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In quantum computing, the quantum threshold theorem (or quantum fault-tolerance theorem) 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. This shows that quantum computers can be made fault-tolerant, as an analogue to von Neumann's threshold theorem for classical computation. This result was proven (for various error models) by the groups of Dorit Aharanov and Michael Ben-Or; , Raymond Laflamme, and Wojciech Zurek; and Alexei Kitaev independently. These results built off a paper of Peter Shor, which proved a weaker version of the threshold theorem.