Quantum State Restoration and Single-Copy Tomography for Ground States of Hamiltonians

• Main Authors: Farhi, Edward (Contributor), Gosset, David Nicholas (Contributor), Hassidim, Avinatan (Contributor), Lutomirski, Andrew Michael (Contributor), Nagaj, Daniel (Author), Shor, Peter W. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Center for Theoretical Physics (Contributor), Massachusetts Institute of Technology. Department of Mathematics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor), Shor, Peter (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2011-06-15T14:51:15Z.
• Subjects: Article
• Online Access: Get fulltext

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.
United States. Dept. of Energy (No. DE-FG02-94ER40818)
W. M. Keck Foundation Center for Extreme Quantum Information Theory
United States. Army Research Office (Grant No. W911NF-09-1-0438)
National Science Foundation (U.S.) (Grant No. CCF-0829421)
Natural Sciences and Engineering Research Council of Canada
Microsoft Research
European Union (Project OP CE QUTE ITMS NFP 26240120009)
Slovak Research and Development Agency (Contract No. APVV LPP-0430-09)