Speaker
Description
Quantum cellular automata (QCA) for quantum electrodynamics (QED) is a quantum algorithm that can be coded on a quantum computer to simulate QED. It is a unitary-based, strictly local discrete space-time formulation of QED. The space-time of the QCA is a square lattice and qubits in the lattice sites encode the information of occupation number of fermions. The dynamics of the QCA is done by quantum gates that simulate the evolution operator of QED. One of the well-known problems of discrete space-time formulation of quantum field theories is fermion doubling. This phenomenon appeared in the context of early lattice gauge theories, their lattice formulation of free fermions suggested that some of the infinite momentum modes contribute to the correlators in the continuum limit as much as the finite ones. To tackle this problem, several strategies have been developed immediately after identifying the doubling but it is shown that these strategies break chirality for non-massive particles. The QCA has less problematic fermion doubling properties than LGT, allowing solutions without breaking the chirality. In this talk, I will introduce the QCA model that we use to simulate QED, give details of the fermion dynamics that QCA for QED has, then I will continue with the analysis of fermion doubling in QCA for QED on 1+1 and 3+1 dimensions which requires considering topological aspects of the corresponding Brillouin zones. I will mention our strategies for solving the problem and give generalizations of the solution.
