TY - JOUR

T1 - Quantum state restoration and single-copy tomography for ground states of Hamiltonians

AU - Farhi, Edward

AU - Gosset, David

AU - Hassidim, Avinatan

AU - Lutomirski, Andrew

AU - Nagaj, Daniel

AU - Shor, Peter

PY - 2010/11/5

Y1 - 2010/11/5

N2 - Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties of its ground state, even though in principle all the information about the ground state is encoded in the Hamiltonian. We show in this Letter that if you know the Hamiltonian of a system and have a single copy of its ground state, you can use a quantum computer to efficiently compute its local properties. Specifically, in this scenario, we give efficient algorithms that copy small subsystems of the state and estimate the full statistics of any local measurement.

AB - Given a single copy of an unknown quantum state, the no-cloning theorem limits the amount of information that can be extracted from it. Given a gapped Hamiltonian, in most situations it is impractical to compute properties of its ground state, even though in principle all the information about the ground state is encoded in the Hamiltonian. We show in this Letter that if you know the Hamiltonian of a system and have a single copy of its ground state, you can use a quantum computer to efficiently compute its local properties. Specifically, in this scenario, we give efficient algorithms that copy small subsystems of the state and estimate the full statistics of any local measurement.

UR - http://www.scopus.com/inward/record.url?scp=78149314913&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.105.190503

DO - 10.1103/PhysRevLett.105.190503

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

C2 - 21231156

AN - SCOPUS:78149314913

SN - 0031-9007

VL - 105

JO - Physical Review Letters

JF - Physical Review Letters

IS - 19

M1 - 190503

ER -