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2008

Higher Order Decompositions of Ordered Operator Exponentials

Wiebe, Nathan, Berry, Dominic W., Hoyer, Peter et al.

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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.

Higher Order Decompositions of Ordered Operator Exponentials · Around

Built on

M. Suzuki, “Fractal decomposition of exponential operators with applications to many-body theories and monte carlo simulations”, Phys. Lett. A. 146
1990
Earlier work this paper cites.
H. Huyghebaert, and H. De Raedt “Product formula methods for time dependent Schrödinger problems”, J. Phys. A: Math. Gen. 23
1990
Earlier work this paper cites.
M. Suzuki, “General theory of fractal path integrals with applications to many-body theories and statistical physics”, J. Math. Phys. 32
1991
Earlier work this paper cites.

Similar

M. Suzuki, “General decomposition theory of ordered exponentials”, Proc. Japan Acad. 69
1993
Cited alongside, same era.
M. Suzuki, “Convergence of general decompositions of exponential operators”, Comm. Math. Phys 163
Original
1994
Cited alongside, same era.
S. Chin, “Symplectic integrators from composite operator factorizations”. Phys. Lett. A. 226
1997
Cited alongside, same era.

Then

M. Nielsen and I. Chuang, “Quantum computation and quantum Information”. Cambridge University Press (2000)
2000
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A. Das and B. Chakrabarti (Eds.), Quantum Annealing and Related Optimization Methods
2005
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D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, “Efficient quantum algorithms for simulating sparse Hamiltonians”, Comm. Math. Phys. 270
2007
Later among the works it cites.

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