Holonomic Surface Codes for Fault-Tolerant Quantum Computation

TL;DR

This paper introduces holonomic surface codes that utilize quantum holonomy and auxiliary qubits in their ground state, offering a potentially more fault-tolerant method for quantum error correction.

Contribution

It proposes a novel holonomic surface code scheme using auxiliary qubits in ground states, differing from traditional methods that involve multilevel systems.

Findings

Holonomic gates are constructed via auxiliary qubits in ground states.

The approach maintains auxiliary qubits outside the surface code operation cycles.

Potential for improved fault-tolerance in quantum computation.

Abstract

Surface codes can protect quantum information stored in qubits from local errors as long as the per-operation error rate is below a certain threshold. Here we propose holonomic surface codes by harnessing the quantum holonomy of the system. In our scheme, the holonomic gates are built via auxiliary qubits rather than the auxiliary levels in multilevel systems used in conventional holonomic quantum computation. The key advantage of our approach is that the auxiliary qubits are in their ground state before and after each gate operation, so they are not involved in the operation cycles of surface codes. This provides an advantageous way to implement surface codes for fault-tolerant quantum computation.