Integrability and charge transport in asymmetric quantum-circuit geometries

We revisit the integrability of quantum circuits constructed from two-qubit unitary gates $U$ that satisfy the Yang-Baxter equation. A brickwork arrangement of $U$ typically corresponds to an integrable Trotterization of some Hamiltonian dynamics. Here, we consider more general circuit geometries which include circuits without any nontrivial space periodicity. We show that any time-periodic quantum circuit in which $U$ is applied to each pair of neighbouring qubits exactly once per period remains integrable. We further generalize this framework to circuits with time-varying two-qubit gates. The spatial arrangement of gates in the integrable circuits considered herein can break the space-reflection symmetry even when $U$ itself is symmetric. By analyzing the dynamical spin susceptibility on ballistic hydrodynamic scale, we investigate how an asymmetric arrangement of gates affects the spin transport. While it induces nonzero higher odd moments in the dynamical spin susceptibility, the first moment, which corresponds to a drift in the spreading of correlations, remains zero. We explain this within a quasiparticle picture which suggests that a nonzero drift necessitates gates acting on distinct degrees of freedom.