Quantum Cellular Automaton for Simulating Static Magnetic Fields

This paper proposes a new quantum cellular automaton (quantum CA) for simulating macroscopic electromagnetic fields. The final target is to simulate the macroscopic electromagnetic fields on a quantum computer. In the proposal approach, Maxwell´s historical model, which was explained the nature of electromagnetic fields in 1861, has been modified for a quantum CA model to simulate the electromagnetic fields. Then, a state transition rule for CA is determined by a strategy based on the quantum mechanics and the quantum computation theories. One of originalities of the proposed approach is that a system using quantum gates is superstructed to simulate magneto-static fields from currents. First, a modified Maxwell model for applying to quantum CA was shown. Second, by using the quantum computation theory, a quantum gate system to simulate the magnetic fields from currents was described. Finally, the proposed approach was applied to an example of magnetostatic field simulation.