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Quantum Computing: From Bragg Reflections to Decoherence Estimates

Published online by Cambridge University Press:  10 February 2011

Peter Pfeifer  and
Chen Hou
Peter Pfeifer
Affiliation:
Department of Physics, University of Missouri, Columbia, MO 65211, U.S.A.
Chen Hou
Affiliation:
Department of Physics, University of Missouri, Columbia, MO 65211, U.S.A.
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Abstract

We give an exposition of the principles of quantum computing (logic gates, exponential parallelism from polynomial hardware, fast quantum algorithms, quantum error correction, hardware requirements, and experimental milestones). A compact description of the quantum Fourier transform to find the period of a function—the key step in Shor's factoring algorithm—illustrates how parallel state evolution along many classical computational paths produces fast algorithms by constructive interference similar to Bragg reflections in x-ray crystallography. On the hardware side, we present a new method to estimate critical time scales for the operation of a quantum computer. We derive a universal upper bound on the probability of a computation to fail due to decoherence (entanglement of the computer with the environment), as a function of time. The bound is parameter-free, requiring only the interaction between the computer and the environment, and the time-evolving state in the absence of any interaction. For a simple model we find that the bound performs well and decoherence is small when the energy of the computer state is large compared to the interaction energy. This supports a recent estimate of minimum energy requirements for quantum computation.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 746: Symposia Q/R – Magnetoelectronics-Novel Magnetic Phenomena in Nanostructures – Advanced Characterization of Artificially Structured Magnetic Materials , 2002 , Q8.5
Copyright
Copyright © Materials Research Society 2003

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References

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