Chaos and integrability in non-unitary Kraus quantum circuits

Local quantum circuits have become an important paradigm of many-body physics, particularly due to the ability to simulate them by 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 the discrete-time Kraus map representation of completely positive quantum dynamics. We do this in two complementary settings: we model chaotic circuits by random Kraus circuits [1] and introduce the Trotterizattion of the Hubbard model at imaginary interaction strength as a paradigmatic integrable non-unitary circuit [2].
In the former, through random matrix theory techniques and numerical exact diagonalization, we find the statistical properties of local circuits to be qualitatively the same as those of nonlocal Kraus maps, namely a transition in the spectral support and the same universal steady state identified for random Lindblad dynamics.
In the latter, we prove integrability by constructing an inhomogeneous transfer matrix generating conserved super-operator charges, identify regimes of integrability-breaking, and confirm all our analytical results by using complex spacing ratios [3].

[1]Sá et al, PRB 102,134310 (2020)
[2]Sá et al, to appear (2020)
[3]Sá et al, PRX 10,021019 (2020)