Emergence symmetry protected topological phase in spatially tuned measurement-only circuit

TL;DR

This paper explores a topological phase transition in a measurement-only quantum circuit induced by spatially-tuned measurements, revealing a symmetry protected topological phase and its critical properties akin to 2D percolation.

Contribution

It demonstrates how spatially-tuned measurements can induce and recover SPT phases in measurement-only circuits, providing new insights into measurement-induced topological transitions.

Findings

SPT phase can be recovered on even sublattice by specific measurement tuning.

The phase transition exhibits critical exponents similar to 2D percolation.

Spatial arrangement of measurements controls topological properties.

Abstract

Topological phase transition induced by spatially-tuned single-site measurement is investigated in a measurement-only circuit, in which three different types of projective measurement operator. Specific spatial setting and combination of commutation relations among three measurement operators generate such a transition. In practice, symmetry protected topological (SPT) phase is recovered on even sublattice by eliminating a projective measurement disturbing the SPT via applying another spatially-tuned projective measurement on odd sublattice. We further investigate the critical properties of the phase transition and find that it has the same critical exponents with the two-dimensional percolation transition.