Non-adiabatic holonomic quantum computation in linear system-bath coupling

TL;DR

This paper proposes a robust non-adiabatic holonomic quantum computation scheme in decoherence-free subspaces that uses only two-qubit interactions, reducing experimental complexity and protecting against decoherence.

Contribution

It introduces a new implementation of universal non-adiabatic holonomic gates in non-collective decoherence settings using minimal qubit interactions.

Findings

Achieves universal quantum gates in decoherence-free subspaces.

Reduces implementation complexity by using only two-qubit interactions.

Demonstrates robustness against control errors and decoherence.

Abstract

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of $\frac{N-2}{N}$. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.