Quantum annealing = continuous time (natural) evolution of a quantum system described

by the Hamiltonian𝐻 𝑡 = 𝐴 𝑡 𝐻` + 𝐵 𝑡 𝐻_

in the time period 0 ≤ 𝑡 ≤ 𝑡b

• The total Hamiltonian changes from 𝐻` at 𝑡 = 0 to 𝐻_ at 𝑡 = 𝑡b• At 𝑡 = 0 the system is prepared in the lowest energy state of 𝐻`• If the time evolution is adiabatic, then at 𝑡 = 𝑡b the system is in the lowest-energy state of 𝐻_ à

the solution of the optimization problem has been found


Kristel Michielsen

QUANTUM ANNEALING

• Quantum theoretical description of the quantum annealing process: Landau-Zener theory


Energy spectrum of the lowest lying states

Minimum gap Landau-Zener formula:probability to remain in the lowest energy state during annealing

𝑡/𝑡b

𝐸`𝐸_

Δ

Δ_

𝑃 = 1 − 𝑒4Mghij

𝑡b → ∞:𝑃 = 1𝑡b → 0: 𝑃 = 0

QUANTUM COMPUTERS IN THE WORLD THAT HUMANS EXPERIENCE

Benchmarking

Kristel Michielsen

PHYSICAL QUBIT DEVICES


Transmon qubit / IBM Flux qubit / D-Wave

Xmon qubit / Google

Kristel Michielsen

• The IBM QX processor with 5 and 16 qubits can be tested freely from “outside” the lab

• Allows for an independent assessment of a quantum processor as a computing device

• We tested the performance of the IBM QX processors• Simple algorithms: identity operations, 2+2 qubit adder,

measurement of singlet state, error correction

SIMULATION ON IBM QUANTUM EXPERIENCE (IBM QX)


IBM QX, Yorktown Heights, USA

K. Michielsen, M. Nocon, D. Willsch, F. Jin, Th. Lippert, H. De Raedt, Benchmarking gate-based quantum computers, Comp. Phys. Comm. 220, 44 (2017)

General conclusion: The current IBM QX device does not meet the elementary requirements for a computing device.

Kristel Michielsen

SIMULATION ON/OF SYSTEMS WITH TWO TRANSMONQUBITS

• Simulation of the real-time dynamics of physical models of systems with two transmon qubits

• Comparison with IBM QX1 device


D. Willsch, M. Nocon, F. Jin, H. De Raedt, K. Michielsen, Gate error analysis in simulations of quantum computers with transmon qubits, Phys. Rev. A 96, 062302 (2017)

Gate metrics provide insights into errors of the implemented gate pulses, but this information is not enough to assess the error induced by repeatedly using the gate in quantum algorithms.

JURECA, Jülich, Germany

IBM QX, Yorktown Heights, USA

Kristel Michielsen

SIMULATION ON/OF D-WAVE QUANTUM ANNEALERS

• Comparison test for the analysis and exploration of D-Wave quantum annealers

• Solve small but hard Ising problems, characterized by a known unique ground state and a highly degenerate first excited state, on a D-Wave system and on a simulated ideal quantum annealer modeled as a quantum spin-1/2 system• Use problems that can be directly mapped on the Chimera

architecture• Use D-Wave system parameters for the simulation


K. Michielsen, F. Jin, and H. De Raedt, Solving 2-satisfiability problems on a quantum annealer (in preparation)

D-Wave, Burnaby, Canada

Kristel Michielsen

SIMULATION ON/OF D-WAVE QUANTUM ANNEALERS


K. Michielsen, F. Jin, and H. De Raedt, Solving 2-satisfiability problems on a quantum annealer (in preparation)

D-Wave, Burnaby, Canada

Measured frequency distribution as a function of the minimal spectral gap shows Landau-Zener ( = quantum) behavior.

Kristel Michielsen

ASSESSMENT PROJECTS WITH USERS AND HARDWARE PROVIDERS • Volkswagen project The effect of anneal path control on hard 2-SAT problems with a

known energy landscape• Volkswagen collaboration on the simulation of small molecules for battery research• Assessment of IBM, Google,

Rigetti Computing, and D-Wave devices

• Joint PhD student with DLR | Simulation and Software Technology | High Performance Computing


