Quantum memory based on concatenating surface codes and quantum Hamming codes

TL;DR

This paper explores concatenating surface codes with quantum Hamming codes to create a quantum memory with high error thresholds, low resource overhead, and efficient decoding, advancing fault-tolerant quantum computing.

Contribution

It introduces a novel concatenation of surface and quantum Hamming codes, showing improved error suppression and threshold estimates for quantum memory.

Findings

High error threshold achievable, close to surface code threshold.

Concatenated codes significantly reduce logical errors at intermediate scales.

Provides a pathway for small-scale fault-tolerant quantum circuits.

Abstract

Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming code is one of the potential candidates that allows for constant space overhead and efficient decoding. We study the concatenation of surface codes with quantum Hamming codes as a quantum memory, and estimate its error threshold, resource overhead and decoding time. A high error threshold is achieved, which can in principle be pushed up to the threshold of the surface code. Furthermore, the concatenated codes can suppress logical errors to a much lower level than the surface codes, under the assumption of comparable amount of resource overhead. The advantage in suppressing errors starts to show for a quantum memory of intermediate scale. Concatenating surface codes with quantum Hamming codes therefore provides a promising avenue to demonstrate small-scale fault-tolerant quantum circuits in the near future, and also paves a way for large-scale fault-tolerant quantum computation.