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 controlled-not operations necessary, is 12LT/Δt, where L is the number of spatial sites, T the maximum time extent, and Δt the time spacing.
Highlights
Introduction.—The advent of quantum computers opens up a new method to attack several physics problems which have, up to now, remained intractable
The naive expectation is that fermionic fields can be more implemented in quantum computers, as a qubit can encode the presence or absence of a fermion in a given state
Classical bits seem more amenable to describing fermionic fields than bosonic ones, as the cost of storing and manipulating reasonable approximations to real numbers was too high to be practical in the early days
Summary
Introduction.—The advent of quantum computers opens up a new method to attack several physics problems which have, up to now, remained intractable. The attempts made up to now involve either eliminating the bosonic fields using some special property of the model or truncating the occupation number at any given site [7,8,9,10,11,12,13,14,15,16,17,18]. In all of these schemes, the symmetry of the model is reduced by the discretization of the bosonic fields.
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