Sigma models on quantum computers. (arXiv:1903.06577v1 [hep-lat])
We formulate a discretization of sigma models suitable for simulation by
quantum computers. Space is substituted by 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 non-commutative 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 CNOT operations necessary,
is $12 L T/\Delta t $, where $L$ is the number of spatial sites, $T$ the
maximum time extent and $\Delta t$ the time spacing.