Measurement as a Shortcut to Long-Range Entangled Quantum Matter
Measurement as a Shortcut to Long-Range Entangled Quantum Matter
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DOI：
10.1103/prxquantum.3.040337
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发表时间：
2022-06
期刊：
影响因子：
9.7
通讯作者：
Tsung-Cheng Lu;Leonardo A. Lessa;Isaac H. Kim;T. Hsieh
中科院分区：
文献类型：
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作者：
Tsung-Cheng Lu;Leonardo A. Lessa;Isaac H. Kim;T. Hsieh
使用单一电路制备远程纠缠态受到利布-罗宾逊界的限制，但具有投影测量和反馈的电路（“自适应电路”）可以避开这些限制。我们介绍了三种局部自适应电路，它们能够低深度制备具有间隙拓扑序和共形场理论（CFTs）特征的远程纠缠量子物质。这三个类的灵感来自于不同的物理见解，包括张量网络结构、多尺度纠缠重整化分析（MERA）和部分子结构。可以在一定深度或时间内制备包括手性拓扑序在内的一大类拓扑序，一维CFT态和具有可解群和不可解群的非阿贝尔拓扑序可以在深度上与系统大小成对数比例。我们还建立了最近发现的对称保护拓扑相和远程纠缠之间的对应关系，以获得制备对称丰富的拓扑顺序和任意CSS （calderbank - shorr - steane）码的有效协议。我们的工作说明了状态准备测量的实际和概念上的多功能性。
The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The three classes are inspired by distinct physical insights, including tensor-network constructions, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral topological order, can be prepared in constant depth or time, and one-dimensional CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size. We also build on a recently discovered correspondence between symmetry-protected topological phases and long-range entanglement to derive efficient protocols for preparing symmetry-enriched topological order and arbitrary CSS (Calderbank-Shor-Steane) codes. Our work illustrates the practical and conceptual versatility of measurement for state preparation.