Improved Pairwise Measurement-Based Surface Code

Abstract

We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements and three auxiliary qubits per plaquette. This realization gains substantial advantages over prior pairwise measurement-based realizations of the surface code. It has a short operation period of 4 steps and our performance analysis for a standard circuit noise model yields a high fault-tolerance threshold of approximately $0.66\%$. The syndrome extraction circuits avoid bidirectional hook errors, so we can achieve full code distance by choosing appropriate boundary conditions. We also construct variants of the syndrome extraction circuits that entirely prevent hook errors, at the cost of larger circuit depth. This achieves full distance regardless of boundary conditions, with only a modest decrease in the threshold. Furthermore, we propose an efficient strategy for dealing with dead components (qubits and measurements) in our surface code realization, which can be adopted more generally for other surface code realizations. This new surface code realization is highly optimized for Majorana-based hardware, accounting for constraints imposed by layouts and the implementation of measurements, making it competitive with the recently proposed Floquet codes.

41 pages, 32 figures; v2: computer parsable description of circuits added in ancillary files, corrected discussion of dead component strategy for interleaved circuits, minor edits throughout for improved clarity

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Cited by in corpus (5)

• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
• LUCI in the Surface Code with Dropouts
• Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements
• Logical Error Rates for the Surface Code Under a Mixed Coherent and Stochastic Circuit-Level Noise Model Inspired by Trapped Ions
• Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes