Integrable nonunitary quantum circuits

Abstract

We show that the integrable Lindblad superoperators found recently can be used to build integrable nonunitary quantum circuits with two-site gates by demonstrating that the $\check{R}$-matrices are completely positive and trace preserving. Using the bond-site transformation, we obtain the corresponding integrable nonunitary quantum circuits with three-site gates. When restricted to the diagonals of the density matrix, these quantum models reduce to integrable classical cellular automata. This approach may pave the way for a systematic construction of integrable nonunitary quantum circuits.

13 pages, 5 figures. Published version

References in corpus (6)

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• Many body localization and thermalization in quantum statistical mechanics
• Postselection-free entanglement dynamics via spacetime duality
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Integrable nonunitary open quantum circuits
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Cited by in corpus (9)

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• Circuits of space and time quantum channels
• The Floquet Baxterisation
• Quantum Zeno Effect in Noisy Integrable Quantum Circuits for Impurity Models
• Information Flow in Non-Unitary Quantum Cellular Automata
• Hidden quasi-local charges and Gibbs ensemble in a Lindblad system
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations