title: Quantum state restoration and single-copy tomography for ground states of Hamiltonians.
abstract: 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.
authors.affiliation: Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Edward
authors.initials: E
authors.lastname: Farhi
authors.forename: David
authors.initials: D
authors.lastname: Gosset
authors.forename: Avinatan
authors.initials: A
authors.lastname: Hassidim
authors.forename: Andrew
authors.initials: A
authors.lastname: Lutomirski
authors.forename: Daniel
authors.initials: D
authors.lastname: Nagaj
authors.forename: Peter
authors.initials: P
authors.lastname: Shor