Stoquastic ground states are classical thermal distributions
arXiv:2011.08572
Abstract
We study the structure of the ground states of local stoquastic Hamiltonians and show that under mild assumptions the following distributions can efficiently approximate one another: (a) distributions arising from ground states of stoquastic Hamiltonians, (b) distributions arising from ground states of stoquastic frustration-free Hamiltonians, (c) Gibbs distributions of local classical Hamiltonian, and (d) distributions represented by real-valued Deep Boltzmann machines. In addition, we highlight regimes where it is possible to efficiently classically sample from the above distributions.
arXiv comment12 pages, 4 figures. Proof of Lemma 2 fixed making use of the Detectability Lemma
References in corpus (8)
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Criticality, the area law, and the computational power of PEPS
- A Neural Decoder for Topological Codes
- Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
- Universal Quantum Hamiltonians
- A Quantum Approach to Classical Statistical Mechanics
- A simple proof of the detectability lemma and spectral gap amplification
- Monte Carlo simulation of stoquastic Hamiltonians