Year: 2023
Type: article
Abstract: Projective measurements in random quantum circuits lead to a rich breadth of entanglement phases and extend the realm of nonunitary 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 worldlines.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 ðLÞ scaling of the entanglement entropy.In turn, when orientability is preserved, the longwavelength 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 one-state Potts model (percolation), the two-state Potts model (Ising), and coupled Potts models (Berezhinskii-Kosterlitz-Thouless) 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.
Source: Physical Review X
Authors: Kai Klocke, Michael Buchhold
Institutions: University of California, Berkeley, University of Cologne
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,200
OpenAlex ID: W4388540655