Abstract
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)t 1+1/2k) accesses to matrix entries of H. We also show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.
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Communicated by M.B. Ruskai
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Berry, D.W., Ahokas, G., Cleve, R. et al. Efficient Quantum Algorithms for Simulating Sparse Hamiltonians. Commun. Math. Phys. 270, 359–371 (2007). https://doi.org/10.1007/s00220-006-0150-x
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DOI: https://doi.org/10.1007/s00220-006-0150-x