Efficient Discrete Approximations of Quantum Gates

Details Efficient Discrete Approximations of Quantum Gates Efficient Discrete Approximations of Quantum Gates

2001-11-06

arxiv.org/abs/quant-ph/0111031v3

J. Math. Phys. 43, 4445 (2002)

Physics

Quantum Physics

7 pages, no figures, v3 revised to correct major error in previous versions

Scientific paper

10.1063/1.1495899

Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that the number of gates required for precision epsilon is only polynomial in log 1/epsilon. Here we prove that using certain sets of base gates quantum compiling requires a string length that is linear in log 1/epsilon, a result which matches the lower bound from counting volume up to constant factor.

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