# Lucas Sa: Chaos and integrability in non-unitary open quantum circuits

**Lucas Sa ***(University of Lisbon***)**

Local quantum circuits have become an important paradigm of many-body physics as, in particular, they allow for the simulation of complex quantum systems in emerging quantum computing facilities. While much is already known about unitary and projective-measurement circuits, it is also of interest to extend their study to open and nonequilibrium quantum setups. With this goal, we consider quantum circuits in the Kraus map representation of completely positive quantum dynamics and discuss the first exactly-solvable, yet strongly-interacting, non-unitary open quantum circuit. On the analytical side, we prove integrability by constructing an inhomogeneous transfer matrix generating conserved super-operator charges, show that the circuit is completely positive and trace-preserving, and identify regimes of integrability-breaking. From the numerical point of view, the study of dissipative chaos and integrability requires the generalization of the standard signatures of quantum chaos; we will introduce complex spacing ratios and show that they allow us to confirm all our analytical results.

BASED ON:

L. Sá, P. Ribeiro, and T. Prosen, PRX 10,021019 (2020) [arXiv:1910.12784]

L. Sá, P. Ribeiro, and T. Prosen, arXiv:2011.06565

More information on the seminar webpage.

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