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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2305.18559 |
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| _version_ | 1866914684207104000 |
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| author | Klocke, Kai Buchhold, Michael |
| author_facet | Klocke, Kai Buchhold, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18559 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Majorana Loop Models for Measurement-Only Quantum Circuits Klocke, Kai Buchhold, Michael Statistical Mechanics Quantum Physics 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. |
| title | Majorana Loop Models for Measurement-Only Quantum Circuits |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2305.18559 |