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 …

Date

July 16, 2014

Authors

Walter Vinci, Klas Markström, Sergio Boixo, Aidan Roy, Federico M Spedalieri, Paul A Warburton, Simone Severini

Journal

Scientific reports

Volume

4

Issue

1

Pages

5703

Publisher

Nature Publishing Group UK