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Kristel Michielsen
INTEREST IN QUANTUM COMPUTING
29 March 2018
from the perspective of a supercomputer centre is โฆ
Page 2
โฆ to go beyond classical digital computing FOR & WITH the users
Kristel Michielsen
COMPUTATIONALLY HARD PROBLEMS
29 March 2018 Page 3
Machine Learning
Production Planning
Quantum simulations
Optimization
Kristel Michielsen
CHALLENGES AND OPPORTUNITIES
29 March 2018 Page 4
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 new computing technology
UCSB/Google
IBM
D-Wave
Rigetti Computing
JARA-IQI
Intel
KIT
Kristel Michielsen29 March 2018 Page 5
ยฉ Kristel Michielsen, Thomas Lippert โ Forschungszentrum Jรผlich(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 !
โข Quantum Gate Based Systemsโข Quantum Annealersโข Quantum Simulators
29 March 2018
as a new compute technology?
Page 6
QUANTUM COMPUTER IN THE MATHEMATICAL WORLDGate-based quantum computer: pen-and-paper (PaP) version
Test models /
Simulation
Kristel Michielsen
QUANTUM COMPUTER & QUANTUM ALGORITHM
โข Quantum computerโข System with 1 qubit โก system with 1 spin-1/2 particle
| โฉ๐๐ = ๐๐0| โฉ0 + ๐๐1| โฉ1 ; ๐๐0 2 + ๐๐1 2 = 1 ๐๐0,๐๐1 โ โ
โข System with ๐๐ qubits โก system with ๐๐ spin-1/2 particles
| โฉ๐๐ = ๐๐ 0โฏ 00 | โฉ0 ๐๐โ1 โฏ | โฉ0 1| โฉ0 0 + โฏ+ ๐๐ 1โฏ 11 | โฉ1 ๐๐โ1 โฏ | โฉ1 1| โฉ1 0
| โฉ๐๐ can be represented as a vector of length 2๐๐, containing all complex amplitudes ๐๐โข Quantum algorithm = sequence of elementary operations (gates) that change the state
| โฉ๐๐ of the quantum processor
29 March 2018 Page 8
Kristel Michielsen
WHERE DOES THE POWER OF THE PEN-AND-PAPER QC (PaP-QC) COME FROM?โข An operation of a PaP-QC amounts to multiplying the wave function with a unitary matrix
โข It is believed, without any empirical evidence, that Nature knows how to do such an operation in 1 step many-world interpretation?
โข It follows that the PaP-QC is a superb parallel computer that multiplies a 2๐๐ ร 2๐๐ matrix and a 2๐๐ vector in 1 step
โข In theory: exponential speed-up (order of 1 instead of 22๐๐ operations) for algorithms that can exploit this parallelism (hard to find!), e.g. Shorโs number factoring algorithm
โข In practice: measurement of the outcome might destroy the parallelism
29 March 2018 Page 9
Kristel Michielsen
MEASUREMENT
โข PaP-QC outputs | โฉ๐๐โฒ = ๐๐| โฉ๐๐
all 2๐๐ complex amplitudes ๐๐๐๐; ๐๐ = 0,โฏ , 2๐๐โ1 are known
all probabilities ๐๐๐๐2; ๐๐ = 0,โฏ , 2๐๐โ1 can be calculated
โข Measurement with a real gate-based QC deviceโข In each measurement, every qubit is read-out returning a value 0 OR 1 for each qubit Each measurement returns one of the 2๐๐ basis states
Many measurements are required to determine ๐๐๐๐2; ๐๐ = 0,โฏ , 2๐๐โ1 How many?
If each ๐๐๐๐ โ 0, then 2๐๐ ร ๐ ๐ ๐๐๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ ๐ measurements are requiredShor algorithm: small fraction of ๐๐๐๐ โ 0
29 March 2018 Page 10
Kristel Michielsen
JรLICH QUANTUM COMPUTER SIMULATOR (JUQCS)
โข ๐๐ qubits | โฉ๐๐ is a superposition of 2๐๐ basis statesโข Represent a quantum state with 2 bytes ๐๐ qubits requires at least
2๐๐+1 bytes of memory new world record in 2018
29 March 2018 Page 11
JUQUEEN, Jรผlich, 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 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
โข Quantum computer / annealer hardware can be modeled in terms of qubits that evolve in time (dynamics) according to the time-dependent Schrรถdinger equation (TDSE)
๐๐โ๐๐๐๐๐๐
| โฉ๐๐ ๐๐ = ๐ป๐ป ๐๐ | โฉ๐๐ ๐๐
โข | โฉ๐๐ ๐๐ : linear combination of all possible qubit states (2๐๐), describes the state of the whole quantum computer at time ๐๐
โข ๐ป๐ป ๐๐ : 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
29 March 2018 Page 13
Kristel Michielsen
QUANTUM ALGORITHMS
โข Gate-based quantum computer: A quantum algorithm consists of a sequence of elementary operations (gates) that change the state | โฉ๐๐ ๐๐ of the quantum processor according to the TDSE.
