A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware

Here we present qFlex, a flexible tensor network-based quantum circuit simulator. qFlex can compute both the exact amplitudes, essential for the verification of the quantum hardware, as well as low-fidelity amplitudes, to mimic sampling from Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we focus on random quantum circuits (RQCs) in the range of sizes expected for supremacy experiments. Fidelity f simulations are performed at a cost that is 1/f lower than perfect fidelity ones. We also present a technique to eliminate the overhead introduced by rejection sampling in most tensor network approaches. We benchmark the simulation of square lattices and Google’s Bristlecone QPU. Our analysis is supported by extensive simulations on NASA HPC clusters Pleiades and Electra. For our most computationally demanding simulation, the two clusters combined reached a peak of 20 Peta Floating Point Operations per Second (PFLOPS) (single precision), i.e., 64% of their maximum achievable performance, which represents the largest numerical computation in terms of sustained FLOPs and the number of nodes utilized ever run on NASA HPC clusters. Finally, we introduce a novel multithreaded, cache-efficient tensor index permutation algorithm of general application.

[1]  Lov K. Grover A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[2]  Carlton M. Caves,et al.  Sufficient Conditions for Efficient Classical Simulation of Quantum Optics , 2015, 1511.06526.

[3]  Aram W. Harrow,et al.  Quantum computational supremacy , 2017, Nature.

[4]  Joseph Emerson,et al.  Scalable and robust randomized benchmarking of quantum processes. , 2010, Physical review letters.

[5]  John M. Martinis,et al.  Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing , 2014 .

[6]  Alán Aspuru-Guzik,et al.  qHiPSTER: The Quantum High Performance Software Testing Environment , 2016, ArXiv.

[7]  Igor L. Markov,et al.  Simulating Quantum Computation by Contracting Tensor Networks , 2008, SIAM J. Comput..

[8]  John A. Gunnels,et al.  Breaking the 49-Qubit Barrier in the Simulation of Quantum Circuits , 2017, 1710.05867.

[9]  M. Head‐Gordon,et al.  Simulated Quantum Computation of Molecular Energies , 2005, Science.

[10]  Thomas Häner,et al.  0.5 Petabyte Simulation of a 45-Qubit Quantum Circuit , 2017, SC17: International Conference for High Performance Computing, Networking, Storage and Analysis.

[11]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[12]  Alex Arkhipov,et al.  BosonSampling is robust against small errors in the network matrix , 2014, 1412.2516.

[13]  M. Mariantoni,et al.  Surface codes: Towards practical large-scale quantum computation , 2012, 1208.0928.

[14]  Guangwen Yang,et al.  Quantum Supremacy Circuit Simulation on Sunway TaihuLight , 2018, IEEE Transactions on Parallel and Distributed Systems.

[15]  Ashley Montanaro,et al.  Average-case complexity versus approximate simulation of commuting quantum computations , 2015, Physical review letters.

[16]  Dorothy Moyle Needham,et al.  RED AND WHITE MUSCLE , 1926 .

[17]  H. Neven,et al.  Low-Depth Quantum Simulation of Materials , 2018 .

[18]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[19]  H. Neven,et al.  Characterizing quantum supremacy in near-term devices , 2016, Nature Physics.

[20]  E. Rieffel,et al.  Quantum Computing: A Gentle Introduction , 2011 .

[21]  Ashley Montanaro,et al.  Achieving quantum supremacy with sparse and noisy commuting quantum computations , 2016, 1610.01808.

[22]  U. Vazirani,et al.  On the complexity and verification of quantum random circuit sampling , 2018, Nature Physics.

[23]  Yaoyun Shi,et al.  Classical Simulation of Intermediate-Size Quantum Circuits , 2018, 1805.01450.

[24]  H. Neven,et al.  Simulation of low-depth quantum circuits as complex undirected graphical models , 2017, 1712.05384.

[25]  L. Duan,et al.  Efficient classical simulation of noisy quantum computation , 2018, 1810.03176.

[26]  Alan Mycroft,et al.  Optimal bit-reversal using vector permutations , 2007, SPAA '07.

[27]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[28]  R. Barends,et al.  Digital quantum simulation of fermionic models with a superconducting circuit , 2015, Nature Communications.

[29]  R. Barends,et al.  Superconducting quantum circuits at the surface code threshold for fault tolerance , 2014, Nature.

[30]  Kevin J. Sung,et al.  Quantum algorithms to simulate many-body physics of correlated fermions. , 2017, 1711.05395.

[31]  Vibhav Gogate,et al.  A Complete Anytime Algorithm for Treewidth , 2004, UAI.

[32]  R. Feynman Simulating physics with computers , 1999 .

[33]  H Neven,et al.  A blueprint for demonstrating quantum supremacy with superconducting qubits , 2017, Science.

[34]  Scott Aaronson,et al.  Complexity-Theoretic Foundations of Quantum Supremacy Experiments , 2016, CCC.

[35]  E. Knill,et al.  Randomized Benchmarking of Quantum Gates , 2007, 0707.0963.

[36]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[37]  David Gosset,et al.  Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates. , 2016, Physical review letters.

[38]  Ching-Hsien Hsu,et al.  A Practical OpenMP Implementation of Bit-Reversal for Fast Fourier Transform , 2009, Infoscale.

[39]  Ramis Movassagh,et al.  Efficient unitary paths and quantum computational supremacy: A proof of average-case hardness of Random Circuit Sampling , 2018, 1810.04681.

[40]  Xia Yang,et al.  64-qubit quantum circuit simulation. , 2018, Science bulletin.

[41]  Igor L. Markov,et al.  Quantum Supremacy Is Both Closer and Farther than It Appears , 2018, ArXiv.

[42]  Alexandru Paler,et al.  Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity , 2018, Physical Review X.

[43]  Hartmut Neven,et al.  Fourier analysis of sampling from noisy chaotic quantum circuits , 2017, 1708.01875.

[44]  Vincenzo Grillo,et al.  Twisting neutrons may reveal their internal structure , 2018, Nature Physics.

[45]  Guangwen Yang,et al.  Quantum-Teleportation-Inspired Algorithm for Sampling Large Random Quantum Circuits. , 2019, Physical review letters.

[46]  Nobuyasu Ito,et al.  Massively parallel quantum computer simulator, eleven years later , 2018, Comput. Phys. Commun..

[47]  Guy Kindler,et al.  Gaussian Noise Sensitivity and BosonSampling , 2014, ArXiv.

[48]  Xun Gao,et al.  Can Chaotic Quantum Circuits Maintain Quantum Supremacy under Noise , 2017, 1706.08913.

[49]  J. Emerson,et al.  Scalable noise estimation with random unitary operators , 2005, quant-ph/0503243.

[50]  G. Knittel,et al.  QTIB: Quick bit-reversed permutations on CPUs , 2011, 2011 17th International Conference on Digital Signal Processing (DSP).

[51]  Tyson Jones,et al.  QuEST and High Performance Simulation of Quantum Computers , 2018, Scientific Reports.

[52]  A. Harrow,et al.  Approximate Unitary t-Designs by Short Random Quantum Circuits Using Nearest-Neighbor and Long-Range Gates , 2018, Communications in Mathematical Physics.

[53]  Thomas Lippert,et al.  Massively parallel quantum computer simulator , 2006, Comput. Phys. Commun..

[54]  Xiang Fu,et al.  General-Purpose Quantum Circuit Simulator with Projected Entangled-Pair States and the Quantum Supremacy Frontier. , 2019, Physical review letters.