2006/12/21 by M. Van den Nest, K. Luttmer, Wolfgang Dür +3 · 3 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems #quant-ph
paper · pdf · doi:10.1103/physreva.77.012301
published as Phys. Rev. A 77, 012301 (2008) · 10 pages, 1 figure
arxiv created 2006/12/21 · openalex publication_date 2008/01/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider the problem of whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most two-body interactions, we show that no n-qubit graph state can be the exact, nondegenerate ground state. We determine for any graph state the minimal d such that it is the nondegenerate ground state of a d-body interaction Hamiltonian, while we show for d^\ensuremath'-body Hamiltonians H with d^\ensuremath'<d that the resulting ground state can only be close to the graph state at the cost of H having a small energy gap relative to the total energy. When allowing for ancilla particles, we show how to utilize a gadget construction introduced in the context of the k-local Hamiltonian problem, to obtain n-qubit graph states as nondegenerate (quasi)ground states of a two-body Hamiltonian acting on n^\ensuremath'>n spins.