A major hurdle in building a quantum computer is overcoming noise, since quantum superpositions are fragile. Developed over the last couple of years, schemes for achieving fault tolerance based on error detection, rather than error correction, appear to tolerate as much as 3–6% noise per gate—an order of magnitude higher than previous procedures. However, proof techniques could not show that these promising fault-tolerance schemes tolerated any noise at all; the distribution of errors in the quantum state has correlations that conceivably could grow out of control. With an analysis based on decomposing complicated probability distributions into mixtures of simpler ones, we rigorously prove the existence of constant tolerable noise rates (“noise thresholds”) for error-detection-based schemes. Numerical calculations indicate that the actual noise threshold this method yields is lower-bounded by 0.1% noise per gate.
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