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

• URL: http://arxiv.org/abs/2208.11699v2
• Date: Tue, 6 Sep 2022 16:28:58 GMT
• Title: Decoding Measurement-Prepared Quantum Phases and Transitions: from Ising model to gauge theory, and beyond
• Authors: Jong Yeon Lee, Wenjie Ji, Zhen Bi, Matthew P. A. Fisher
• Abstract summary: Measurements allow efficient preparation of interesting quantum many-body states with long-range entanglement. We demonstrate that the so-called conformal quantum critical points can be obtained by performing general single-site measurements.
• Score: 3.079076817894202
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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