Title | Exact sampling hardness of Ising spin models |

Publication Type | Journal Article |

Year of Publication | 2017 |

Authors | Fefferman, B, Foss-Feig, M, Gorshkov, AV |

Journal | Physical Review A |

Volume | 96 |

Issue | 3 |

Pages | 032324 |

Date Published | 2017/09/14 |

Abstract | We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of |

URL | https://arxiv.org/abs/1701.03167 |

DOI | 10.1103/PhysRevA.96.032324 |