Production of lattice gauge Higgs topological states in a measurement-only quantum circuit
Yoshihito Kuno, Ikuo Ichinose
Abstract
By imaginary-time evolution with the Hamiltonian, an arbitrary state arrives in the system's ground state. In this paper, we conjecture that this dynamics can be simulated by a 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 the symmetry-protected topological phase, deconfinement phase, etc. We find that the MOC constructed by the guiding principle reproduces the phase diagram in a very similar way to that of the ground state of the gauge Higgs Hamiltonian. The present paper 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.