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arXiv · 2103.00693

High-performance parallel classical scheme for simulating shallow quantum circuits

Shihao Zhang·Jiacheng Bao·Yifan Sun·Lvzhou Li·Houjun Sun·Xiangdong Zhang
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Abstract

Recently, constant-depth quantum circuits are proved more powerful than their classical counterparts at solving certain problems, e.g., the two-dimensional (2D) hidden linear function (HLF) problem regarding a symmetric binary matrix. To further investigate the boundary between classical and quantum computing models, in this work we propose a high-performance two-stage classical scheme to solve a full-sampling variant of the 2D HLF problem, which combines traditional classical parallel algorithms and a gate-based classical circuit model together for exactly simulating the target shallow quantum circuits. Under reasonable parameter assumptions, a theoretical analysis reveals our classical simulator consumes less runtime than that of near-term quantum processors for most problem instances. Furthermore, we demonstrate the typical all-connected 2D grid instances by moderate FPGA circuits, and show our designed parallel scheme is a practically scalable, high-efficient and operationally convenient tool for simulating and verifying graph-state circuits performed by current quantum hardware.

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Shihao Zhang, Jiacheng Bao, Yifan Sun, Lvzhou Li, Houjun Sun, Xiangdong Zhang. 2021-03-01. High-performance parallel classical scheme for simulating shallow quantum circuits. https://arxiv.org/abs/2103.00693

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