simulation on / of various types of quantum...
TRANSCRIPT
Kristel Michielsen
INTEREST IN QUANTUM COMPUTING
29 March 2018
from the perspective of a supercomputer centre is …
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… to go beyond classical digital computing FOR & WITH the users
Kristel Michielsen
COMPUTATIONALLY HARD PROBLEMS
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Machine Learning
Production Planning
Quantum simulations
Optimization
Kristel Michielsen
CHALLENGES AND OPPORTUNITIES
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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
© 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
29 March 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
| ⟩𝜓𝜓 = 𝑎𝑎0| ⟩0 + 𝑎𝑎1| ⟩1 ; 𝑎𝑎0 2 + 𝑎𝑎1 2 = 1 𝑎𝑎0,𝑎𝑎1 ∈ ℂ
• System with 𝑁𝑁 qubits ≡ system with 𝑁𝑁 spin-1/2 particles
| ⟩𝜓𝜓 = 𝑎𝑎 0⋯ 00 | ⟩0 𝑁𝑁−1 ⋯ | ⟩0 1| ⟩0 0 + ⋯+ 𝑎𝑎 1⋯ 11 | ⟩1 𝑁𝑁−1 ⋯ | ⟩1 1| ⟩1 0
| ⟩𝜓𝜓 can be represented as a vector of length 2𝑁𝑁, containing all complex amplitudes 𝑎𝑎• Quantum algorithm = sequence of elementary operations (gates) that change the state
| ⟩𝜓𝜓 of the quantum processor
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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 many-world interpretation?
• It follows that the PaP-QC is a superb parallel computer that multiplies a 2𝑁𝑁 × 2𝑁𝑁 matrix and a 2𝑁𝑁 vector in 1 step
• In theory: exponential speed-up (order of 1 instead of 22𝑁𝑁 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
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Kristel Michielsen
MEASUREMENT
• PaP-QC outputs | ⟩𝜓𝜓′ = 𝑈𝑈| ⟩𝜓𝜓
all 2𝑁𝑁 complex amplitudes 𝑎𝑎𝑗𝑗; 𝑗𝑗 = 0,⋯ , 2𝑁𝑁−1 are known
all probabilities 𝑎𝑎𝑗𝑗2; 𝑗𝑗 = 0,⋯ , 2𝑁𝑁−1 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 qubit Each measurement returns one of the 2𝑁𝑁 basis states
Many measurements are required to determine 𝑎𝑎𝑗𝑗2; 𝑗𝑗 = 0,⋯ , 2𝑁𝑁−1 How many?
If each 𝑎𝑎𝑗𝑗 ≠ 0, then 2𝑁𝑁 × 𝑠𝑠𝑎𝑎𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 measurements are requiredShor algorithm: small fraction of 𝑎𝑎𝑗𝑗 ≠ 0
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Kristel Michielsen
JÜLICH QUANTUM COMPUTER SIMULATOR (JUQCS)
• 𝑁𝑁 qubits | ⟩𝜓𝜓 is a superposition of 2𝑁𝑁 basis states• Represent a quantum state with 2 bytes 𝑁𝑁 qubits requires at least
2𝑁𝑁+1 bytes of memory new world record in 2018
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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 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)
𝑖𝑖ℏ𝜕𝜕𝜕𝜕𝜕𝜕
| ⟩𝜓𝜓 𝜕𝜕 = 𝐻𝐻 𝜕𝜕 | ⟩𝜓𝜓 𝜕𝜕
• | ⟩𝜓𝜓 𝜕𝜕 : linear combination of all possible qubit states (2𝑁𝑁), describes the state of the whole quantum computer at time 𝜕𝜕
• 𝐻𝐻 𝜕𝜕 : 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
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Kristel Michielsen
QUANTUM ALGORITHMS
• Gate-based quantum computer: A quantum algorithm consists of a sequence of elementary operations (gates) that change the state | ⟩𝜓𝜓 𝜕𝜕 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.
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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
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Solutions
Quality
Kristel Michielsen
QUANTUM ANNEALING: HOW TO SOLVE AN OPTIMIZATION PROBLEM?• Write the cost function 𝐹𝐹 = ∑𝑖𝑖,𝑗𝑗 𝑄𝑄𝑖𝑖𝑗𝑗𝑥𝑥𝑖𝑖𝑥𝑥𝑗𝑗 with 𝑥𝑥𝑖𝑖 ∈ 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)
𝐻𝐻𝑃𝑃 = −�𝑖𝑖=1
𝑁𝑁
ℎ𝑖𝑖𝑠𝑠𝑖𝑖 −�𝑖𝑖,𝑗𝑗
𝐽𝐽𝑖𝑖,𝑗𝑗𝑠𝑠𝑖𝑖𝑠𝑠𝑗𝑗
𝐽𝐽𝑖𝑖,𝑗𝑗: exchange interactionℎ𝑖𝑖: external magnetic field
• Add a term 𝐻𝐻𝐼𝐼 representing quantum fluctuations to induce quantum transitions between the states
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Kristel Michielsen
QUANTUM ANNEALING: HOW TO SOLVE AN OPTIMIZATION PROBLEM?• Quantum annealing = continuous time (natural) evolution of a quantum system described
by the Hamiltonian𝐻𝐻 𝜕𝜕 = 𝐴𝐴 𝜕𝜕 𝐻𝐻𝐼𝐼 + 𝐵𝐵 𝜕𝜕 𝐻𝐻𝑃𝑃
in the time period 0 ≤ 𝜕𝜕 ≤ 𝜕𝜕𝑎𝑎
• The total Hamiltonian changes from 𝐻𝐻𝐼𝐼 at 𝜕𝜕 = 0 to 𝐻𝐻𝑃𝑃 at 𝜕𝜕 = 𝜕𝜕𝑎𝑎• At 𝜕𝜕 = 0 the system is prepared in the lowest energy state of 𝐻𝐻𝐼𝐼• If the time evolution is adiabatic, then at 𝜕𝜕 = 𝜕𝜕𝑎𝑎 the system is in the lowest-energy state of 𝐻𝐻𝑃𝑃
the solution of the optimization problem has been found
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Kristel Michielsen
QUANTUM ANNEALING
• Quantum theoretical description of the quantum annealing process: Landau-Zener theory
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Energy spectrum of the lowest lying states
Minimum gap Landau-Zener formula:probability to remain in the lowest energy state during annealing
𝜕𝜕/𝜕𝜕𝑎𝑎
𝐸𝐸𝐼𝐼
𝐸𝐸𝑃𝑃
∆
∆𝑃𝑃
𝑃𝑃 = 1 − 𝑠𝑠−𝛼𝛼𝑡𝑡𝑎𝑎∆2
𝜕𝜕𝑎𝑎 → ∞:𝑃𝑃 = 1𝜕𝜕𝑎𝑎 → 0:𝑃𝑃 = 0
Kristel Michielsen
QUANTUM ANNEALING
• In theory: “Quantum annealing hardness” of the problem is determined by the minimal spectral gap ∆ between the lowest-energy state and the first excited state during the annealing process• The minimal gap is determined by 𝐻𝐻𝑃𝑃, 𝐻𝐻𝐼𝐼 and the annealing scheme specified by 𝐴𝐴 𝜕𝜕
and 𝐵𝐵 𝜕𝜕
• In practice: also a finite operating temperature and noise influence the annealing process
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Kristel Michielsen
PHYSICAL QUBIT DEVICES
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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)
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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
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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
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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
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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
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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
HOW TO BRING QUANTUM COMPUTING INTO PRACTICE?
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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 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
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Kristel Michielsen
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
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Kristel Michielsen
EQUIPE - ENABLE QUANTUM INFORMATION PROCESSING IN EUROPE• Germany: Airbus, Thyssenkrupp AG, BASF SE, BAYER, T-Systems SfR, DLR, HLRS, Universität Greifswald, DKFZ, Volkswagen, RWTH Aachen, KIT
• The Netherlands: Leiden Institute of Advanced Computer Science (LIACS)
• Spain: ITMATI, Repsol Technology Center, CESGA• Finland: CSC-IT Center for Science Ltd, Aalto University School of Science, VTT Technical Research Center of Finland
• Italy/Greece: Planetek• Poland: University of Silesia in Katowice
• Romania: Terrasigna• United Kingdom: Rolls-Royce PLC, Numerical Algorithms Group Ltd, University College London, EPCC - The University of Edinburgh
• France: Université de Bretagne-Sud, Université de Bordeaux
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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)
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Kristel Michielsen
PRACTICAL USAGE OF QUANTUM COMPUTERS, A CASTLE IN THE AIR ?
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Kristel Michielsen
BUILDING CASTLES IN THE AIR IS USELESS UNLESS WE HAVE A LADDER TO REACH THEM
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Matshona Dhliwayo