Kristel Michielsen

VOLKSWAGEN PROJECT

• Linear annealing scheme: 𝐴 𝑡/𝑡b = 1 − 𝑡/𝑡b,

𝐵 𝑡/𝑡b = 𝑡/𝑡b

• Anneal offset:𝐴 𝑡/𝑡b = 1 − 𝑡/𝑡b )4m,

𝐵 𝑡/𝑡b = 𝑡/𝑡b )4m

• Examples:• Advanced:𝛾 = −0.5• Retarded: 𝛾 = 0.5

The effect of anneal path control on hard Ising problems with a known energy landscape


Kristel Michielsen

VOLKSWAGEN PROJECT


Annealing offset for all spins based on an iterative process involving the floppiness

𝑡b = 0.05ns 𝑡b = 0.5ns 𝑡b = 5ns

T. Lanting, A.D. King, B. Evert, and E. Hoskinson, Experimental demonstration of perturbative anticrossing mitigation using nonuniform driver Hamiltonians, Phys. Rev. A 96, 042322 (2017)

Kristel Michielsen

VOLKSWAGEN PROJECT

Linear annealing: Minimal spectral gap Δ = 0.85 GHz


𝑡b = 0.05ns 𝑡b = 0.5ns 𝑡b = 5ns

Problem 487

Kristel Michielsen

Annealing offset for all spins based on an iterative process: 𝑡b = 5 ns

VOLKSWAGEN PROJECT


Δ = 0.85 GHz

Problem 487

Δ = 3.98 GHz Δ = 8.37 GHz

0 iterations 15 iterations 40 iterations

QUANTUM COMPUTER USER FACILITY AND USER GROUP

Kristel Michielsen

PRACTICAL USAGE OF QUANTUM COMPUTERS, A CASTLE IN THE AIR ?


Kristel Michielsen

BUILDING CASTLES IN THE AIR IS USELESS UNLESS WE HAVE A LADDER TO REACH THEM


Matshona Dhliwayo

Kristel Michielsen

BUILDING CASTLES IN THE AIR IS USELESS UNLESS WE HAVE A LADDER TO REACH THEM


Matshona Dhliwayo

User Facilities

Kristel Michielsen

• Establish a QC User Facility: Provide available computing devices for users in science and industry in Europe

• Create a maturity ramp of systems available• Host and operate annealers exploiting quantum phenomena • Provide access to multi-qubit devices for quantum computing without error correction

(e.g. IBM, Google, Rigetti Computing)• Provide access to experimental devices

• Provide access to quantum computer simulators

QTRL2-3

USER FACILITYHow to bring Quantum computing into practice?


QTRL4-5

QTRL8

Kristel Michielsen

TOWARDS A QUANTUM COMPUTER USER FACILITY

JSCModularHPCcenter D-Wave

2000Q annealer

ApproximateQuantumComputer

Experimentalqubit

devices

New classical computers

Unified Q

uantum C

omputing Platform

FZJ12 April 2018 Page 39

Kristel Michielsen

PLANNED JÜLICH USER INFRASTRUCTURE FOR R&D IN QUANTUM COMPUTING – JUNIQ

Emulator for physical gate-

based QCs with up to 36

qubits

D-Wave quantum annealer

Emulator for ideal gate-based QCs

with up to 46 qubits

IBM Q device

Google device

Emerging experimental

systems(FET

Flagship)

Hosted in JülichRemote accessHosted in Jülich orremote access

Academic useIndustrial use


Kristel Michielsen

USER GROUP EQUIPE - ENABLE QUANTUM INFORMATION PROCESSING IN EUROPE• motivates JÜLICH to establish the user facility JUNIQ in order to Enable QUantum

Information Processing in Europe (EQUIPE)

• promotes the exploitation of Quantum Computing and Annealing for scientific and industry oriented research, such as optimization and machine learning

• welcomes unified access and objective comparison of different systems

• supports the co-design of models, algorithms, and software tailored to the specific system architectures

• is interested in the application of quantum information processing technologies on real-world applications


CONCLUSIONS

Kristel Michielsen

CONCLUSIONS

• Simulating the behavior of (physical models) of quantum computing devices (D-Wave, IBM, …) on supercomputers sheds light on the physical processes involved

• Applications for currently available gate-based quantum computers (< 50 qubits) CAN be tested on supercomputers

• Applications for currently available quantum annealers (> 2000 qubits) CANNOT be tested on supercomputers• Simulation time required to simulate small quantum annealing problems (≈ 20 qubits) is

much larger than the physical annealing time (≈ 20 µs)• Establishment of user facility JUNIQ and user group EQUIPE


SIMULATION ON / OF QUANTUM COMPUTERS AND … Europe_April_2018_michielsen.pdf · simulation on / of quantum computers and quantum annealers qubits europe 2018, d-wave users conference

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