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

Edward Farhi, David Gosset, Avinatan Hassidim, Andrew Lutomirski, Daniel Nagaj, Peter Shor

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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.

Original languageEnglish
Article number190503
JournalPhysical Review Letters
Volume105
Issue number19
DOIs
StatePublished - 5 Nov 2010
Externally publishedYes

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