Ground-state spin logic

J. D. Whitfield, M. Faccin, J. D. Biamonte

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground-state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground-state subspace encoding the truth tables of Boolean formulas. The ground-state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground-state embeddings found in both classical optimization as well as adiabatic quantum optimization.

Original languageEnglish (US)
Article number57004
JournalEPL
Volume99
Issue number5
DOIs
StatePublished - Sep 2012

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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