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Hamiltonian simulation with optimal sample complexity

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Kimmel, S 
Lin, CYY 
Low, GH 
Yoder, TJ 


© 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.



quant-ph, quant-ph

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npj Quantum Information

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Springer Science and Business Media LLC
European Commission (600700)
S.K. and C.Y.L. are funded by the Department of Defense. G.H.L. is funded by the NSF CCR and the ARO quantum computing projects. M.O. acknowledges Leverhulme Trust Early Career Fellowship (ECF-2015-256) and European Union project QALGO (Grant Agreement No. 600700) for financial support. T.J.Y. thanks the DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. The authors are grateful to the University of Maryland Libraries’ Open Access Publishing Fund and the Massachusetts Institute of Technology Open Access Publishing Fund for partial funding for open access.