低秩量子最优控制的解析梯度
Analytic gradients for low-rank quantum optimal control
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中文总结 AI 辅助
研究在开放量子系统中设计控制脉冲，提出低秩最优控制方法（LROC），利用量子计算特性，通过推导伴随方程以低成本获梯度，在超导电路任务中展示其广度，扩展脉冲级优化到更大系统规模。
中文摘要 AI 辅助
我们引入了低秩最优控制（LROC），这是一种用于在全密度矩阵模拟成本过高的开放量子系统中设计控制脉冲的方法。该方法利用量子计算本身的一个特性：由于协议旨在保持纯度，密度矩阵由少数纯态主导，并允许进行精确的低秩分解。LROC仅传播这种分解形式，并通过推导相应的伴随方程，以与模拟相同的降低成本获得任何可微目标的梯度，与完整的主方程相比，在时间和内存上实现了二次改进。我们在四个超导电路任务上展示了该方法的广度：制备五比特GHZ态、CNOT门、量子比特读出和一个纠错原语，使用现实的多能级跨导量子比特、衰减和强驱动进行建模，在每种情况下都达到了与固有耗散极限一致的保真度。LROC从而将脉冲级优化扩展到现有基于梯度的方法无法企及的系统规模
英文摘要
We introduce low-rank optimal control (LROC), a method for designing control pulses in open quantum systems whose full density-matrix simulation is prohibitively expensive. The method exploits a feature of quantum computing itself: because protocols are designed to preserve purity, the density matrix is dominated by a few pure states and admits an accurate low-rank factorization. LROC propagates only this factorized form and, by deriving the corresponding adjoint equation, obtains the gradient of any differentiable objective at the same reduced cost as the simulation, leading to a quadratic improvement in time and memory compared to the full master equation. We illustrate the breadth of the method on four superconducting-circuit tasks: preparation of a five-qubit GHZ state, a CNOT gate, qubit readout, and an error correction primitive, modeled with realistic multilevel transmons, decay, and strong drives, in each case reaching fidelities consistent with the intrinsic dissipation limits. LROC thereby extends pulse-level optimization to system sizes beyond the reach of existing gradient-based methods.
