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

我们研究了d级系统 (qudits)链上的一类局部量子电路，它们共享所谓的“双重单一性”属性。从本质上讲，后一种特性意味着这些系统不仅在时间传播时，而且在空间传播时都会产生单一动力学。我们考虑时空同质（Floquet）电路并用淬灭的单点无序扰乱它们，即通过应用从\(\mathrm{SU}(d)\) 上的任意非奇异分布中提取的独立单点随机幺正，例如，在电路的每一层之后，一个集中在身份周围。我们将长链极限中时间t处的谱形状因子识别为 qudit 环上的有限算子集的交换体的维数Ť网站。对于量子位\((d=2)\) 的一般双幺正电路及其对更高\(d>2\) 的一系列扩展，我们提供了一个明确的换向式构造，并证明谱形状因子与预测完全匹配对于所有t的圆形幺正系综，如果只有局部 2-qubit 门不同于 SWAP（非相互作用门）。