具有共形预测不确定性的固定协议摊销MPS层析成像

中文摘要 AI 辅助

量子态层析成像缺乏样本，所制备的态存在于狭窄且可学习的流形上。k = 0的仅先验控制表明，在集中族上先验估计已接近最优，所以‘少量测量下的高保真度’可能是族记忆而非层析成像；真正的测量效率需要一个基于测量并能有效利用测量值的模型。在共享矩阵乘积态（MPS）核心参数化上研究了两条路径。方法A通过测量引导的后验推理学习MPS核心上的生成先验（经金标准验证，但控制表明其少量测量精度很大程度上是先验的）。方法B是我们的主要提议，是一种固定协议摊销MPS估计器，用规范不变保真度损失训练一次；不依赖排列不变集编码器（普通多层感知器与之匹配）。关键在于测量设计：基于局部约化密度矩阵决定χ - MPS这一事实，以信息丰富的局部泡利集而非随机串为条件，可将易记忆的适度估计器转变为高保真估计器（约0.95，比仅先验估计高0.59，决定性地通过混洗测量控制）。经共形重新校准的随机失活集成给出约90%的覆盖区间，包括未测量可观测量的情况，而基于单次测量的区间不存在。随着系统规模增长质量保持（n = 10时保真度0.90，增益随n增长；键维度χ = 4时为0.88），参数化是多项式的（原生收缩到20个量子比特），并在IBM硬件上完成闭环（从硬件测量的泡利算符得到5个态，保真度0.97）。

英文摘要

Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold. A $k{=}0$ prior-only control shows that on concentrated families a prior estimate is already near-optimal, so ``high fidelity at few measurements'' can be family memorization rather than tomography; genuine measurement-efficiency needs a model that conditions on the measurements and demonstrably uses them. On a shared matrix-product-state (MPS) core parameterization we study two routes. Approach~A learns a generative prior over MPS cores with measurement-guided posterior inference (gold-standard-validated, but whose few-measurement accuracy the control shows is largely the prior). Approach~B, our main proposal, is a \emph{fixed-protocol amortized} MPS estimator trained once with a gauge-invariant fidelity loss; we deliberately do not rest it on a permutation-invariant set encoder (a plain MLP matches it). The decisive lever is the measurement design: motivated by the fact that local reduced density matrices determine a $χ$-MPS, conditioning on an \emph{informative local} Pauli set rather than random strings turns a modest, memorization-prone estimator into a high-fidelity one ($\approx\!0.95$, up to $+0.59$ over prior-only, decisively passing a shuffled-measurement control). A dropout ensemble, conformally recalibrated, gives $\approx\!90\%$-coverage intervals -- including for observables never measured, where a shot-based interval does not exist. Quality holds as the system grows (fidelity $0.90$ at $n{=}10$, gain \emph{growing} in $n$; $0.88$ at bond dimension $χ{=}4$), the parameterization is polynomial (native contraction to $20$ qubits), and we close the loop on IBM hardware ($5$ states at $0.97$ from hardware-measured Paulis).

发表机构

• RIKEN iTHEMS
• RIKEN AIP
• South China University of Technology（华南理工大学）
• Columbia University（哥伦比亚大学）

机构由 AI 辅助整理，请以论文原文为准。