D. Gottesman, \Theory of fault-tolerant quantum computation," Physical Review A, 57(1998), pp. 127-137.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for all the results in this paper. The technique is known as the hybrid argument among cryptographers. Using quantum error correction techniques, faulttolerant quantum circuits can be created that are resilient to constant error in the rotation gates, independent of the size of the circuit [AB, Go, KLZ]. How does one explain the power of quantum computation The dimension of the Hilbert space associated with an n qubit system is 2 n . Therefore, just describing the state of this system requires 2 n complex numbers. Moreover, Nature must update the 2 n complex numbers to evolve the system ....

Gottesman, D., "A theory of fault-tolerant quantum computation", quant-ph/9702029.

....to a constant transmission rate which is non zero. This is analogous to Shannon s result from noisy classical communication[171] Many different examples of quantum error correcting codes followed[181, 134, 59, 131, 165, 138] and a group theoretical framework for most quantum codes was established[55, 54, 106]. Resilient quantum computation is more complicated than simply protecting quantum information which is sent through a noisy quantum channel. Naturally, to protect the information we would compute on encoded states. There are two problems with noisy computation on encoded states. The first is ....

....found by Bennett et al.[35] and by Laflamme et.al. 134] If we restrict the error, e.g. only bit flips or only phase flips occur than one qubit can be encoded on less than 5 qubits. The theory of quantum error correcting codes has further developed. A group theoretical structure was discovered [54, 55, 105, 106, 129, 175], which most of the known quantum error correcting codes obey. Codes that obey this structure are called stabilizer codes[105, 106] and their group theoretical structure gives a recipe for constructing more quantum codes. Quantum codes are used for purposes of quantum communication with noisy ....

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Gottesman D A theory of fault-tolerant quantum computation, in Phys. Rev. A,57 127--137

....restriction. iii) DiVincenzo and Shor [30] have shown how to correct errors in additive codes even when using imperfect computational gates. The techniques of Shor [66] for performing computations on encoded qubits using imperfect gates have been extended to general additive codes by Gottesman [37]. However, the most efficient methods currently known for fault tolerant computation [2] 44] 48] 75] use only Calderbank Shor Steane codes (cf. Theorem 9) iv) It turns out that the proofs of the lower bounds on the capacity of quantum channels given in Bennett et al. 4] 5] and ....

D. Gottesman, "A theory of fault-tolerant quantum computation," LANL e-print quantph /9702029.

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D. Gottesman, \Theory of fault-tolerant quantum computation," Physical Review A, 57(1998), pp. 127-137.

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D. Gottesman. Theory of fault-tolerant quantum computation. Phys. Rev. A, 57:1, January 1998.

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Gottesman D A theory of fault-tolerant quantum computation, in Phys. Rev. A,57 127--137

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Gottesman D A theory of fault-tolerant quantum computation, in Phys. Rev. A,57 127-137

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Gottesman, D. 1997a A theory of fault-tolerant quantum computation. (Online preprint quantph /9702029.) Gottesman, D. 1997b Stabilizer codes and quantum error correction. Ph.D. thesis, California Institute of Technology.

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