Establishing the quantum supremacy frontier with a 281 Pflop/s simulation

Noisy Intermediate-Scale Quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of Quantum Supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the World. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.

[1]  Adam Bouland,et al.  Quantum Supremacy and the Complexity of Random Circuit Sampling , 2018, ITCS.

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

[3]  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.

[4]  Dmitry I. Lyakh,et al.  cuTT: A High-Performance Tensor Transpose Library for CUDA Compatible GPUs , 2017, ArXiv.

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

[6]  John A. Gunnels,et al.  Pareto-Efficient Quantum Circuit Simulation Using Tensor Contraction Deferral , 2017 .

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

[8]  Jay M. Gambetta,et al.  Characterizing Quantum Gates via Randomized Benchmarking , 2011, 1109.6887.

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

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

[11]  Rupak Biswas,et al.  A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware , 2018, npj Quantum Information.

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

[13]  D. Gottesman The Heisenberg Representation of Quantum Computers , 1998, quant-ph/9807006.

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

[15]  Erik M. Ferragut,et al.  Unbiased simulation of near-Clifford quantum circuits , 2017, 1703.00111.

[16]  March,et al.  Quantum Volume , 2017 .

[17]  Travis S. Humble,et al.  Simulated execution of hybrid quantum computing systems , 2018, Commercial + Scientific Sensing and Imaging.

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

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

[20]  Scott Aaronson,et al.  Improved Simulation of Stabilizer Circuits , 2004, ArXiv.

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

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

[23]  Travis S. Humble,et al.  Quantum Accelerators for High-Performance Computing Systems , 2017, 2017 IEEE International Conference on Rebooting Computing (ICRC).

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

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

[26]  Fang Zhang,et al.  Alibaba Cloud Quantum Development Platform: Large-Scale Classical Simulation of Quantum Circuits , 2019 .

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

[28]  Rupak Biswas,et al.  A flexible high-performance simulator for the verification and benchmarking of quantum circuits implemented on real hardware , 2018 .

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

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

[31]  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.

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

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

[34]  Manuela Herman,et al.  Quantum Computing: A Gentle Introduction , 2011 .

[35]  J. Biamonte,et al.  Tensor Networks in a Nutshell , 2017, 1708.00006.

[36]  Dmitry I. Lyakh Domain‐specific virtual processors as a portable programming and execution model for parallel computational workloads on modern heterogeneous high‐performance computing architectures , 2019, International Journal of Quantum Chemistry.

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

[38]  S. Aaronson,et al.  Improved simulation of stabilizer circuits (14 pages) , 2004 .

[39]  Travis S. Humble,et al.  Quantum supremacy using a programmable superconducting processor , 2019, Nature.

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

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

[42]  John M. Martinis,et al.  State preservation by repetitive error detection in a superconducting quantum circuit , 2015, Nature.

[43]  S. Lloyd Quantum-Mechanical Computers , 1995 .

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

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

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

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

[48]  H. Neven,et al.  Digitized adiabatic quantum computing with a superconducting circuit. , 2015, Nature.

[49]  Dmitry I. Lyakh An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU , 2015, Comput. Phys. Commun..

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

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

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

[53]  M. B. Hastings,et al.  Locality in Quantum Systems , 2010, 1008.5137.

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

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

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

[57]  Hartmut Neven,et al.  Nonergodic Delocalized States for Efficient Population Transfer within a Narrow Band of the Energy Landscape , 2018, Physical Review X.

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

[59]  Alexander McCaskey,et al.  Validating quantum-classical programming models with tensor network simulations , 2018, PloS one.

[60]  Bei Zeng,et al.  16-qubit IBM universal quantum computer can be fully entangled , 2018, npj Quantum Information.

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

[62]  Rainer Blatt,et al.  Characterizing large-scale quantum computers via cycle benchmarking , 2019, Nature Communications.