Fault-tolerant Compass Codes

Abstract

We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achieved by direct measurements of the stabilizers. By simulating our fault-tolerant scheme under biased noise, we show the possibility of optimizing the performance of the surface code by stretching the bulk stabilizer geometry. To decode the syndrome efficiently and accurately, we generalize the union-find decoder to biased noise models. Our decoder obtains a $0.83\%$ threshold value for the surface code in quadratic time complexity.

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Cited by in corpus (12)

• Building a fault-tolerant quantum computer using concatenated cat codes
• Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
• Fault-Tolerant Weighted Union-Find Decoding on the Toric Code
• Combined Dissipative and Hamiltonian Confinement of Cat Qubits
• Optimization of the surface code design for Majorana-based qubits
• High-Fidelity Magic-State Preparation with a Biased-Noise Architecture
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Alibaba Cloud Quantum Development Platform: Surface Code Simulations with Crosstalk
• Surface Code with Imperfect Erasure Checks
• Optimization tools for distance-preserving flag fault-tolerant error correction
• Mitigating Temporal Fragility in the XY Surface Code
• Between Shor and Steane: A unifying construction for measuring error syndromes