2014/09/27 by David Gosset, Barbara M. Terhal, Anna Vershynina · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Computation #Ground state #Hamiltonian (control theory) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum computer #Quantum many-body systems #Quantum mechanics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevlett.114.140501
published as Phys. Rev. Lett. 114, 140501 (2015)
arxiv created 2014/09/27 · openalex publication_date 2015/04/06 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.