TY - JOUR

T1 - Quantum adiabatic algorithm and scaling of gaps at first-order quantum phase transitions

AU - Laumann, C. R.

AU - Moessner, R.

AU - Scardicchio, A.

AU - Sondhi, S. L.

PY - 2012/7/19

Y1 - 2012/7/19

N2 - 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.

AB - 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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U2 - 10.1103/PhysRevLett.109.030502

DO - 10.1103/PhysRevLett.109.030502

M3 - Article

C2 - 22861831

AN - SCOPUS:84864218390

SN - 0031-9007

VL - 109

JO - Physical review letters

JF - Physical review letters

IS - 3

M1 - 030502

ER -