A qubit field theory is a quantum field theory in which the canonical commutation relations involved in the quantisation of pairs of observables are relaxed. Specifically, it is a quantum field theory in which, unlike most other quantum field theories, the pair of observables is not required to always commute.
Theory
David Deutsch has presented a group of qubit field theories which, despite not requiring commutation of certain observables, still presents the same observable results as ordinary quantum field theory.
J. Hruby has presented a supersymmetric extension.