A Fault-Tolerant Scheme of Holonomic Quantum Computation on Stabilizer Codes with Robustness to Low-weight Thermal Noise

TL;DR

This paper introduces a fault-tolerant holonomic quantum computation scheme on stabilizer codes that leverages adiabatic processes and energy gaps to protect quantum information from thermal noise, enabling universal quantum gates.

Contribution

It establishes an equivalence between fault-tolerant circuits and adiabatic HQC, providing a systematic way to construct robust, universal quantum gates on stabilizer codes.

Findings

Fault-tolerant HQC can be systematically constructed from stabilizer code circuits.

Quantum information is protected by an energy gap unaffected by system size.

Universal quantum gates are implemented via adiabatic Hamiltonian deformation.

Abstract

We show an equivalence relation between fault-tolerant circuits for a stabilizer code and fault-tolerant adiabatic processes for holonomic quantum computation (HQC), in the case where quantum information is encoded in the degenerated ground space of the system Hamiltonian. By this equivalence, we can systematically construct a fault-tolerant HQC scheme, which can geometrically implement a universal set of encoded quantum gates by adiabatically deforming the system Hamiltonian. During this process, quantum information is protected from low weight thermal excitations by an energy gap that does not change with the problem size.