Quantum threshold theorem


In quantum computing, the threshold theorem, proved by Michael Ben-Or and Dorit Aharonov, states that a quantum computer with a physical error rate below a certain threshold can, through application of quantum error correction schemes, suppress the logical error rate to arbitrarily low levels. Current estimates put the threshold for the surface code on the order of 1%, though estimates range widely and are difficult to calculate due to the exponential difficulty of simulating large quantum systems. At a 0.1% probability of a depolarizing error, the surface code would require approximately 1,000-10,000 physical qubits per logical data qubit, though more pathological error types could change this figure drastically.
According to quantum information theorist Scott Aaronson:
"The entire content of the Threshold Theorem is that you're correcting errors faster than they're created. That's the whole point, and the whole non-trivial thing that the theorem shows. That's the problem it solves."

Books

From of the American Physical Society:
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