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Recently, constant-depth quantum circuits are proved more powerful than theirclassical 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 computingmodels, in this work we propose a high-performance two-stage classical schemeto solve a full-sampling variant of the 2D HLF problem, which combinestraditional classical parallel algorithms and a gate-based classical circuitmodel together for exactly simulating the target shallow quantum circuits.Under reasonable parameter assumptions, a theoretical analysis reveals ourclassical simulator consumes less runtime than that of near-term quantumprocessors for most problem instances. Furthermore, we demonstrate the typicalall-connected 2D grid instances by moderate FPGA circuits, and show ourdesigned parallel scheme is a practically scalable, high-efficient andoperationally convenient tool for simulating and verifying graph-state circuitsperformed by current quantum hardware.

High-performance parallel classical scheme for simulating shallow quantum circuits