On Complexity of the Quantum Ising Model

@article{Bravyi2014OnCO,
  title={On Complexity of the Quantum Ising Model},
  author={Sergey Bravyi and Matthew B. Hastings},
  journal={Communications in Mathematical Physics},
  year={2014},
  volume={349},
  pages={1-45}
}
  • S. Bravyi, M. Hastings
  • Published 2 October 2014
  • Mathematics, Physics
  • Communications in Mathematical Physics
We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem (LHP). It is shown that the LHP for TIM on degree-3 graphs is equivalent modulo polynomial reductions to the LHP for general k-local ‘stoquastic’ Hamiltonians with any constant $${k \ge 2}$$k≥2. This result implies that estimating the ground state energy of TIM on degree-3 graphs is a complete… 

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