A benchmark test of boson sampling on Tianhe-2 supercomputer

Abstract

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. arXiv:1606.05836v2 [quant-ph] 21 Aug 2018FIG. 1: A schematic view of computational task with the Tianhe-2 supercomputer (A) and a quantum boson-sampling machine (B). A quantum boson-sampling machine obtains an n-photon sample T directly through a measurement on the m output ports from the network that described by a unitary matrix U with input S. To simulate the generation of a sample on Tianhe-2, it is necessary to compute the probability Pr[S → T ], in which the main time-consuming task is to calculate the permanent of an n × n sub-matrix U S,T of U . The capacity of computing the permanent on Tianhe-2 is employed to benchmark the state of the art and set an upper bound on the classical execution time to be beaten by quantum boson-sampling machine. II. SPEED PERFORMANCEThe two most efficient permanent-computing algorithms, Ryser's algorithm and BB/FG's algorithm, are both in the time complexity of O(n 2 · 2 n ).We implemented Ryser's algorithm and BB/FG's algorithm (see the supplementary material for details), and ran them on the Tianhe-2 supercomputer. This supercomputer consists of 16,000 computing nodes, each containing three CPUs and two co-processors, denoted as MIC. The programs were tested under two types of configurations: running with only CPUs, or hybrid running with both CPUs and MICs.We ran Ryser's algorithms with the number of nodes ranging from 2,048 to 13,000, as shown in TABLE I. It is difficult for a system of very large scale to complete long-running-time execution, because the system reliability becomes worse as the number of processing units increases [38]. Occasionally, slow nodes would prolong the total execution time. This phenomenon can be seen from the data in TABLE I, since the time used is not reduced in proportion (more specifically, the time used for a 46 × 46 permanent using 4, 096, 8,192 and 13,000 nodes). Up to now, the 48 × 48 matrix's permanent is the largest problem computed on 8,192 nodes, which accounts for more than half of the nodes of Tianhe-2, and the 13,000-node test uses 81.25% CPUs of Tianhe-2, the largest amount of computing resources ever, for the boson-...

Classical simulation of photonic linear optics with lost particles

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“…23) and R = 10 GHz, which is faster than any experimentally demonstrated photon source to our knowledge, we can plot QA against n and η.…”

Cryptographic one-way function based on boson sampling

“…The present work is the first attempt in the direction of cryptographic applications. Our analysis, together with existing results [32,33], suggests that evaluation of the proposed OWF for a given input can be performed on a classical computer for N 40, while due to the nature of the underlying problem, construction of inversion algorithms is conjectured to be practically impossible. Moreover, the resources required for its brute-force inversion scale exponentially with N , for both classical and quantum adversaries.…”

“…The fastest known classical algorithm for boson sampling requires O(N 2 N ) operations to produce a single sample [32], and thus we obtain Given that d scales polynomially with (M, N ), the evaluation of the function for a given x ∈ Z |S| is only polynomially harder than the evaluation of a permanent of an N × N complex matrix by means of Ryser's algorithm, whose run-time is O(N 2 N ) [32,37]. In view of recent numerical studies on the computation of permanents [32,37,33], evaluation of the proposed OWF for N 40 is expected to be a feasible task for classical computers.…”