σ Models on Quantum Computers
Abstract
We formulate a discretization of σ models suitable for simulation by quantum computers. Space is substituted with a lattice, as usually done in lattice field theory, while the target space (a sphere) is replaced by the "fuzzy sphere", a construction well known from noncommutative geometry. Contrary to more naive discretizations of the sphere, in this construction the exact O(3) symmetry is maintained, which suggests that the discretized model is in the same universality class as the continuum model. That would allow for continuum results to be obtained for very rough discretizations of the target space as long as the space discretization is made fine enough. The cost of performing time evolution, measured as the number of controlleduc(not) operations necessary, is 12 L T /Δ t , where L is the number of spatial sites, T the maximum time extent, and Δ t the time spacing.
 Publication:

Physical Review Letters
 Pub Date:
 August 2019
 DOI:
 10.1103/PhysRevLett.123.090501
 arXiv:
 arXiv:1903.06577
 Bibcode:
 2019PhRvL.123i0501A
 Keywords:

 High Energy Physics  Lattice;
 Condensed Matter  Strongly Correlated Electrons;
 Nuclear Theory;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 5 pages, 2 figures, v2 includes additional references and refined discussion