Corpus ID: 34395233

Commutative version of the local Hamiltonian problem and common eigenspace problem

@article{Bravyi2005CommutativeVO,
  title={Commutative version of the local Hamiltonian problem and common eigenspace problem},
  author={S. Bravyi and M. Vyalyi},
  journal={Quantum Inf. Comput.},
  year={2005},
  volume={5},
  pages={187-215}
}
  • S. Bravyi, M. Vyalyi
  • Published 2005
  • Mathematics, Physics, Computer Science
  • Quantum Inf. Comput.
  • We study the complexity of a problem "Common Eigenspace" -- verifying consistency of eigenvalue equations for composite quantum systems. The input of the problem is a family of pairwise commuting Hermitian operators H1,..., Hr on a Hilbert space (Cd)⊗n and a string of real numbers λ =(λ1,...,λr). The problem is to determine whether the common eigenspace specified by equalities Ha|O〉 = λa|O〉, a = 1, ..., r has a positive dimension. We consider two cases: (i) all operators Ha are k-local; (ii… CONTINUE READING
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