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fault-tolerant-quantum
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The threshold theorem says error correction works if physical error rates are low enough. In 2024 a surface code crossed that threshold, with logical errors halving at each step up in code size. A machine large enough to run Shor's algorithm on real key sizes needs roughly a million physical qubits or much better codes.
Closed 2024, Google's Willow chip shows error rates falling as code size grows.
Related problems
- The original curation links this problem to Post-quantum cryptography; the argument for the link has not been written yet.