Computing Permanents for Boson Sampling on Tianhe-2 Supercomputer

Boson sampling, thought to be intractable classically, can be solved by a quantum machine composed of merely generation, linear evolution and detection of single photons. Such an analog quantum computer for this specific problem provides a shortcut to boost the absolute computing power of quantum computers to beat classical ones. However, the capacity bound of classical computers for simulating boson sampling has not yet been identified. Here we simulate boson sampling on the Tianhe-2 supercomputer which occupied the first place in the world ranking six times from 2013 to 2016. We computed the permanent of the largest matrix using up to 312,000 CPU cores of Tianhe-2, and inferred from the current most efficient permanent-computing algorithms that an upper bound on the performance of Tianhe-2 is one 50-photon sample per ~100 min. In addition, we found a precision issue with one of two permanent-computing algorithms.

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

[2]  Kaushik P. Seshadreesan,et al.  Sampling arbitrary photon-added or photon-subtracted squeezed states is in the same complexity class as boson sampling , 2014, 1406.7821.

[3]  Timothy C. Ralph,et al.  Error tolerance of the boson-sampling model for linear optics quantum computing , 2011, 1111.2426.

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

[5]  A. Crespi,et al.  Integrated multimode interferometers with arbitrary designs for photonic boson sampling , 2013, Nature Photonics.

[6]  B. J. Metcalf,et al.  Boson Sampling on a Photonic Chip , 2012, Science.

[7]  A Laing,et al.  Boson sampling from a Gaussian state. , 2014, Physical review letters.

[8]  Nicolò Spagnolo,et al.  Experimental scattershot boson sampling , 2015, Science Advances.

[9]  J. O'Brien,et al.  Universal linear optics , 2015, Science.

[10]  I. Chuang,et al.  Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance , 2001, Nature.

[11]  Canqun Yang,et al.  MilkyWay-2 supercomputer: system and application , 2014, Frontiers of Computer Science.

[12]  Scott Aaronson,et al.  Bosonsampling is far from uniform , 2013, Quantum Inf. Comput..

[13]  Andrew G. White,et al.  Photonic Boson Sampling in a Tunable Circuit , 2012, Science.

[14]  Brian J. Smith,et al.  Two-photon quantum walk in a multimode fiber , 2015, Science Advances.

[15]  D. Deutsch Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[16]  S. Scheel,et al.  MACROSCOPIC QUANTUM ELECTRODYNAMICS — CONCEPTS AND APPLICATIONS , 2008, 0902.3586.

[17]  Peter P Rohde,et al.  Scalable boson sampling with time-bin encoding using a loop-based architecture. , 2014, Physical review letters.

[18]  A. Politi,et al.  Shor’s Quantum Factoring Algorithm on a Photonic Chip , 2009, Science.

[19]  Jian-Wei Pan,et al.  Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits. , 2007, Physical review letters.

[20]  Isaac L. Chuang,et al.  Quantum Computation and Quantum Information (10th Anniversary edition) , 2011 .

[21]  Peter P. Rohde Optical quantum computing with photons of arbitrarily low fidelity and purity , 2012 .

[22]  B. Lanyon,et al.  Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement. , 2007, Physical review letters.

[23]  Sheng-Tao Wang,et al.  Certification of Boson Sampling Devices with Coarse-Grained Measurements , 2016, 1601.02627.

[24]  Jonathan P. Dowling,et al.  Implementing BosonSampling with time-bin encoding: Analysis of loss, mode mismatch, and time jitter , 2015 .

[25]  M B Plenio,et al.  Efficient factorization with a single pure qubit and logN mixed qubits. , 2000, Physical review letters.

[26]  Philip Walther,et al.  Experimental boson sampling , 2012, Nature Photonics.

[27]  William J. Munro,et al.  Evidence for the conjecture that sampling generalized cat states with linear optics is hard , 2015 .

[28]  Jonathan P. Dowling,et al.  Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit for boson sampling , 2013, 1307.8238.

[29]  Yun Zhou,et al.  The Reliability Wall for Exascale Supercomputing , 2012, IEEE Transactions on Computers.

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

[31]  T. Monz,et al.  Realization of a scalable Shor algorithm , 2015, Science.

[32]  X-Q Zhou,et al.  Experimental realization of Shor's quantum factoring algorithm using qubit recycling , 2011, Nature Photonics.

[33]  James C. Gates,et al.  Chip-based array of near-identical, pure, heralded single-photon sources , 2016, 1603.06984.

[34]  Kaushik P. Seshadreesan,et al.  Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states: The quantum-classical divide and computational-complexity transitions in linear optics , 2014, 1402.0531.

[35]  Nicolò Spagnolo,et al.  Experimental validation of photonic boson sampling , 2014, Nature Photonics.