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.
journal_name
Sci Repjournal_title
Scientific reportsauthors
Vinci W,Markström K,Boixo S,Roy A,Spedalieri FM,Warburton PA,Severini Sdoi
10.1038/srep05703subject
Has Abstractpub_date
2014-07-16 00:00:00pages
5703issn
2045-2322pii
srep05703journal_volume
4pub_type
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