Spin lattices with two-body Hamiltonians for which the ground state encodes a cluster state
arXiv:0805.2980 · doi:10.1103/PhysRevA.78.062306
Abstract
We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbour two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one-, two-, and three-dimensions, investigating both periodic and fixed boundary conditions, as well as present a proof for the applicability of this procedure to any graph. We determine the energy gap of these systems, which is shown to be independent of the size of the lattice but dependent on the type of lattice (in particular, the coordination number), and investigate the scaling of this gap in terms of the coupling constants of the Hamiltonian. We provide a comparative analysis of the different lattice types with respect to their usefulness for measurement-based quantum computation.
16 pages, 5 figures, comments welcome; v2 added some new results about exact solutions to this model; v3 published version
References in corpus (12)
- Resource-efficient linear optical quantum computation
- Topological fault-tolerance in cluster state quantum computation
- Valence Bond Solids for Quantum Computation
- Novel schemes for measurement-based quantum computation
- Universal resources for measurement-based quantum computation
- Measurement-based quantum computation beyond the one-way model
- Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
- Quantum Information Processing in Optical Lattices and Magnetic Microtraps
- Fundamentals of universality in one-way quantum computation
- A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
- The computational difficulty of finding MPS ground states
- Graph states as ground states of many-body spin-1/2 Hamiltonians
Cited by in corpus (4)
- Identifying phases of quantum many-body systems that are universal for quantum computation
- Quantum computational capability of a 2D valence bond solid phase
- Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
- Quantum computation via measurements on the low-temperature state of a many-body system