Expedited Holonomic Quantum Computation in Decoherence-Free Subspace

TL;DR

This paper proposes a fast, fault-tolerant holonomic quantum computation method using external control fields within decoherence-free subspaces, significantly reducing the adiabatic runtime while maintaining robustness against noise.

Contribution

It introduces an expedited HQC protocol that uses zero-energy-cost control fields, unifying robustness features of HQC and decoherence-free subspaces.

Findings

Control fields can accelerate HQC without energy cost.

The scheme is fault-tolerant against noise and fluctuations.

It demonstrates practical realization via decoherence-free subspaces.

Abstract

Holonomic quantum computation (HQC) may not show its full potential in quantum speedup due to the prerequisite of a long coherent runtime imposed by the adiabatic condition. Here we show that the conventional HQC can be dramatically accelerated by using external control fields, of which the effectiveness is exclusively determined by the integral of the control fields in the time domain. Remarkably this control scheme can be realized with net zero energy cost and it is fault-tolerant against fluctuation and noise, significantly relaxing the experimental constraints. We demonstrate how to realize the scheme via decoherence-free subspaces. In this way we unify quantum robustness merits of this fault-tolerant control scheme, the conventional HQC and decoherence-free subspace, and propose an {\em expedited} holonomic quantum computation protocol.