Efficient Quantum Algorithms for Simulating Sparse Hamiltonians - Berry, Dominic W.; Ahokas, Graeme; Cleve, Richard; Sanders, Barry C. (Communications in mathematical physics, 2007)
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 scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.