تقرير
Majorana Loop Models for Measurement-Only Quantum Circuits
| العنوان: | Majorana Loop Models for Measurement-Only Quantum Circuits |
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| المؤلفون: | Klocke, Kai, Buchhold, Michael |
| المصدر: | Physical Review X 13 (4), 041028 (2023) |
| سنة النشر: | 2023 |
| المجموعة: | Condensed Matter Quantum Physics |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics, Quantum Physics |
| الوصف: | Projective measurements in random quantum circuits lead to a rich breadth of entanglement phases and extend the realm of non-unitary quantum dynamics. Here we explore the connection between measurement-only quantum circuits in one spatial dimension and the statistical mechanics of loop models in two dimensions. While Gaussian Majorana circuits admit a microscopic mapping to loop models, for non-Gaussian, i.e., generic Clifford, circuits a corresponding mapping may emerge only on a coarse grained scale. We then focus on a fundamental symmetry of loop models: the orientability of world lines. We discuss how orientability enters in the measurement framework, acting as a separatrix for the universal long-wavelength behavior in a circuit. When orientability is broken, the circuit falls into the universality class of closely packed loops with crossings (CPLC) and features a Goldstone phase with a peculiar, universal $\log^2(L)$-scaling of the entanglement entropy. In turn, when orientability is preserved, the long-wavelength behavior of the circuit mimics that of (coupled) two-dimensional Potts models. We demonstrate the strength of the loop model approach by numerically simulating a variety of measurement-only Clifford circuits. Upon varying the set of measured operators, a rich circuit dynamics is observed, ranging from CPLC to the $1$-state Potts model (percolation), the $2$-state Potts model (Ising) and coupled Potts models (BKT) universality class. Loop models thus provide a handle to access a large class of measurement-only circuits and yield a blueprint on how to realize desired entanglement phases by measurement. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevX.13.041028 |
| URL الوصول: | http://arxiv.org/abs/2305.18559 |
| رقم الأكسشن: | edsarx.2305.18559 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevX.13.041028 |
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