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机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在固定测量预算下，对比随机、手动及学习策略在砖墙型随机Clifford电路中的测量布置效果，发现连续扫描可消除纠缠相变并降低半割熵，且优于其他策略。
AI 中文摘要
受监控量子电路中，纠缠会随测量率p发生体积律与面积律之间的测量诱导相变。现有研究将测量置于随机位置，并以测量率作为控制参数；而我们固定测量预算，改变测量位置布置过程，在匹配预算的砖墙型随机Clifford电路中，对比随机布置、手动设计策略与学习策略的表现。首先，布置几何结构比布置信息更重要：确定性连续扫描相比随机布置，将半割熵降低了3.4倍；而等覆盖非结构化布置、具备全状态访问的贪心策略表现差得多。该效应仅由空间顺序导致：测量k个最近未被测量的位点，采用随机平局决胜时得分为4.14±0.06比特，采用位置有序平局决胜时得分为1.29±0.04比特。其次，扫描会消除相变而非仅移动它：三方互信息交叉点随p*∝1/L后退，稳态熵饱和于与L无关的上限（约0.46/p），且64≤L≤512的数据符合弹道重生长论证预测的形式S=p⁻¹f(pL)。第三，稳定子动力学中，每个结果是确定的或公平抛硬币，因此记录的香农熵可精确计数；扫描在熵-记录成本前沿占优，且每测量一次的成本约1比特，与随机布置相同。经交叉熵和近端策略优化训练的策略未发现扫描：基于分数的策略参数化要测量的位点，而非分数相等时的决胜顺序，而该效应正存在于此顺序中。受监控动力学的相图是布置过程的属性，而非仅测量率的属性。
英文摘要
Monitored quantum circuits exhibit a measurement-induced phase transition between volume-law and area-law entanglement as a function of the measurement rate $p$. Prior work places measurements at random locations and treats the rate as the control parameter. We instead fix the measurement budget and vary the placement process, comparing random placement against hand-designed and learned policies in brickwork random Clifford circuits at matched budget. First, placement geometry matters more than placement information. A deterministic contiguous sweep cuts the half-cut entropy by a factor of 3.4 relative to random placement, while equal-coverage unstructured placement and a greedy policy with full state access do far worse. The effect is carried by spatial order alone: measuring the $k$ least recently measured sites gives $4.14 \pm 0.06$ bits with random tie-breaking and $1.29 \pm 0.04$ bits with position-ordered tie-breaking. Second, the sweep eliminates the transition rather than shifting it. Tripartite mutual information crossings recede as $p^* \propto 1/L$, the steady-state entropy saturates at an $L$-independent ceiling near $0.46/p$, and data for $64 \le L \le 512$ collapse onto the form $S = p^{-1} f(pL)$ predicted by a ballistic regrowth argument. Third, in stabilizer dynamics every outcome is deterministic or a fair coin flip, so the record's Shannon entropy is exactly countable; the sweep dominates the entropy-versus-record-cost frontier while paying the same roughly one bit per measurement as random placement. Policies trained by cross-entropy and proximal policy optimization do not find the sweep: score-based policies parameterize which sites to measure, not the order in which degenerate scores are resolved, and the effect lives in that order. The phase diagram of monitored dynamics is a property of the placement process, not only of the measurement rate.
Comments10 pages
