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

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.

arXiv comment15 pages; 9 figures; 3 tables

References in corpus (25)

• Surface codes: Towards practical large-scale quantum computation
• Introduction to Quantum Noise, Measurement and Amplification
• Topological quantum memory
• Improved Simulation of Stabilizer Circuits
• Quantum Error Correction for Quantum Memories
• An introduction to quantum machine learning
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• Elucidating Reaction Mechanisms on Quantum Computers
• Quantum Error Correction for Beginners
• Topological Quantum Distillation
• Quantum computing for finance: overview and prospects
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Stim: a fast stabilizer circuit simulator
• Fidelity benchmarks for two-qubit gates in silicon
• Low-distance Surface Codes under Realistic Quantum Noise
• Quantum computing for energy systems optimization: Challenges and opportunities
• Fault-tolerant operation of a logical qubit in a diamond quantum processor
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• InAs-Al Hybrid Devices Passing the Topological Gap Protocol
• A fast, low-leakage, high-fidelity two-qubit gate for a programmable superconducting quantum computer
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Tensor-Network Simulations of the Surface Code under Realistic Noise
• Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code