Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases

By Nathanan Tantivasadakarn, Ryan Thorngren, Ashvin Vishwanath, R. Verresen. Physical Review X, 2021

184 citations recorded by the source corpus.

A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter cannot be created by finite-depth circuits, underscoring the nonlocal nature of Schrödinger cat states, topological order, and quantum criticality. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE, such as the toric code from measuring a sublattice of a 2D cluster state. However, a systematic understanding of when and how measurements of SRE give rise to LRE is still lacking. Here, we establish that LRE appears upon performing measurements on symmetry-protected topological (SPT) phases—of which the cluster state is one example. For instance, we show how to implement the Kramers-Wannier transformation by adding a cluster SPT to an input state followed by measurement. This transformation naturally relates states with SRE and LRE. An application is the realization of double-semion order when the input state is the Z2 Levin-Gu SPT. Similarly, the addition of fermionic SPTs and measurement leads to an implementation of the Jordan-Wigner transformation of a general state. More generally, we argue that a large class of SPT phases protected by G×H symmetry gives rise to anomalous LRE upon measuring G-charges, and we prove that this persists for generic points in the SPT phase under certain conditions. Our work introduces a new practical tool for using SPT phases as resources for creating LRE, and we uncover the classification result that all states related by sequentially gauging Abelian groups or by Jordan-Wigner transformation are in the same equivalence class, once we augment finite-depth circuits with single-site measurements. In particular, any topological or fracton order with a solvable finite gauge group can be obtained from a product state in this way. Published by the American Physical Society 2024

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/2974f5a84cb51d608023e642529d27f8e68fd57b

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Midcircuit Operations Using the omg Architecture in Neutral Atom Arrays (2023, methodology): “In a similar vein, the use of mid-circuit reset might open new paths to dissipative preparation of long-range entangled states or even autonomous error correction, in an atom array of 100s of qubits [10, 21, 25].”
Measurement as a Shortcut to Long-Range Entangled Quantum Matter (2022, methodology): “We note that a low-depth preparation of chiral Ising topological order via measurements has been proposed in Ref.[7], which nevertheless differs from our protocol.”
Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout (2022, background): “Our work paves the way for the use of mid-circuit measurement as an effective resource for quantum simulation on near-term quantum computers, for instance by facilitating the study of dynamic and long-range entangled quantum phases [21, 22].”
Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward (2022, unknown): “This generalizes a previous result which was the Abelian case with lG = 1 [15].”