# Production of lattice gauge-Higgs topological states in measurement-only quantum circuit

## TL;DR

This paper demonstrates that measurement-only quantum circuits, guided by Hamiltonian parameters, can simulate complex topological states in lattice gauge-Higgs models, reproducing rich phase diagrams without traditional Hamiltonian evolution.

## Contribution

It introduces a guiding principle for designing measurement-only circuits to emulate Hamiltonian dynamics, enabling the creation of topological phases in quantum systems.

## Key findings

- MoC reproduces phase diagrams similar to Hamiltonian ground states
- Guiding principle links measurement probabilities to Hamiltonian parameters
- Potential to generate complex topological states without Hamiltonian evolution

## Abstract

By imaginary-time evolution with Hamiltonian, an arbitrary state arrives in the system's ground state. In this work, we conjecture that this dynamics can be simulated by measurement-only circuit (MoC), where each projective measurement is set in a suitable way. Based on terms in the Hamiltonian and ratios of their parameters (coefficients), we propose a guiding principle for the choice of the measured operators called stabilizers and also the probability of projective measurement in the MoC. In order to examine and verify this conjecture of the parameter ratio and probability ratio correspondence in a practical way, we study a generalized (1+1)-dimensional $Z_2$ lattice gauge-Higgs model, whose phase diagram is very rich including symmetry-protected topological phase, deconfinement phase, etc. We find that the MoC constructed by the guiding principle reproduces phase diagram very similar to that of the ground state of the gauge-Higgs Hamiltonian. The present work indicates that the MoC can be broadly used to produce interesting phases of matter, which are difficult to be simulated by ordinary Hamiltonian systems composed of stabilizer-type terms.