01826nas a2200169 4500008004100000245005800041210005800099260001500157490000700172520131900179100001901498700002401517700002001541700001701561700002401578856005401602 2017 eng d00aHamiltonian Simulation with Optimal Sample Complexity0 aHamiltonian Simulation with Optimal Sample Complexity c2017/03/310 v133 aWe investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631--633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.

1 aKimmel, Shelby1 aLin, Cedric, Yen-Yu1 aLow, Guang, Hao1 aOzols, Maris1 aYoder, Theodore, J. uhttps://www.nature.com/articles/s41534-017-0013-7