Fermion-mediated Casimir effect on mesoscopic rings implementing non-Clifford SWAP$^α$ gates

Abstract

The Casimir effect is typically governed by intrinsic material properties and lacks in situ tunability. We show that, in mesoscopic rings, both the magnitude and sign of the fermion-mediated Casimir interaction can be controlled via the Aharonov-Bohm effect. The resulting interplay between the Aharonov-Bohm phase and the Casimir interaction provides a route to engineer long-range interactions. In particular, this mechanism enables the implementation of non-Clifford SWAP$^α$ gates between spatially separated spin qubits, thereby reducing the overhead for universal quantum computation and quantum error correction in spin-qubit architectures.