On the efficiency of quantum algorithms for Hamiltonian simulation

On the efficiency of quantum algorithms for Hamiltonian simulation We study algorithms simulating a system evolving with Hamiltonian $${H = \sum_{j=1}^m H_j}$$ , where each of the H j , j = 1, . . . ,m, can be simulated efficiently. We are interested in the cost for approximating $${e^{-iHt}, t \in \mathbb{R}}$$ , with error $${\varepsilon}$$ . We consider algorithms based on high order splitting formulas that play an important role in quantum Hamiltonian simulation. These formulas approximate e −iHt by a product of exponentials involving the H j , j = 1, . . . ,m. We obtain an upper bound for the number of required exponentials. Moreover, we derive the order of the optimal splitting method that minimizes our upper bound. We show significant speedups relative to previously known results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On the efficiency of quantum algorithms for Hamiltonian simulation

, Volume 11 (2) – Jul 28, 2011
21 pages

/lp/springer_journal/on-the-efficiency-of-quantum-algorithms-for-hamiltonian-simulation-OQjI3cfqtr
Publisher
Springer US
Subject
Physics; Physics, general; Theoretical, Mathematical and Computational Physics; Quantum Physics; Computer Science, general; Mathematics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0263-9
Publisher site
See Article on Publisher Site

Abstract

We study algorithms simulating a system evolving with Hamiltonian $${H = \sum_{j=1}^m H_j}$$ , where each of the H j , j = 1, . . . ,m, can be simulated efficiently. We are interested in the cost for approximating $${e^{-iHt}, t \in \mathbb{R}}$$ , with error $${\varepsilon}$$ . We consider algorithms based on high order splitting formulas that play an important role in quantum Hamiltonian simulation. These formulas approximate e −iHt by a product of exponentials involving the H j , j = 1, . . . ,m. We obtain an upper bound for the number of required exponentials. Moreover, we derive the order of the optimal splitting method that minimizes our upper bound. We show significant speedups relative to previously known results.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 28, 2011

References

• An example of the difference between quantum and classical random walks
Childs, A.; Farhi, E.; Gutmann, S.
• General theory of fractal path integrals with application to many-body theories and statistical physics
Suzuki, M.

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