Mixing and localisation in random time-periodic quantum circuits of Clifford unitaries

Understand

How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation.

• We analyse a Floquet model with disorder, characterised by a family of local, time-periodic, random quantum circuits in one spatial dimension.
• We observe that the evolution operator enjoys an extra symmetry at times that are a half-integer multiple of the period.
• With this we prove that after the scrambling time, namely when any initial perturbation has propagated throughout the system, the evolution operator cannot be distinguished from a (Haar) random unitary when all qubits are measured with Pauli operators.