Using concatenated quantum codes for universal fault-tolerant quantum gates

TL;DR

This paper introduces a concatenated quantum code scheme that enables universal fault-tolerant quantum computation without the need for special ancillary states, potentially reducing overhead compared to existing methods.

Contribution

It presents a novel concatenation approach leveraging transversal properties of two codes to achieve universal fault-tolerance without magic state distillation.

Findings

Uses Steane and Reed-Muller codes as an example

Provides conditions for codes to ensure fault-tolerance

Suggests potential for reduced overhead in quantum computation

Abstract

We propose a method for universal fault-tolerant quantum computation using concatenated quantum error correcting codes. Namely, other than computational basis state preparation as required by the DiVincenzo criteria [1], our scheme requires no special ancillary state preparation to achieve universality, as opposed to schemes such as magic state distillation. The concatenation scheme exploits the transversal properties of two different codes, combining them to provide a means to protect against low-weight arbitrary errors. We give the required properties of the error correcting codes to ensure universal fault-tolerance and discuss a particular example using the 7-qubit Steane and 15-qubit Reed-Muller codes. We believe that optimizing the codes used in such a scheme could provide a useful alternative to state distillation schemes that exhibit high overhead costs.