Higher Order Decompositions of Ordered Operator Exponentials

2008/12/04 by Nathan Wiebe, Dominic W. Berry, Peter Hoyer +1 · 3 citations
Mathematics · Physics and Astronomy · #math-ph #math.MP #msc:81Q15 #quant-ph

paper · pdf · doi:10.1088/1751-8113/43/6/065203

published as J. Phys. A: Math. Theor. 43, 065203 (2010) · 16 pages, 1 figure

Abstract

We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved.

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