Union-find decoder for surface code achieves finite threshold under circuit-level stochastic errors with quasi-polylog parallel runtime bound.
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Logical error rates in [[7,1,3]] and [[12,2,4]] codes are suppressed 9.8-800 times below physical rates on trapped-ion hardware, with repeated correction cycles approaching the error rate of two physical CNOTs.
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Proof of a finite threshold for the union-find decoder
Union-find decoder for surface code achieves finite threshold under circuit-level stochastic errors with quasi-polylog parallel runtime bound.
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Demonstration of logical qubits and repeated error correction with better-than-physical error rates
Logical error rates in [[7,1,3]] and [[12,2,4]] codes are suppressed 9.8-800 times below physical rates on trapped-ion hardware, with repeated correction cycles approaching the error rate of two physical CNOTs.