โข 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.
29 March 2018 Page 14
Kristel Michielsen
QUANTUM ANNEALING: ALGORITHM FOR OPTIMIZATION
= finding the best solution among a finite set of feasible solutions
= minimization of a cost function
= finding the minimum energy state of a physical system
29 March 2018 Page 15
Solutions
Quality
Kristel Michielsen
QUANTUM ANNEALING: HOW TO SOLVE AN OPTIMIZATION PROBLEM?โข Write the cost function ๐น๐น = โ๐๐,๐๐ ๐๐๐๐๐๐๐ฅ๐ฅ๐๐๐ฅ๐ฅ๐๐ with ๐ฅ๐ฅ๐๐ โ 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)
๐ป๐ป๐๐ = โ๏ฟฝ๐๐=1
๐๐
โ๐๐๐ ๐ ๐๐ โ๏ฟฝ๐๐,๐๐
๐ฝ๐ฝ๐๐,๐๐๐ ๐ ๐๐๐ ๐ ๐๐
๐ฝ๐ฝ๐๐,๐๐: exchange interactionโ๐๐: external magnetic field
โข Add a term ๐ป๐ป๐ผ๐ผ representing quantum fluctuations to induce quantum transitions between the states
29 March 2018 Page 16
Kristel Michielsen
QUANTUM ANNEALING: HOW TO SOLVE AN OPTIMIZATION PROBLEM?โข Quantum annealing = continuous time (natural) evolution of a quantum system described
by the Hamiltonian๐ป๐ป ๐๐ = ๐ด๐ด ๐๐ ๐ป๐ป๐ผ๐ผ + ๐ต๐ต ๐๐ ๐ป๐ป๐๐
in the time period 0 โค ๐๐ โค ๐๐๐๐
โข The total Hamiltonian changes from ๐ป๐ป๐ผ๐ผ at ๐๐ = 0 to ๐ป๐ป๐๐ at ๐๐ = ๐๐๐๐โข At ๐๐ = 0 the system is prepared in the lowest energy state of ๐ป๐ป๐ผ๐ผโข If the time evolution is adiabatic, then at ๐๐ = ๐๐๐๐ the system is in the lowest-energy state of ๐ป๐ป๐๐
the solution of the optimization problem has been found
29 March 2018 Page 17
Kristel Michielsen
QUANTUM ANNEALING
โข Quantum theoretical description of the quantum annealing process: Landau-Zener theory
29 March 2018 Page 18
Energy spectrum of the lowest lying states
Minimum gap Landau-Zener formula:probability to remain in the lowest energy state during annealing
๐๐/๐๐๐๐
๐ธ๐ธ๐ผ๐ผ
๐ธ๐ธ๐๐
โ
โ๐๐
๐๐ = 1 โ ๐ ๐ โ๐ผ๐ผ๐ก๐ก๐๐โ2
๐๐๐๐ โ โ:๐๐ = 1๐๐๐๐ โ 0:๐๐ = 0
Kristel Michielsen
QUANTUM ANNEALING
โข In theory: โQuantum annealing hardnessโ of the problem is determined by the minimal spectral gap โ between the lowest-energy state and the first excited state during the annealing processโข The minimal gap is determined by ๐ป๐ป๐๐, ๐ป๐ป๐ผ๐ผ and the annealing scheme specified by ๐ด๐ด ๐๐
and ๐ต๐ต ๐๐
โข In practice: also a finite operating temperature and noise influence the annealing process
29 March 2018 Page 19
Kristel Michielsen
PHYSICAL QUBIT DEVICES
29 March 2018 Page 21
Transmon qubit / IBM Flux qubit / D-Wave
Xmon qubit / Google
Kristel Michielsen
โข The IBM QX processor with 5 and 16 qubits can be tested freely from โoutsideโ the lab
โข Allows for an independent assessment of a quantum processor as a computing device
โข We tested the performance of the IBM QX processorsโข Simple algorithms: identity operations, 2+2 qubit adder,
measurement of singlet state, error correction
SIMULATION ON IBM QUANTUM EXPERIENCE (IBM QX)
29 March 2018 Page 22
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
โข Simulation of the real-time dynamics of physical models of systems with two transmon qubits
โข Comparison with IBM QX1 device
29 March 2018 Page 23
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, Jรผlich, Germany
IBM QX, Yorktown Heights, USA
Kristel Michielsen
SIMULATION ON/OF D-WAVE QUANTUM ANNEALERS
โข Comparison test for the analysis and exploration of D-Wave quantum annealers
โข 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 systemโข Use problems that can be directly mapped on the Chimera
architectureโข Use D-Wave system parameters for the simulation
29 March 2018 Page 24
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
29 March 2018 Page 25
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 โข Volkswagen project The effect of anneal path control on hard 2-SAT problems with a
known energy landscape
โข Volkswagen collaboration on the simulation of small molecules for battery research
โข Assessment of IBM, Google, Rigetti Computing, and D-Wave devices
29 March 2018 Page 26
Kristel Michielsen
โข Establish a QC User Facility: Provide available computing devices for users in science and industry in Europe
โข Create a maturity ramp of systems availableโข Host and operate annealers exploiting quantum phenomena โข Provide access to multi-qubit devices for quantum computing without error correction
(e.g. IBM, Google, Rigetti Computing)โข Provide access to experimental devices
โข Provide access to quantum computer simulators
QTRL2-3
HOW TO BRING QUANTUM COMPUTING INTO PRACTICE?
29 March 2018 Page 28
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
FZJ29 March 2018 Page 29
Kristel Michielsen
PLANNED JรLICH USER INFRASTRUCTURE FOR R&D IN QUANTUM COMPUTING โ 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 JรผlichRemote accessHosted in Jรผlich orremote access
Academic useIndustrial use
29 March 2018 Page 30
Kristel Michielsen
EQUIPE - ENABLE QUANTUM INFORMATION PROCESSING IN EUROPEโข motivates JรLICH to establish the user facility JUNIQ in order to Enable QUantum
Information Processing in Europe (EQUIPE)
โข promotes the exploitation of Quantum Computing and Annealing for scientific and industry oriented research, such as optimization and machine learning
โข welcomes unified access and objective comparison of different systems
โข supports the co-design of models, algorithms, and software tailored to the specific system architectures
โข is interested in the application of quantum information processing technologies on real-world applications
29 March 2018 Page 34
Kristel Michielsen
EQUIPE - ENABLE QUANTUM INFORMATION PROCESSING IN EUROPEโข Germany: Airbus, Thyssenkrupp AG, BASF SE, BAYER, T-Systems SfR, DLR, HLRS, Universitรคt Greifswald, DKFZ, Volkswagen, RWTH Aachen, KIT
โข The Netherlands: Leiden Institute of Advanced Computer Science (LIACS)
โข Spain: ITMATI, Repsol Technology Center, CESGAโข Finland: CSC-IT Center for Science Ltd, Aalto University School of Science, VTT Technical Research Center of Finland
โข Italy/Greece: Planetekโข Poland: University of Silesia in Katowice
โข Romania: Terrasignaโข United Kingdom: Rolls-Royce PLC, Numerical Algorithms Group Ltd, University College London, EPCC - The University of Edinburgh
โข France: Universitรฉ de Bretagne-Sud, Universitรฉ de Bordeaux
29 March 2018 Page 35
Kristel Michielsen
CONCLUSIONS
โข Simulating the behavior of (physical models) of quantum computing devices (D-Wave, IBM, โฆ) on supercomputers sheds light on the physical processes involved
โข Applications for currently available gate-based quantum computers (< 50 qubits) CAN be tested on supercomputers
โข Applications for currently available quantum annealers (> 2000 qubits) CANNOT be tested on supercomputersโข Simulation time required to simulate small quantum annealing problems (โ 20 qubits) is
much larger than the physical annealing time (โ 20 ยตs)
29 March 2018 Page 37
Kristel Michielsen
PRACTICAL USAGE OF QUANTUM COMPUTERS, A CASTLE IN THE AIR ?
21 March 2018 Page 38
Kristel Michielsen
BUILDING CASTLES IN THE AIR IS USELESS UNLESS WE HAVE A LADDER TO REACH THEM
21 March 2018 Page 39
Matshona Dhliwayo