Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases

TL;DR

This paper proposes a new scheme for nonadiabatic geometric quantum computation in decoherence-free subspaces that uses unconventional geometric phases, eliminating the need to remove dynamical phases and simplifying implementation.

Contribution

It introduces a novel approach based on unconventional geometric phases for nonadiabatic quantum gates, avoiding extra operations needed in traditional methods.

Findings

Achieves universal geometric gates nonadiabatically

Maintains robustness against control errors and decoherence

Simplifies implementation by removing phase cancellation steps

Abstract

Nonadiabatic geometric quantum computation in decoherence-free subspaces has received increasing attention due to the merits of its high-speed implementation and robustness against both control errors and decoherence. However, all the previous schemes in this direction have been based on the conventional geometric phases, of which the dynamical phases need to be removed. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases, of which the dynamical phases do not need to be removed. Specifically, by using three physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of geometric gates nonadiabatically and unconventionally. Our scheme not only maintains all the merits of nonadiabatic geometric quantum computation in decoherence-free subspaces, but also avoids the additional operations required in the conventional schemes to cancel the dynamical phases.