The quantum field as a quantum computer

It is supposed that at very small scales a quantum field is an infinite homogeneous quantum computer. On a quantum computer the information cannot propagate faster than c = a/tau, a and tau being the minimum space and time distances between gates, respectively. For one space dimension it is shown that the information flow satisfies a Dirac equation, with speed v = zeta c and zeta = zeta(m) mass-dependent. For c the speed of light zeta(-1) is a vacuum refraction index that increases monotonically from zeta(-1)(0) = 1 to zeta(-1)(M) = infinity, M being the Planck mass for 2a the Planck length. The Fermi anticommuting field can be entirely qubitized, i.e. it can be written in terms of local Pauli matrices and with the field interaction remaining local on qubits. Extensions to larger space dimensions are discussed. (C) 2011 Elsevier B.V. All rights reserved.