Andrew Steane

Multiple-particle interference and quantum error correction

The concept of multiple-particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer. Methods of error correction in the quantum regime are presented, and their limitations assessed. A quantum channel can recover from arbitrary decoherence of x qubits if K bits of quantum information are encoded using n quantum bits, where K /n can be greater than 1 - 2H(2x/n), but must be less than 1 - 2H(2x/n) This implies exponential reduction of decoherence with only a polynomial increase in the computing resources required. Therefore quantum computation can be made free of errors in the presence of physically realistic levels of decoherence. The methods also allow isolation of quantum communication from noise and evesdropping (quantum privacy amplification).

Simple quantum error correcting codes

Methods of finding good quantum error-correcting codes are discussed, and many example codes are presented. The recipe

Overhead and noise threshold of fault-tolerant quantum error correction

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The ion trap quantum information processor

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Active stabilization, quantum computation and quantum state synthesis

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Efficient fault-tolerant quantum computing

, where

Quantum Reed-Muller codes

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High-Fidelity Readout of Trapped-Ion Qubits

and

Isotope-selective photoionization for calcium ion trapping

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Speed of ion-trap quantum-information processors

are classical codes, is used to obtain codes for up to 16 information quantum bits (qubits) with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing