Prof Andrew Steane

Abstract:

Quantum computing - the processing of information according to the fundamental laws of physics - offers a means to solve efficiently a small but significant set of classically intractable problems. Quantum computers are based on the controlled manipulation of entangled quantum states, which are extremely sensitive to noise and imprecision; active correction of errors must therefore be implemented without causing loss of coherence. Quantum error-correction theory has made great progress in this regard, by predicting error-correcting 'codeword' quantum states. But the coding is inefficient and requires many quantum bits, which results in physically unwieldy fault- tolerant quantum circuits. Here I report a general technique for circumventing the trade-off between the achieved noise tolerance and the scale-up in computer size that is required to realize the error correction. I adapt the recovery operation (the process by which noise is suppressed through error detection and correction) to simultaneously correct errors and perform a useful measurement that drives the computation. The result is that a quantum computer need be only an order of magnitude larger than the logic device contained within it. For example, the physical scale-up factor required to factorize a thousand-digit number is reduced from 1,500 to 22, while preserving the original tolerated gate error rate (10-5) and memory noise per bit (10-7). The difficulty of realizing a useful quantum computer is therefore significantly reduced.

Abstract:

It is shown that a classical error correcting code C = [n, k, d] which contains its dual, C⊥ ⊆ C, and which can be enlarged to C′ = [n, k′ > k + 1, d′], can be converted into a quantum code of parameters [[n, k+k′ -n, min (d, [3d′/2])]]. This is a generalization of a previous construction, it enables many new codes of good efficiency to be discovered. Examples based on classical Bose-Chaudhuri-Hocquenghem (BCH) codes are discussed. © 1999 IEEE.

Abstract:

In a previous study, Gottesman found an infinite set of optimal single-error-correcting quantum codes. This report presents a set of quantum codes of which Gottesman's is a subset. The codes are obtained by combining classical Reed-Muller codes.