Quantum computing algorithm for electromagnetic field simulation

Emanuel Colella, Luca Bastianelli, Valter Mariani Primiani +2 more

Gautam Sharma, Apurva Tiwari, Niladri Gomes +3 more

We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwells equations using a Schrodingerisation-based approach. The electromagnetic fields are discretized using finite-difference operators, and the resulting non-unitary matrices are mapped to Bell-basis Trotter blocks, enabling efficient circuit construction. We introduce a measurement procedure that retrieves not only field amplitudes, but also physical directions of the electric and magnetic field values at select spatial points. Implementing this logic on quantum hardware relies on relative-phase-based sign reconstruction. Numerical results obtained using IonQ QPU, show good agreement with analytical solutions of benchmark problems in two dimensions and on simulators; in three dimensions. We further extend our approach to compute fields scattered from simple bodies, by enforcing appropriate boundary conditions. Our work lays the foundational steps towards realizing quantum-hardware solutions for computational electromagnetics.

T. Doi

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.

Kaden R. A. Hazzard, Andrew D. Greentree, R.P. Starrett +3 more

Emanuel Colella, Franco Moglie, Valter Mariani Primiani +1 more

This work presents a novel approach for simulating electromagnetic (EM) wave propagation by leveraging quantum computing techniques. By reformulating Maxwell's equations through the Riemann-Silberstein formalism, we cast the problem into a Schrödinger-like framework, enabling the application of Hamiltonian simulation methods. In particular, we employ the Trotter-Suzuki decomposition to approximate the time evolution operator, facilitating efficient quantum simulation of EM wave generated by a Gaussian pulse propagating within a two-dimensional metallic cavity. Our results illustrate the potential of quantum algorithms to address complex electrodynamics problems, offering promising avenues for future advancements in electromagnetics engineering.

Dhruva Kashyap, Gang Yu, Gabriele Gradoni