TY - JOUR
T1 - Hamiltonian Simulation with Optimal Sample Complexity
JF - npj Quantum Information
Y1 - 2017
A1 - Shelby Kimmel
A1 - Cedric Yen-Yu Lin
A1 - Guang Hao Low
A1 - Maris Ozols
A1 - Theodore J. Yoder
AB - We 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.

VL - 13
UR - https://www.nature.com/articles/s41534-017-0013-7
CP - 3
U5 - 10.1038/s41534-017-0013-7
ER -