[论文解读] Distinguishing synthetic unravelings on quantum computers

Eloy Piñol, Piotr Sierant+7 more|arXiv (Cornell University)|Jan 27, 2026

Quantum Information and Cryptography被引用 0

一句话总结

论文展示在IBM量子硬件上实现的离散时间合成解开，以区分共享相同 GKSL 驱动的平均演化但轨迹不等价的量子轨迹，利用方差和熵等非线性轨迹统计。

ABSTRACT

Distinct monitoring or intervention schemes can produce different conditioned stochastic quantum trajectories while sharing the same unconditional (ensemble-averaged) dynamics. This is the essence of unravelings of a given Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation: any trajectory-ensemble average of a function that is linear in the conditional state is completely determined by the unconditional density matrix, whereas applying a nonlinear function before averaging can yield unraveling-dependent results beyond the average evolution. A paradigmatic example is resonance fluorescence, where direct photodetection (jump/Poisson) and homodyne or heterodyne detection (diffusive/Wiener) define inequivalent unravelings of the same GKSL dynamics. In earlier work, we showed that nonlinear trajectory averages can distinguish such unravelings, but observing the effect in that optical setting requires demanding experimental precision. Here we translate the same idea to a digital setting by introducing synthetic unravelings implemented as quantum circuits acting on one and two qubits. We design two unravelings - a projective measurement unraveling and a random-unitary "kick" unraveling - that share the same ensemble-averaged evolution while yielding different nonlinear conditional-state statistics. We implement the protocols on superconducting-qubit hardware provided by IBM Quantum to access trajectory-level information. We show that the variance across trajectories and the ensemble-averaged von Neumann entropy distinguish the unravelings in both theory and experiment, while the unconditional state and the ensemble-averaged expectation values that are linear in the state remain identical. Our results provide an accessible demonstration that quantum trajectories encode information about measurement backaction beyond what is fixed by the unconditional dynamics.

研究动机与目标

• 激励并说明同一 GKSL 主方程的不同解开如何产生不同的轨道集合。
• 引入离散、基于线路的合成解开，以模拟连续监测。
• 表明非线性轨迹统计能够区分解开，而线性平均值保持相同。
• 通过超导硬件上的单量子比特和两量子比特实验进行方法验证。

提出的方法

• 构造两种合成解开（投影测量和随机单元抖动），使平均态实现相同的去相位通道。
• 使用在两次时间点中断的固定单元演化片段来创建离散轨迹分支。
• 通过事后处理最终测量结果和分支标签来重建轨迹集合。
• 计算非线性轨迹统计量，如 Var_traj[<O>^(r)] 和轨迹平均 von Neumann 熵。
• 在数据分析中实施读出误差缓解和基于自举的误差条。

实验结果

研究问题

• RQ1 在数字量子实验中，非线性轨迹统计是否能区分共享相同 GKSL 动力学的等价解开？
• RQ2 离散、门基的合成解开是否再现连续监测解开的区分特征（如方差和熵的差异）？

主要发现

• 两种解开在理论上对轨迹集合的线性平均值是一致的，确认了相同的无条件演化。
• 轨迹方差 Var_traj[<σ_z>^(r)] 在解开之间存在差异，使得在硬件上可实际区分。
• 在两量子比特情形下，轨迹平均的约简熵 E_r[S(ρ_t^(1,r))] 区分解开并揭示纠缠相关性。
• IBM量子实验结果与仿真一致，证明可观测的非线性条件效应。
• 读出缓解和谨慎的数据分析使轨迹水平统计量的提取更为可靠。