The complexity of stoquastic local Hamiltonian problems

@article{Bravyi2008TheCO,
  title={The complexity of stoquastic local Hamiltonian problems},
  author={Sergey Bravyi and David P. DiVincenzo and Roberto Oliveira and Barbara M. Terhal},
  journal={Quantum Information & Computation},
  year={2008},
  volume={8},
  pages={361-385}
}
We study the complexity of the Local Hamiltonian Problem (denoted as LH-MIN) in the special case when a Hamiltonian obeys the condition that all off-diagonal matrix elements in the standard basis are real and non-positive. We will call such Hamiltonians, which are common in the natural world, stoquastic. An equivalent characterization of stoquastic Hamiltonians is that they have an entry-wise non-negative Gibbs density matrix for any temperature. We prove that LH-MIN for stoquastic Hamiltonians… CONTINUE READING
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