Gate Parameter Lee-Yang Zeros and Dynamical Phases in Quantum Circuits

Abstract:We propose gate-parameter Lee-Yang zeros of Loschmidt amplitudes as probes of dynamical phases in finite quantum circuits. We study Floquet circuits constructed from two-qubit fSim gates with identical parameters, for which the Loschmidt amplitude becomes a rational function of the gate parameters after a suitable change of variables. At fixed system size and large circuit depth, the zeros in one complexified gate parameter, with the other held fixed, condense onto limiting curves. In contrast to conventional Loschmidt or Fisher zeros in complex time, these zeros live directly in the complex plane of a tunable gate parameter. We show that the limiting set has two origins: a state-dependent component controlled by overlaps with Floquet eigenstates, and a universal component fixed by the Floquet spectrum. As the remaining gate parameter is varied, the universal zero set reorganizes abruptly, providing a finite-qubit diagnostic of a dynamical phase transition. We demonstrate this behavior in a Bethe ansatz solvable brickwork circuit and in longer-range fSim circuits outside this solvable structure. The mechanism follows from the Beraha-Kahane-Weiss theorem together with local unitarity, and is therefore spectral rather than a special consequence of integrability.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)

arXiv:2605.29838 [quant-ph]

(or arXiv:2605.29838v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.29838 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.