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arXiv:2009.01177 · IEEE Transactions on Parallel and Distributed Systems

Benchmarking 50-Photon Gaussian Boson Sampling on the Sunway TaihuLight

Yuxuan Li, Lin Gan, Ming-Cheng Chen, Yaojian Chen, Haitian Lu, Chao‐Yang Lu, Jian-Wei Pan, Haohuan Fu, Guangwen Yang

Published Sep 9, 2021• 19 citations
arXivHTMLPDF

Abstract

Boson sampling is expected to be an important milestone that will demonstrate quantum computational advantage (or quantum supremacy). This work establishes the benchmarking of Gaussian boson sampling (GBS) with threshold detection based on the Sunway TaihuLight supercomputer. To achieve the best performance and provide a competitive scenario for future quantum computing studies, the selected simulation algorithm is fully optimized based on a set of innovative approaches, including a parallel framework with almost perfect load balance and an instruction-level optimizing scheme based on a shortest-path-based instruction scheduling. In addition, data precision is carefully processed by an integer-instruction-based and multiple-precision fixed-point implementation, including 128- and 256-bit precison mode, which can be appropriately selected based on an adaptive precision optimizing scheme. Based on these methods, a highly efficient parallel quantum sampling algorithm is designed. The largest run enables us to obtain one Torontonian function of a$100\times 100$submatrix from 50-photon GBS within 20 hours in 128-bit precision and 2 days in 256-bit precision. To our knowledge, this was the largest quantum computing simulation based on Boson Sampling by using modern supercomputers.

DOI
10.1109/tpds.2021.3111185

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Boson sampling is expected to be an important milestone that will demonstrate quantum computational advantage (or quantum supremacy). This work establishes the benchmarking of Gaussian boson sampling (GBS) with threshold detection based on the Sunway TaihuLight supercomputer. To achieve the best performance and provide a competitive scenario for future quantum computing studies, the selected simulation algorithm is fully optimized based on a set of innovative approaches, including a parallel framework with almost perfect load balance and an instruction-level optimizing scheme based on a shortest-path-based instruction scheduling. In addition, data precision is carefully processed by an integer-instruction-based and multiple-precision fixed-point implementation, including 128- and 256-bit precison mode, which can be appropriately selected based on an adaptive precision optimizing scheme. Based on these methods, a highly efficient parallel quantum sampling algorithm is designed. The largest run enables us to obtain one Torontonian function of a100×100100\times 100100×100submatrix from 50-photon GBS within 20 hours in 128-bit precision and 2 days in 256-bit precision. To our knowledge, this was the largest quantum computing simulation based on Boson Sampling by using modern supercomputers.
Identifying the boundary beyond which quantum machines provide a computational advantage over their classical counterparts is a crucial step in charting their usefulness. Gaussian boson sampling (GBS), in which photons are measured from a highly entangled Gaussian state, is a leading approach in pursuing quantum advantage. State-of-the-art GBS experiments that run in minutes would require 600 million years to simulate using the best preexisting classical algorithms. Here, we present faster classical GBS simulation methods, including speed and accuracy improvements to the calculation of loop hafnians. We test these on a ∼100,000-core supercomputer to emulate GBS experiments with up to 100 modes and up to 92 photons. This reduces the simulation time for state-of-the-art GBS experiments to several months, a nine-orders of magnitude improvement over previous estimates. Last, we introduce a distribution that is efficient to sample from classically and that passes a variety of GBS validation methods.
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors, and how do they affect the complexity of the problem solved? Large-scale Gaussian boson sampling (GBS) experiments give an example in which random numbers are generated. Despite classical hardness, these have computable benchmarks for checking data validity. While there are other quantum computing architectures, Gaussian boson sampling is uniquely testable at all scales. Several large, pioneering quantum computing (QC) experiments have been carried out to investigate quantum advantage. Here, we introduce a highly scalable but classical algorithm that can solve GBS approximately. Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes. This algorithm outperforms all previous classical, approximate algorithms and scales efficiently to larger experiments. Our results show that effects beyond losses can cause the errors that allow classical simulability. This work will lead to more precise algorithms and is a step towards understanding how QC quantum advantage is affected by the underlying physics.
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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.
If classical algorithms have been successful in reproducing the estimation of expectation values of observables of some quantum circuits using off-the-shelf computing resources, matching the performance of the most advanced quantum devices on sampling problems usually requires extreme cost in terms of memory and computing operations, making them accessible to only a handful of supercomputers around the world. In this work, we demonstrate for the first time a classical simulation outperforming Gaussian boson sampling experiments of one hundred modes on established benchmark tests using a single CPU or GPU. Being embarrassingly parallelizable, a small number of CPUs or GPUs allows us to match previous sampling rates that required more than one hundred GPUs. We believe algorithmic and implementation improvements will generalize our tools to photo-counting, single-photon inputs, and pseudo-photon-number-resolving scenarios beyond one thousand modes. Finally, most of the innovations in our tools remain valid for generic probability distributions over binary variables, rendering it potentially applicable to the simulation of qubit-based sampling problems and creating classical surrogates for classical-quantum algorithms.