Hamiltonian simulation with optimal sample complexity
Name
s41534-017-0013-7.pdf
Description
Published version
Size
505.93 KB
Format
Adobe PDF
Checksum (MD5)
d09101f418cf9ca07b1fb6f79177dd04
Author(s)
Kimmel, S
Lin, CYY
Low, GH
Ozols, M
Yoder, TJ
Date Issued
December 1, 2017
Journal
npj Quantum Information
Publisher
Springer Science and Business Media LLC
Citation
Kimmel, Shelby, et al. "Hamiltonian Simulation with Optimal Sample Complexity." Npj Quantum Information 3 (2017).
Version
Final published version
Abstract
© 2017 Author(s). 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1038/s41534-017-0013-7
