title: Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions.
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.
authors.affiliation: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: C R
authors.initials: CR
authors.lastname: Laumann
authors.forename: R
authors.initials: R
authors.lastname: Moessner
authors.forename: A
authors.initials: A
authors.lastname: Scardicchio
authors.forename: S L
authors.initials: SL
authors.lastname: Sondhi