量子多体时间演化算子到砖墙电路的最优压缩
Optimal compression of quantum many-body time evolution operators into brickwall circuits
AI总结：
针对近期量子硬件电路深度受限问题，本文将 S=1/2 量子 Heisenberg 模型的时间演化算子编译为一维最优砖墙电路，在固定门数下取得优于 Trotter 分解的保真度并避免 SWAP 门。
摘要：
近期量子计算机存在一定程度的退相干，这使得利用深层电路进行高保真度模拟无法实现。因此，经济地使用电路深度至关重要。对于量子多体系统的数字量子模拟，实时演化通常通过将时间演化算子进行 Trotter 分解来实现，所得到的电路仅包含双量子比特门。为了匹配物理系统的几何结构以及量子处理器的 CNOT 连接性，需要额外的 SWAP 门。我们表明，对于链和梯上的 S=1/2 量子 Heisenberg 模型，当映射到一维量子处理器时，通过将演化算子编译为最优砖墙电路，可以获得在固定门数量下超越简单 Trotter 分解所能达到的最优保真度，且无需额外的 SWAP 门。
英文摘要：
Near term quantum computers suffer from a degree of decoherence which is prohibitive for high fidelity simulations with deep circuits. An economical use of circuit depth is therefore paramount. For digital quantum simulation of quantum many-body systems, real time evolution is typically achieved by a Trotter decomposition of the time evolution operator into circuits consisting only of two qubit gates. To match the geometry of the physical system and the CNOT connectivity of the quantum processor, additional SWAP gates are needed. We show that optimal fidelity, beyond what is achievable by simple Trotter decompositions for a fixed gate count, can be obtained by compiling the evolution operator into optimal brickwall circuits for the $S = 1/2$ quantum Heisenberg model on chains and ladders, when mapped to one dimensional quantum processors without the need of additional SWAP gates.
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