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-...
Machine learning (ML) has achieved remarkable success in a wide range of applications. In recent ML research, deep anomaly detection (AD) has been a hot topic with the aim of discriminating among anomalous data with deep neural networks (DNNs). Notably, image AD is one of the most representative tasks in current deep AD research. ML’s interaction with quantum computing is giving rise to a heated topic named quantum machine learning (QML), which enjoys great prospects according to recent academic research. This paper attempts to address the image AD problem in a deep manner with a novel QML solution. Specifically, we design a quantum-classical hybrid DNN (QHDNN) that aims to learn directly from normal raw images to train a normality model and then exclude images that do not conform to this model as anomalies during its inference. To enable the QHDNN to perform satisfactorily in deep image AD, we explore multiple quantum layer architectures and design a VQC-based QHDNN solution. Extensive experiments were conducted on commonly used benchmarks to test the proposed QML solution, whose results demonstrate the feasibility of addressing deep image AD with QML. Importantly, the experimental results show that our quantum-classical hybrid solution can even yield superior performance to that of its classical counterpart when they share the same number of learnable parameters.
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