Measurement-induced phase transitions in the toric code

TL;DR

This paper explores how random measurements on the toric code induce phase transitions, revealing new phases and entanglement properties through a classical loop model analogy and boundary manipulations.

Contribution

It introduces a novel framework linking measurement-induced phases in the toric code to classical loop models and boundary unitaries, enabling new ways to generate and analyze quantum phases.

Findings

Measurement probabilities induce phase transitions in boundary entanglement.

Boundary unitaries create mixed state ordered phases detectable by linear observables.

Parton constructions connect measurement dynamics to classical loop models.

Abstract

We show how distinct phases of matter can be generated by performing random single-qubit measurements on a subsystem of toric code. Using a parton construction, such measurements map to random Gaussian tensor networks, and in particular, random Pauli measurements map to a classical loop model in which watermelon correlators precisely determine measurement-induced entanglement. Measuring all but a 1d boundary of qubits realizes hybrid circuits involving unitary gates and projective measurements in 1+1 dimensions. We find that varying the probabilities of different Pauli measurements can drive transitions in the un-measured boundary between phases with different orders and entanglement scaling, corresponding to short and long loop phases in the classical model. Furthermore, by utilizing single-site boundary unitaries conditioned on the bulk measurement outcomes, we generate mixed state ordered phases and transitions that can be experimentally diagnosed via linear observables. This demonstrates how parton constructions provide a natural framework for measurement-based quantum computing setups to produce and manipulate phases of matter.