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σ Models on Quantum Computers.

Andrei Alexandru1,2, Paulo F Bedaque2, Henry Lamm2

  • 1Department of Physics, The George Washington University, Washington, D.C. 20052, USA.

Physical Review Letters
|September 17, 2019
PubMed
Summary
This summary is machine-generated.

We developed a quantum computer-friendly discretization for sigma models using a lattice and a "fuzzy sphere". This approach preserves O(3) symmetry, enabling accurate continuum results with efficient quantum simulations.

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Area of Science:

  • Quantum Computing
  • Lattice Field Theory
  • Noncommutative Geometry

Background:

  • Discretization of sigma models is crucial for numerical simulations.
  • Traditional methods often struggle with preserving symmetries on discrete spaces.
  • Quantum computing offers new possibilities for complex model simulations.

Purpose of the Study:

  • To formulate a sigma model discretization suitable for quantum computers.
  • To maintain exact O(3) symmetry in the discretized model.
  • To enable accurate continuum limit extrapolations.

Main Methods:

  • Replacing continuous space with a lattice.
  • Replacing the spherical target space with a "fuzzy sphere" from noncommutative geometry.
  • Analyzing the symmetry properties and simulation cost.

Main Results:

  • The proposed discretization maintains exact O(3) symmetry.
  • The model is expected to be in the same universality class as the continuum model.
  • The cost of time evolution scales as 12LT/Δt.

Conclusions:

  • The "fuzzy sphere" discretization is a promising approach for quantum simulations of sigma models.
  • This method allows for continuum results even with coarse target space discretizations.
  • The preserved symmetry ensures the fidelity of quantum simulations.