Quantum Computation as Geometry

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path betwe...

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Bibliographic Details
Published inScience (American Association for the Advancement of Science) Vol. 311; no. 5764; pp. 1133 - 1135
Main Authors Nielsen, Michael A, Dowling, Mark R, Gu, Mile, Doherty, Andrew C
Format Journal Article
LanguageEnglish
Published Washington, DC American Association for the Advancement of Science 24.02.2006
The American Association for the Advancement of Science
Subjects
Algorithms
Approximation
Classical and quantum physics: mechanics and fields
Computers
Cost control
Cost functions
Exact sciences and technology
Geometry
Physics
Polynomials
Problem solving
Quantum computation
Quantum computers
Quantum information
Quantum theory
Tangents
Unit costs
Geometry
Quantum algorithm
Quantum computing
Riemann space
Quantum computer
Quantum circuits
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Summary:Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.
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ISSN:0036-8075
1095-9203
DOI:10.1126/science.1121541