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

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.

14 pages, 9 figures, Physical Review B accepted version

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Cited by in corpus (11)

• Gapless symmetry-protected topological phases and generalized deconfined critical points from gauging a finite subgroup
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Steering-induced phase transition in measurement-only quantum circuits
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit
• Interplay between lattice gauge theory and subsystem codes
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state