Bohmian Quantum Field Theory and Quantum Computing

Abrams and Lloyd proved that if quantum mechanics has a small nonlinear component then theoretical quantum computers would be able to solve NP-complete problems. We show that a semiclassical theory of electrodynamics in which the fermions are quantized but the electromagnetic field is not, and in which the particles and the field interact in a natural way, does have such a nonlinear component. We argue that in many situations this semiclassical theory will be a close approximation to quantum field theory. In a more speculative argument, we discuss the possibility that the apparent quantization of the electromagnetic field could be a result of (1) quantization of interactions of the electromagnetic field with matter and (2) wave packets, regions within the electromagnetic field that are approximate photons. At the least this gives a theory which, if crude, avoids the major divergences of standard quantum field theory. We suggest how this might be extended to a quantum theory of the other three forces by modifying the Standard Model and using a model of gravity equivalent to spin 2 gravitons. This also provides a quantum field theory that agrees with Bohmian ideas.