## Abstract

We introduce antiferromagnetic quantum fluctuations into quantum annealing in addition to the conventional transverse-field term. We apply this method to the infinite-range ferromagnetic p-spin model, for which the conventional quantum annealing has been shown to have difficulties in finding the ground state efficiently due to a first-order transition. We study the phase diagram of this system both analytically and numerically. Using the static approximation, we find that there exists a quantum path to reach the final ground state from the trivial initial state that avoids first-order transitions for intermediate values of p. We also study numerically the energy gap between the ground state and the first excited state and find evidence for intermediate values of p for which the time complexity scales polynomially with the system size at a second-order transition point along the quantum path that avoids first-order transitions. These results suggest that quantum annealing would be able to solve this problem with intermediate values of p efficiently, in contrast to the case with only simple transverse-field fluctuations.

Original language | English |
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Article number | 051112 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 85 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2012 May 10 |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics