Equation 32 · Error Correction Is the Whole Problem in Quantum Computing
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That constraint is a choice, not a law, and the alternatives are now concrete. Bravyi and colleagues at IBM presented a family of quantum low-density parity-check codes achieving an error threshold of 0.8\% for the standard circuit-based noise model, with a syndrome cycle requiring n ancillary qubits and a depth-7 circuit of nearest-neighbour CNOT gates on a degree-6 connectivity graph made of two edge-disjoint planar subgraphs [ 19 ] . Their worked example preserves 12 logical qubits for nearly one million syndrome cycles using 288 physical qubits at a physical error rate of 0.1\% , and they argue the surface code would need nearly 3000 physical qubits for the same suppression on 12 logical…
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That constraint is a choice, not a law, and the alternatives are now concrete. Bravyi and colleagues at IBM presented a family of quantum low-density parity-check codes achieving an error threshold of 0.8\% for the standard circuit-based noise model, with a syndrome cycle requiring n ancillary qubits and a depth-7 circuit of nearest-neighbour CNOT gates on a degree-6 connectivity graph made of two edge-disjoint planar subgraphs [ 19 ] . Their worked example preserves 12 logical qubits for nearly one million syndrome cycles using 288 physical qubits at a physical error rate of 0.1\% , and they argue the surface code would need nearly 3000 physical qubits for the same suppression on 12 logical qubits. The comparison is an engineering estimate under a stated noise model, not a demonstrated device; but it shows that the overhead multiplier is a design variable rather than a constant.
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