Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits

We investigate a class of brickwork-like quantum circuits on chains $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these generate unitary dynamics not only when propagating in time direction, but also space direction. consider space-time homogeneous (Floquet) and perturb them with quenched single-site disorder, i.e. by applying independent single site random unitaries drawn from arbitrary non-singular distribution over ${\rm SU}(d)$, e.g. one concentrated around identity, after each layer circuit. identify spectral form factor at $t$ limit long as dimension commutant finite set operators qudit ring sites. For general dual qubits $(d=2)$ family their extensions to higher $d>2$, we provide explicit construction prove exactly matches prediction circular ensemble for all $t$, if local 2-qubit gates are different SWAP (non-interacting gate). discuss partly possible our results weaker (more singular) forms disorder averaging, well time-reversal symmetry, computing moments factor.