# Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

@article{Berry2005EfficientQA, title={Efficient Quantum Algorithms for Simulating Sparse Hamiltonians}, author={Dominic W. Berry and Graeme Ahokas and Richard Cleve and Barry C. Sanders}, journal={Communications in Mathematical Physics}, year={2005}, volume={270}, pages={359-371} }

We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and ||H|| is bounded by a constant, we may select any positive integer k such that the simulation requires O((log*n)t1+1/2k) accesses to matrix entries of H. We also show that the temporal…

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