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Efficient quantum algorithms for simulating sparse Hamiltonians

Dominic W. Berry·Graeme Ahokas·Richard Cleve·Barry C. Sanders
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Abstract

We present an efficient quantum algorithm for simulating the evolution of a sparse Hamiltonian H for 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)t^{1+1/2k}) accesses to matrix entries of H. We show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.

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Dominic W. Berry, Graeme Ahokas, Richard Cleve, Barry C. Sanders. 2006-02-08. Efficient quantum algorithms for simulating sparse Hamiltonians. https://doi.org/10.1007/s00220-006-0150-x

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