Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits

TL;DR

This paper introduces a measurement-based quantum circuit exhibiting various ordered phases, including incommensurate time crystals, which are linked to complex-temperature phases of an exactly solvable Ising model.

Contribution

It demonstrates a novel quantum circuit model with measurement and post-selection that realizes incommensurate time crystals and connects non-equilibrium phases to equilibrium Ising model phases.

Findings

Realization of incommensurate time crystals in non-unitary circuits

Phases correspond to complex-temperature equilibrium Ising model phases

Tunable period of time crystals via circuit parameters

Abstract

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found in unitary models, those that occur here are \emph{incommensurate} with the drive frequency. The period of the incommensurate time-crystal phase may be tuned by adjusting the circuit parameters. We demonstrate that the phases of our quantum circuit, including the inherently non-equilibrium dynamical ones, correspond to complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model.