Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions.
Phys Rev Lett
; 109(3): 030502, 2012 Jul 20.
Article
en En
| MEDLINE
| ID: mdl-22861831
Motivated by the quantum adiabatic algorithm (QAA), we consider the scaling of the Hamiltonian gap at quantum first-order transitions, generally expected to be exponentially small in the size of the system. However, we show that a quantum antiferromagnetic Ising chain in a staggered field can exhibit a first-order transition with only an algebraically small gap. In addition, we construct a simple classical translationally invariant one-dimensional Hamiltonian containing nearest-neighbor interactions only, which exhibits an exponential gap at a thermodynamic quantum first-order transition of essentially topological origin. This establishes that (i) the QAA can be successful even across first-order transitions but also that (ii) it can fail on exceedingly simple problems readily solved by inspection, or by classical annealing.
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01-internacional
Base de datos:
MEDLINE
Tipo de estudio:
Prognostic_studies
Idioma:
En
Revista:
Phys Rev Lett
Año:
2012
Tipo del documento:
Article
País de afiliación:
Estados Unidos
Pais de publicación:
Estados Unidos