Quantum-Merlin-Arthur-complete translationally invariant Hamiltonian problem and the complexity of finding ground-state energies in physical systems
- Centre for Quantum Computation, DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
Here we present a problem related to the local Hamiltonian problem (identifying whether the ground-state energy falls within one of two ranges) which is restricted to being translationally invariant. We prove that for Hamiltonians with a fixed local dimension and O(log(N))-body local terms, or local dimension N and two-body terms, there are instances where finding the ground-state energy is quantum-Merlin-Arthur-complete and simulating the dynamics is BQP-complete (BQP denotes ''bounded error, quantum polynomial time''). We discuss the implications for the computational complexity of finding ground states of these systems and hence for any classical approximation techniques that one could apply including density-matrix renormalization group, matrix product states, and multiscale entanglement renormalization ansatz. One important example is a one-dimensional lattice of bosons with nearest-neighbor hopping at constant filling fraction--i.e., a generalization of the Bose-Hubbard model.
- OSTI ID:
- 21015897
- Journal Information:
- Physical Review. A, Vol. 76, Issue 3; Other Information: DOI: 10.1103/PhysRevA.76.030307; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians
Foundations of variational discrete action theory