Stabilisation of Quantum Computations by Symmetrisation

TL;DR

This paper introduces a symmetrisation-based method to stabilize quantum computations by projecting onto the symmetric subspace, aiming to mitigate errors from hardware and environmental interactions.

Contribution

It presents an efficient algorithm for symmetric subspace projection and analyzes its effectiveness in stabilizing quantum computations against various errors.

Findings

Effective in reducing unitary errors from hardware imprecision

Mitigates nonunitary errors due to environmental interactions

Discusses limitations and potential of the symmetrisation method

Abstract

We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into $\cal SYM$, the symmetric subspace of the full state space of $R$ redundant copies of the computer. We describe an efficient algorithm and quantum network effecting $\cal SYM$--projection and discuss the stabilising effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.