Quantum Computation as Geometry

Details Quantum Computation as Geometry Quantum Computation as Geometry

2006-03-19

arxiv.org/abs/quant-ph/0603161v2

M. A. Nielsen, M. Dowling, M. Gu, A. Doherty, Science 311, 1133 (2006)

Physics

Quantum Physics

13 Pages, 1 Figure

Scientific paper

10.1126/science.1121541

Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. 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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