Integrable nonunitary open quantum circuits

TL;DR

This paper constructs an exactly solvable, integrable dissipative quantum circuit based on a Trotterized Hubbard model with imaginary interactions, revealing new insights into non-Hermitian symmetry classes and spectral properties.

Contribution

It introduces a novel integrable dissipative quantum circuit model derived from the Hubbard model, with explicit construction and analysis of its spectral and symmetry properties.

Findings

The circuit is integrable with conserved superoperator charges.

Adding interactions or removing dephasing breaks integrability.

Spectral analysis confirms the analytical predictions.

Abstract

We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from which conserved superoperator charges can be derived, in particular, the circuit's dynamical generator. After showing the trace preservation and complete positivity of local maps, we reinterpret them as the Kraus representation of the local dynamics of free fermions with single-site dephasing. The integrability of the map is broken by adding interactions to the local coherent dynamics or by removing the dephasing. In particular, even circuits built from convex combinations of local free-fermion unitaries are nonintegrable. Moreover, the construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes, which are characterized by the behavior under transposition instead of complex conjugation. We confirm all our analytical results by using complex spacing ratios to examine the spectral statistics of the dissipative circuits.