Scheme for fault-tolerant holonomic computation on stabilizer codes

TL;DR

This paper presents a scalable fault-tolerant holonomic quantum computation scheme on stabilizer codes, leveraging geometric robustness and error correction to enhance quantum computing reliability.

Contribution

It generalizes previous work by demonstrating a scalable, fault-tolerant HQC scheme compatible with stabilizer codes and practical Hamiltonian implementations.

Findings

HQC can be implemented on stabilizer codes with error resilience.

The scheme is scalable and compatible with error correction.

Hamiltonians of weight 2 and 3 suffice for implementation.

Abstract

This paper generalizes and expands upon the work [Phys. Rev. Lett. 102, 070502 (2009)] where we introduced a scheme for fault-tolerant holonomic quantum computation (HQC) on stabilizer codes. HQC is an all-geometric strategy based on non-Abelian adiabatic holonomies, which is known to be robust against various types of errors in the control parameters. The scheme we present shows that HQC is a scalable method of computation, and opens the possibility for combining the benefits of error correction with the inherent resilience of the holonomic approach. We show that with the Bacon-Shor code the scheme can be implemented using Hamiltonian operators of weight 2 and 3.