Gate Sequence Controlled Operator Cover Time in U(1) Clifford Circuits

Utilizing sequences of U(1) Clifford gates, we are able to control the number of circuit layers necessary for a given operator to explore the entirety of its accessible operator space. Additionally, we construct an analytic formula for this ‘cover time’ of the operator space for random sequences of gates. This operator cover time in simple qubit circuits can be understood as an analogue to the rate of information scrambling in a quantum system.