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Simple glass models and their quantum annealing.

Thomas Jörg1, Florent Krzakala, Jorge Kurchan

  • 1LPTMS, Université Paris-Sud, CNRS UMR 8626, 91405 Orsay Cedex, France.

Physical Review Letters
|October 15, 2008
PubMed
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We found that first-order quantum phase transitions in spin glasses cause eigenstates to project onto the ground state, leading to exponentially small energy gaps. This finding is crucial for understanding quantum annealing. Keywords: quantum phase transitions, spin glasses, quantum annealing.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • First-order quantum phase transitions are critical phenomena.
  • Spin glasses exhibit complex behavior due to quenched disorder.
  • Understanding these transitions is key to advancements in quantum computing and annealing.

Purpose of the Study:

  • To investigate first-order quantum phase transitions in mean-field spin glasses.
  • To analyze the behavior of eigenstates and energy gaps at the transition point.
  • To explore the implications for quantum annealing and related models.

Main Methods:

  • Solving the quantum random energy model using elementary analytical methods.
  • Introducing a two-time instanton formalism for calculating energy gaps.
  • Analyzing the projection of eigenstates onto the unperturbed ground state.

Main Results:

  • Demonstrated that at the transition, eigenstates suddenly project onto the unperturbed ground state.
  • Showed that the energy gap between the lowest states becomes exponentially small with system size.
  • Argued this phenomenon is characteristic of "random first-order" models, including random satisfiability problems.

Conclusions:

  • The study reveals a generic feature of random first-order models relevant to quantum phase transitions.
  • The exponentially small energy gap has significant consequences for the efficiency of quantum annealing.
  • The developed two-time instanton method provides a general tool for calculating these gaps.