Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions

C. R. Laumann, R. Moessner, A. Scardicchio, S. L. Sondhi

Research output: Contribution to journalArticle

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Abstract

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.

Original languageEnglish (US)
Article number030502
JournalPhysical review letters
Volume109
Issue number3
DOIs
StatePublished - Jul 19 2012

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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