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arXiv 2401.17367quant-ph
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使用酉镜像电路探测测量诱导纠缠相变

Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits

Yariv Yanay, Brian Swingle, Charles Tahan

AI总结:

提出一种基于矩阵乘积态的酉镜像混合量子-经典算法,通过张量网络表示能力在临界点处的指数级失效来探测测量诱导纠缠相变。

摘要:

监测随机电路由交替的纠缠双量子比特门和应用于部分比例 $p$ 量子比特的投影单量子比特测量组成,一直是近期关注的课题。具体而言,由此产生的稳态展现出一种相变:在 $p<p_{c}$ 时,从具有“体积律”纠缠的高度关联态转变为在 $p>p_{c}$ 时具有“面积律”纠缠的局域态。实验上很难观测到这种相变,因为它无法在系综层面上被观测到。直观地说,要观测到它,必须重复实验直到测量结果集自身重复,其可能性在测量数量上呈指数级减小。为克服这一问题,我们提出了一种混合量子-经典算法,该算法基于投影电路创建了基于矩阵乘积态(MPS)的“酉镜像”。多项式规模的张量网络可以表示具有面积律纠缠的量子态,因此酉镜像能很好地近似 $p_{c}$ 以上的实验态,但在其下方则会指数级失效。因此,这种镜像的破裂可以精确定位临界点。我们概述了该算法以及如何获得此类结果。我们给出了任何能被MPS很好表示的给定态的最大纠缠熵界限,并基于该界限建议如何限制体积律相。我们考虑在MPS失效的情况下,纠缠是否同样能从下方被限制。最后,我们给出了少量量子比特以及使用随机 Clifford 门的监测电路的数值结果。

英文摘要:

Monitored random circuits, consisting of alternating layers of entangling two-qubit gates and projective single-qubit measurements applied to some fraction $p$ of the qubits, have been a topic of recent interest. In particular, the resulting steady state exhibits a phase transition from highly correlated states with "volume-law" entanglement at $p<p_{c}$ to localized states with "area-law" entanglement at $p>p_{c}$. It is hard to access this transition experimentally, as it cannot be seen at the ensemble level. Naively, to observe it one must repeat the experiment until the set of measurement results repeats itself, with likelihood that is exponentially small in the number of measurements. To overcome this issue, we present a hybrid quantum-classical algorithm which creates a matrix product state (MPS) based "unitary mirror" of the projected circuit. Polynomial-sized tensor networks can represent quantum states with area-law entanglement, and so the unitary mirror can well-approximate the experimental state above $p_{c}$ but fails exponentially below it. The breaking of this mirror can thus pinpoint the critical point. We outline the algorithm and how such results would be obtained. We present a bound on the maximum entanglement entropy of any given state that is well-represented by an MPS, and from the bound suggest how the volume-law phase can be bounded. We consider whether the entanglement could similarly be bounded from below where the MPS fails. Finally, we present numerical results for small qubit numbers and for monitored circuits with random Clifford gates.

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