title: Hearing the shape of the Ising model with a programmable superconducting-flux annealer.
abstract: Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.
authors.affiliation: London Centre for Nanotechnology, University College London, WC1E 6BT London, UK.
authors.forename: Walter
authors.initials: W
authors.lastname: Vinci
authors.affiliation: Department of Mathematics and Mathematical Statistics, Umeå University, S-901 87 Umeå, Sweden.
authors.forename: Klas
authors.initials: K
authors.lastname: Markström
authors.affiliation: 1] Information Sciences Institute and Ming-Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA [2] Google, Venice Beach, CA 90292, U.S.A.
authors.forename: Sergio
authors.initials: S
authors.lastname: Boixo
authors.affiliation: D-Wave Systems Inc., 100-4401 Still Creek Drive, Burnaby, BC V5C 6G9, Canada.
authors.forename: Aidan
authors.initials: A
authors.lastname: Roy
authors.affiliation: Information Sciences Institute and Ming-Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA.
authors.forename: Federico M
authors.initials: FM
authors.lastname: Spedalieri
authors.affiliation: London Centre for Nanotechnology, University College London, WC1E 6BT London, UK.
authors.forename: Paul A
authors.initials: PA
authors.lastname: Warburton
authors.affiliation: Department of Computer Science, and Department of Physics & Astronomy, University College London, WC1E 6BT London, UK.
authors.forename: Simone
authors.initials: S
authors.lastname: Severini