Synopsis:
          Relaxing the requirements for scalable quantum computing

Fibonacci scheme for fault-tolerant quantum computation

Panos Aliferis and John Preskill

Published January 30, 2009

To carry out a long calculation on a quantum computer, some form of error correction is necessary. If the error probability of each logical operation is below what is called the “fault-tolerance” threshold, an error correction procedure will actually remove more errors than it introduces, and the overall failure rate can then be made arbitrarily small. The fault-tolerant threshold is typically quoted as $10-4$ or $10-5$. This is an extremely stringent tolerance, since it says failure must occur in less than $0.01%$ of the operations.

A few years ago, Emanuel Knill at NIST in Boulder, Colorado, introduced a different approach to error correction that relied primarily on preparing and verifying a (possibly very large) number of auxiliary qubits, called ancillas, in special states that could be used to diagnose the errors in the computer’s qubits, and replace them if necessary. The most attractive feature of these codes was their large error tolerance, which, based on numerical simulations, Knill estimated to be of the order of $1%$.

In a paper appearing in Physical Review A, Panos Aliferis, who is at the IBM Watson Research Center, and John Preskill of the California Institute of Technology, rigorously establish a lower bound for the fault-tolerance threshold for one of Knill’s constructions that has relatively small overhead requirements. Their results indicate that fault-tolerant computation should definitely be possible with this scheme, if the error probability per logical operation does not exceed $0.1%$. While lower than Knill’s original numerical estimate, this analytical bound is still at least one order of magnitude larger than was thought possible with other codes and it makes the prospect of scalable quantum computing appear that much more feasible. – Julio Gea-Banacloche

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