General lower bounds on the depth of quantum-expander circuits

Establish general lower bounds on the circuit depth required to implement families of quantum expanders, beyond the depth-1 constructions provided for Pauli and CNOT gates on one-dimensional geometries.

Background

The paper discusses efficient quantum-expander constructions whose defining unitaries are implemented by quantum circuits. Prior constructions had polynomial or larger depth, and the authors note that general lower bounds on the required depth had not been established. Although the paper constructs constant-degree, constant-gap expanders with depth-1 circuits, it does not determine general lower bounds for quantum-expander circuit depth.