Decoding Measurement-Prepared Quantum Phases and Transitions: from Ising model to gauge theory, and beyond

TL;DR

This paper demonstrates how measurement-based techniques can prepare and decode quantum critical states with long-range entanglement, establishing a link to classical models and conformal field theories, and offering practical protocols for studying quantum phases.

Contribution

It introduces a method to generate and analyze conformal quantum critical points via measurements on cluster states, connecting quantum states to classical models and enabling efficient decoding without post-selection.

Findings

Measurement-based preparation of conformal quantum critical points.

Exact correspondence between quantum states and classical models.

Protocols for decoding quantum phases efficiently.

Abstract

Measurements allow efficient preparation of interesting quantum many-body states with long-range entanglement, conditioned on additional transformations based on measurement outcomes. Here, we demonstrate that the so-called conformal quantum critical points (CQCP) can be obtained by performing general single-site measurements in an appropriate basis on the cluster states in $d\geq2$. The equal-time correlators of the said states are described by correlation functions of certain $d$-dimensional classical models at finite temperatures and feature spatial conformal invariance. This establishes an exact correspondence between the measurement-prepared critical states and conformal field theories of a range of critical spin models, including familiar Ising models and gauge theories. Furthermore, by mapping the long-range entanglement structure of measured quantum states into the correlations of the corresponding thermal spin model, we rigorously establish the stability condition of the long-range entanglement in the measurement-prepared quantum states deviating from the ideal setting. Most importantly, we describe protocols to decode the resulting quantum phases and transitions without post-selection, thus transferring the exponential measurement complexity to a polynomial classical computation. Therefore, our findings suggest a novel mechanism in which a quantum critical wavefunction emerges, providing new practical ways to study quantum phases and conformal quantum critical points.