Journal
QUANTUM INFORMATION PROCESSING
Volume 11, Issue 2, Pages 541-561Publisher
SPRINGER
DOI: 10.1007/s11128-011-0263-9
Keywords
Quantum simulation; Complexity; Hamiltonian evolution; Splitting methods; Order of convergence
Funding
- National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0914345] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1215987] Funding Source: National Science Foundation
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We study algorithms simulating a system evolving with Hamiltonian H = Sigma(m)(j=1) 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 is an element of R, with error epsilon. 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.
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