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On Quantum Algorithms

Richard Cleve, ARTUR K. EKERT, Henderson, L, Chiara Macchiavello, Michele Mosca

Published Jan 1, 1998• 21 citations
OpenAlex

Abstract

Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle) interferometers. We show how most known quantum algorithms, including quantum algorithms for factorising and counting, may be cast in this manner. Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms.

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Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle) interferometers. We show how most known quantum algorithms, including quantum algorithms for factorising and counting, may be cast in this manner. Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms.
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle) interferometers. We show how most known quantum algorithms, including quantum algorithms for factorising and counting, may be cast in this manner. Quantum searching is described as inducing a desired relative phase between two eigenvectors to yield constructive interference on the sought elements and destructive interference on the remaining terms.
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum computation is viewed as multiparticle interference. We use this approach to review (and improve) some of the existing quantum algorithms and to show how they are related to different instances of quantum phase estimation. We provide an explicit algorithm for generating any prescribed interference pattern with an arbitrary precision.
A quantum computer is a device capable of performing computational tasks that depend on characteristically quantum mechanical effects, in particular coherent quantum superposition. Such devices can efficiently perform classes of computation (e.g. factorisation) which are believed to be intractable on any classical computer. This makes it highly desirable to construct such devices. In this paper, we address the last remaining theoretical obstacle to such a construction, namely the problem of stability or error correction. This problem is more substantial in quantum computation than in classical computation because of the delicate nature of the interference phenomena on which quantum computation depends. We present a new, purely quantum mechanical method of error correction, which has no classical analogue, but can serve to stabilise coherent quantum computations. Like the classical methods, it utilises redundancy, but it does not depend on measuring intermediate results of the computation.>
Quantum interference [1] is a cornerstone phenomenon in quantum mechanics, arising when the probability amplitudes associated with different quantum pathways combine, leading to patterns of constructive or destructive interference. Coherent control [2] leverages this phenomenon by using external optical or electromagnetic pulses to steer the outcome of quantum interference. Through careful adjustment of the phase, amplitude, and frequency of these external pulses, it is possible to selectively enhance or suppress specific quantum transitions. This selective manipulation enables researchers to direct quantum pathways toward desired outcomes, making coherent control a powerful tool for exploring and utilizing quantum systems.