Lower bounds to variational problems with guarantees

Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum computing. This work stresses that for translationally invariant lattice Hamiltonians with periodic boundary conditions, one can easily derive efficiently computable lower bounds to ground state energies that can and should be compared with variational principles providing upper bounds. As small technical results, it is shown that (i) the Anderson bound and a (ii) common hierarchy of semidefinite relaxations both provide approximations with performance guarantees that scale as a…

• BF
  Bundesministerium für Wirtschaft und Klimaschutz
• DF
  Deutsche Forschungsgemeinschaft

  Award: CRC 183
• Q
  QuantERA
• HE
  H2020 European Research Council