Unitary Evolution on a Discrete Phase Space

Details Unitary Evolution on a Discrete Phase Space Unitary Evolution on a Discrete Phase Space

2005-10-06

arxiv.org/abs/hep-lat/0510043v1

PoS LAT2005 (2005) 260

Physics

High Energy Physics

High Energy Physics - Lattice

5 pages, contribution to Lattice 2005 (theoretical developments)

Scientific paper

We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the non-commutative 2-torus, T_{2^n}^2$ and thus is relevant for non-commutative field theories as well as theories of quantum space-time. The class of operators may also be useful for the efficient realization of new quantum algorithms.

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