Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits

TL;DR

This paper develops a comprehensive framework for gauging modulated symmetries using multiple gauge operators and adaptive circuits, revealing new dualities and phases such as symmetry-protected topological states.

Contribution

It introduces a novel simultaneous gauging method for modulated symmetries and demonstrates adaptive quantum circuits for implementing associated dualities.

Findings

Broader duality classes captured by simultaneous gauging

Identification of a dipole symmetry-protected topological phase

Analysis of the rank-2 toric code phase diagram

Abstract

We introduce an extended framework for the simultaneous gauging of modulated symmetries in $(d+1)$ dimensions, employing {\it multiple} gauge symmetry operators whose corresponding gauging procedures must be carried out simultaneously. Simultaneous gauging can capture a broader class of dualities than sequential gauging, the latter corresponding to the conventional gauging applied in successive steps. In general, performing simultaneous gauging and conventional gauging in sequence constitutes the most general framework for gauging modulated symmetries. We further show that the associated duality transformations can be implemented via adaptive state preparation protocols. As a concrete example, we consider a dipole symmetry in $(2+1)$D and illustrate both the simultaneous gauging procedure and the adaptive preparation protocol. Interestingly, we find that the intermediate state of the simultaneous gauging/adaptive circuit corresponds to a symmetry-protected topological phase protected by the dipole bundle symmetry. Finally, we utilize the duality to analyze the phase diagram of the rank-2 toric code under transverse fields.