High-performance parallel classical scheme for simulating shallow quantum circuits

TL;DR

This paper introduces a high-performance classical simulation scheme for shallow quantum circuits, combining parallel algorithms and classical circuit models to efficiently simulate quantum problems like the 2D hidden linear function, outperforming near-term quantum processors.

Contribution

The paper presents a novel two-stage classical simulation approach that integrates parallel algorithms and classical circuits, enabling efficient simulation of shallow quantum circuits.

Findings

Classical simulator consumes less runtime than near-term quantum processors for most instances.

The scheme is practically scalable and efficient for simulating graph-state circuits.

Demonstrated effectiveness on FPGA circuits for typical 2D grid instances.

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.