面向可观测量目标的哈密顿动力学变分量子模拟

中文摘要 AI 辅助

标准变分量子模拟旨在重现完整量子态的演化，尽管许多应用仅需要少数几个可观测量的期望值。我们研究了一种针对纯态哈密顿动力学的变分方法，该方法更新电路参数以重现所选期望值的演化。一个精确的误差恒等式指导了可观测量的选择，并促使基于目标与哈密顿量重复对易子的构造。对于泡利可观测量和泡利旋转电路，更新可以在不使用辅助量子比特或受控操作进行重叠估计的情况下进行估计。在六量子比特自旋、费米子和分子基准测试中，与同等射击预算下的标准变分量子模拟相比，目标更新将目标误差容限内的中位时间延长了最多4.2倍。这些结果表明，将变分更新导向目标可观测量可以在不增加每个时间步测量成本的情况下延长精确模拟的时间。

英文摘要

Standard variational quantum simulation seeks to reproduce the evolution of the full quantum state, although many applications require only the expectation values of a few observables. We study a variational method for pure-state Hamiltonian dynamics that updates circuit parameters to reproduce the evolution of selected expectation values. An exact error identity guides the choice of observables, motivating a construction based on repeated commutators of the target with the Hamiltonian. For Pauli observables and Pauli-rotation circuits, the update can be estimated without ancillary qubits or controlled operations for overlap estimation. Across six-qubit spin, fermionic, and molecular benchmarks, the targeted update extends the median time within the target-error tolerance by up to a factor of $4.2$ relative to standard variational quantum simulation at equal shot budgets. These results show that directing the variational update toward the target observable can extend accurate simulation without increasing the measurement cost per time step.

发表机构

• ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科学技术学院）
• ICREA（加泰罗尼亚高级研究院）

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