通过优化测量位置，用更少资源实现更强的量子纠缠调控。
Demons on a Budget: Adaptive Measurement Placement at the Entanglement Phase Transition
- 按空间顺序连续测量可显著降低纠缠熵，效果优于随机或智能策略。
- 连续测量能彻底消除相变，使熵稳定在与系统尺寸无关的水平。
- 测量顺序比位置更重要，适合研究量子纠错与动力学相变的场景。
监测量子电路随测量率 $p$ 变化时，会经历体积律与面积律纠缠之间的相变。以往工作随机放置测量并以 $p$ 为控制参数，本文则固定测量预算，比较随机、手工设计和学习策略在砖墙型随机克莱夫福德电路中的表现。结果表明：测量几何结构比信息选择更重要；确定性连续扫描使半切熵降低3.4倍，而等覆盖非结构化放置和贪心策略表现较差。仅靠空间顺序即有效：测量最近未测的 $k$ 个位置，随机破缺时得 $4.14 \pm 0.06$ 比特，位置有序破缺时得 $1.29 \pm 0.04$ 比特。该扫掠操作消除相变而非平移它：三体互信息交叉点随 $p^* \propto 1/L$ 趋于零，稳态熵在 $L$-无关的上限 $0.46/p$ 饱和，$64 \le L \le 512$ 的数据符合 $S = p^{-1} f(pL)$ 的弹道再生形式。在稳定子动力学中，所有结果为确定或公平抛币，记录的香农熵可精确计算；扫掠策略在熵-成本前沿占优，且每测量一次仍仅耗约1比特。通过交叉熵和近端策略优化训练的策略未发现扫掠，因评分策略仅决定测哪，不决定同分项的顺序，而关键效应正存在于此。监测动力学的相图是放置过程的属性，不仅取决于测量率。
原文摘要 · Abstract (English)
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.
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