Qubit Regularization of Quantum Field Theories

Motivated by the desire to study quantum field theories on a quantum computer, we propose a new type of regularization of quantum field theories where in addition to the usual lattice regularization, quantum field theories are constructed with a finite dimensional Hilbert space per lattice site. This is particularly relevant for studying bosonic field theories using a quantum computer since traditional lattice regularization assumes an infinite dimensional Hilbert space per lattice site and hence difficult to formulate on a quantum computer. Here we show that a two qubit model is sufficient to recover the 3d Wilson-Fisher fixed point and the 4d Gaussian fixed point of the O(3) sigma model. On the other hand in 2d, the continuum limit of our qubit model is difficult to establish because of asymptotic freedom. Even, if it exists it seems to belong to a different universality class.