Q-Pandora Unboxed: Characterizing Noise Resilience of Quantum Error Correction Codes

TL;DR

This study analyzes the noise resilience of rotated and unrotated surface codes in quantum error correction, highlighting their thresholds, resource demands, and the importance of tailoring codes to hardware noise models for reliable quantum computing.

Contribution

It provides a comprehensive simulation-based comparison of surface codes under various noise models, emphasizing the importance of code selection and parameter tuning for practical quantum error correction.

Findings

Rotated surface codes outperform unrotated ones in noise thresholds.

Higher code distances and rounds improve error correction but increase qubit overhead.

Surface codes show advantages over current quantum hardware error rates.

Abstract

Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select optimal codes. This paper conducts a comprehensive study analyzing two QECCs - rotated and unrotated surface codes - under different error types and noise models using simulations. Among them, rotated surface codes perform best with higher thresholds attributed to simplicity and lower qubit overhead. The noise threshold, or the point at which QECCs become ineffective, surpasses the error rate found in contemporary quantum processors. When confronting quantum hardware where a specific error or noise model is dominant, a discernible hierarchy emerges for surface code implementation in terms of resource demand. This ordering is consistently observed across unrotated, and rotated surface codes. Our noise model analysis ranks the code-capacity model as the most pessimistic and circuit-level model as the most realistic. The study maps error thresholds, revealing surface code's advantage over modern quantum processors. It also shows higher code distances and rounds consistently improve performance. However, excessive distances needlessly increase qubit overhead. By matching target logical error rates and feasible number of qubits to optimal surface code parameters, our study demonstrates the necessity of tailoring these codes to balance reliability and qubit resources. Conclusively, we underscore the significance of addressing the notable challenges associated with surface code overheads and qubit improvements.