Learning a local Hamiltonian from local measurements
| Autor: | Netanel H. Lindner, Eyal Bairey, Itai Arad |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Physics
Quantum Physics Strongly Correlated Electrons (cond-mat.str-el) FOS: Physical sciences General Physics and Astronomy Observable Gibbs state 01 natural sciences symbols.namesake Condensed Matter - Strongly Correlated Electrons 0103 physical sciences Quantum system symbols Statistical physics Quantum Physics (quant-ph) 010306 general physics Spatial domain Hamiltonian (quantum mechanics) Finite set Scaling Eigenvalues and eigenvectors |
| Popis: | Recovering an unknown Hamiltonian from measurements is an increasingly important task for certification of noisy quantum devices and simulators. Recent works have succeeded in recovering the Hamiltonian of an isolated quantum system with local interactions from long-ranged correlators of a single eigenstate. Here, we show that such Hamiltonians can be recovered from local observables alone, using computational and measurement resources scaling linearly with the system size. In fact, to recover the Hamiltonian acting on each finite spatial domain, only observables within that domain are required. The observables can be measured in a Gibbs state as well as a single eigenstate; furthermore, they can be measured in a state evolved by the Hamiltonian for a long time, allowing to recover a large family of time-dependent Hamiltonians. We derive an estimate for the statistical recovery error due to approximation of expectation values using a finite number of samples, which agrees well with numerical simulations. 8 pages, 6 figures |
| Databáze: | OpenAIRE |
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