Mitigating Temporal Fragility in the XY Surface Code

Abstract

An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomena of fragile temporal boundaries that arise during the standard logical state preparation and measurement protocols. To address this challenge we propose a new logical state preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure $O(\sqrt{n})$ high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault-configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard one in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement.

9 pages, 9 figures, v2

References in corpus (15)

• Suppressing quantum errors by scaling a surface code logical qubit
• Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits
• Building a fault-tolerant quantum computer using concatenated cat codes
• The XZZX Surface Code
• Fault-tolerant quantum computation against biased noise
• Fault-Tolerant Computing With Biased-Noise Superconducting Qubits
• Improved decoding of circuit noise and fragile boundaries of tailored surface codes
• Error Rates and Resource Overheads of Repetition Cat Qubits
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• Tailored XZZX codes for biased noise
• Clifford-deformed Surface Codes
• Conservation laws and quantum error correction: towards a generalised matching decoder
• Tailoring three-dimensional topological codes for biased noise
• The role of entropy in topological quantum error correction
• Construction of Bias-preserving Operations for Pair-cat Code

Cited by in corpus (1)

• Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers