User:CharlesHBennett/sandbox

In quantum computing, the (quantum) threshold theorem (or quantum fault-tolerance theorem), versions of which (differing, e.g. in the methods of proof and error models assumed) have been proved by several groups of researchers in the late 1990s, states that a quantum computer with noise can simulate an ideal noiseless quantum computer, provided the level of noise is below a certain threshold. Practically, the Threshold Theorem implies that the error in quantum computers can be controlled as the number of qubits scales up, so that arbitrarily large quantum computations can be performed reliably. Fault tolerant quantum computation remains an active area of research in the 21st century, with continuing efforts to raise the noise threshold and lower the error-correction overhead to the point where a nontrivial quantum computation can be performed using available quantum hardware. The relevance of quantum threshold theorems has been criticized on the grounds that noise processes in actual hardware may be correlated in a way not covered by the noise models assumed in proving the theorems.