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S. Venegas-Andraca, J. Gómez-Muñoz, M. Lanzagorta, J. Uhlmann (2013)
Quantum Simulators
I. Kassal, S. Jordan, P. Love, M. Mohseni, A. Aspuru‐Guzik (2008)
Polynomial-time quantum algorithm for the simulation of chemical dynamicsProceedings of the National Academy of Sciences, 105
Masuo Suzuki (1991)
General theory of fractal path integrals with applications to many‐body theories and statistical physicsJournal of Mathematical Physics, 32
I. Buluta, F. Nori (2009)
Quantum SimulatorsScience, 326
E. Farhi, J. Goldstone, S. Gutmann (2007)
A Quantum Algorithm for the Hamiltonian NAND TreeTheory Comput., 4
Nikolay Raychev, I. Chuang (2010)
Quantum Computation and Quantum Information: Bibliography
Masuo Suzuki (1990)
Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulationsPhysics Letters A, 146
N. Wiebe, D. Berry, P. Høyer, B. Sanders (2008)
Higher order decompositions of ordered operator exponentialsJournal of Physics A: Mathematical and Theoretical, 43
S. Lloyd (1996)
Universal Quantum SimulatorsScience, 273
Christof Zalka (1996)
Efficient Simulation of Quantum Systems by Quantum ComputersProtein Science, 46
Andrew Childs (2008)
Universal computation by quantum walk.Physical review letters, 102 18
D. Aharonov, A. Ta-Shma (2003)
Adiabatic quantum state generation and statistical zero knowledge
B. Klar (2000)
BOUNDS ON TAIL PROBABILITIES OF DISCRETE DISTRIBUTIONSProbability in the Engineering and Informational Sciences, 14
Andrew Childs (2008)
On the Relationship Between Continuous- and Discrete-Time Quantum WalkCommunications in Mathematical Physics, 294
M. Abramowitz, A. Stegun (1972)
Handbook of Mathematical Functions
R. Feynman (1999)
Simulating physics with computersInternational Journal of Theoretical Physics, 21
Christof Zalka (1998)
Simulating quantum systems on a quantum computerProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454
(2009)
Science
Andrew Childs, E. Farhi, S. Gutmann (2001)
An Example of the Difference Between Quantum and Classical Random WalksQuantum Information Processing, 1
E. Farhi, J. Goldstone, S. Gutmann, M. Sipser (2000)
Quantum Computation by Adiabatic EvolutionarXiv: Quantum Physics
D. Berry, Graeme Ahokas, R. Cleve, B. Sanders (2005)
Efficient Quantum Algorithms for Simulating Sparse HamiltoniansCommunications in Mathematical Physics, 270
C. Zalka (1998)
Efficient simulation of quantum systems by quantum computersFortschritte der Physik, 46
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.
Quantum Information Processing – Springer Journals
Published: Jul 28, 2011
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