An Example of the Difference Between Quantum and Classical Random Walks
Quantum Information Processing
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
BOUNDS ON TAIL PROBABILITIES OF DISCRETE DISTRIBUTIONS
Probability in the Engineering and Informational Sciences
Hamiltonian simulation using linear combinations of unitary operations
Quantum Information & Computation
A universal quantum circuit scheme for finding complex eigenvalues
Quantum Information Processing
Gate-efficient discrete simulations of continuous-time quantum query algorithms
Quantum Information & Computation
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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 驴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.