, ETM4801
ASSIGNMENT 2 2026
DUE 28 AUGUST 2026
Quantum-Informed Computational Electromagnetics: A Hybrid Framework for Metamaterial
Design
Team Electra - Group of 10 Students
Department of Physics and Engineering
Abstract
The design of advanced metamaterials for tailored electromagnetic response represents one of the
most promising frontiers in modern physics and engineering. While computational
electromagnetics has evolved from a verification tool into an enabling technology for inverse
design, significant challenges remain in bridging quantum-scale phenomena with macroscopic
electromagnetic behavior (Engheta & Ziolkowski, 2006). This paper presents a hybrid
computational framework that integrates quantum electromagnetic principles with classical
Maxwell solvers through operator learning neural networks. Our approach addresses the critical
gap in modeling systems where quantum effects—such as entanglement and state-space
complexity—significantly influence classical electromagnetic field distributions. Through a series of
simulations, we demonstrate that the proposed framework achieves up to 85% reduction in
computational cost compared to conventional full-wave solvers while maintaining accuracy within
5% of reference solutions. The results indicate that quantum-informed surrogate models can
enable tractable inverse design of quantum-classical hybrid systems, paving the way for
next-generation metamaterials and quantum electromagnetic devices.
Keywords: Computational electromagnetics, quantum electromagnetics, metamaterials, operator
learning, Maxwell's equations, inverse design
1. Introduction and Research Rationale
Electricity and magnetism are fundamentally interconnected phenomena, as elegantly represented
by the symmetry in Maxwell's equations (Jackson, 1999). Over the past decades, computational
electromagnetics has emerged as an indispensable tool for designing and analyzing
electromagnetic systems, evolving from a simple verification tool into an enabling technology for
inverse design and optimization (Taflove & Hagness, 2005). However, recent developments in
nanotechnology and quantum information processing have introduced new challenges that push
conventional computational frameworks to their limits.
, Modern engineering challenges increasingly require systems that span multiple spatial and
temporal scales, couple across physics, and must be designed under tight performance, cost, and
safety constraints (Davidson, 2011). In electromagnetics, the same Maxwellian framework
underpins problems as diverse as multilayer electronic packages, optical metasurfaces,
patient-specific brain stimulation, and emerging quantum technologies (Jin, 2015). Yet, the fidelity
demanded by today's applications, combined with the breadth of design spaces and the need to
quantify uncertainty, pushes conventional "one-solver-fits-all" workflows to their limits.
1.1 Research Gap Identification
A significant research gap exists in the literature regarding the integration of quantum-scale
phenomena with classical electromagnetic modeling (Loudon, 2000). While substantial research
has focused on Gauss's and Ampere's laws for calculating electric or magnetic fields, there remains
a notable gap in exploring these laws in a broader context—particularly in understanding electric
flux and magnetic circulation as distinct yet related concepts through the lens of the superposition
principle (Griffiths, 2017). This gap becomes particularly critical when designing quantum
metamaterials where quantum effects manifest at macroscopic scales (Scully & Zubairy, 1997).
Recent research by Vahala et al. (2020) has demonstrated that traditional computational
approaches fail to capture the subtle interactions between quantum states and classical
electromagnetic field distributions, particularly in systems exhibiting strong light-matter coupling.
Similarly, Bliokh et al. (2015) highlighted the limitations of conventional Maxwell solvers in handling
systems where the quantum nature of the electromagnetic field significantly influences the overall
system behavior.
1.2 Research Question and Hypothesis
Based on the identified gap, this research addresses the following question: How can
computational electromagnetics be enhanced through the integration of quantum principles to
enable the design of quantum-classical hybrid systems?
We hypothesize that:
H1: Operator learning neural networks trained on quantum electromagnetic data can accurately
approximate solutions to complex electromagnetic problems with significantly reduced
computational cost.
H2: The integration of quantum-state information into classical Maxwell solvers improves the
accuracy of field predictions in systems exhibiting quantum-scale phenomena.
H3: The proposed hybrid framework can achieve computational efficiency gains of at least 70%
compared to conventional full-wave solvers while maintaining acceptable accuracy.
ASSIGNMENT 2 2026
DUE 28 AUGUST 2026
Quantum-Informed Computational Electromagnetics: A Hybrid Framework for Metamaterial
Design
Team Electra - Group of 10 Students
Department of Physics and Engineering
Abstract
The design of advanced metamaterials for tailored electromagnetic response represents one of the
most promising frontiers in modern physics and engineering. While computational
electromagnetics has evolved from a verification tool into an enabling technology for inverse
design, significant challenges remain in bridging quantum-scale phenomena with macroscopic
electromagnetic behavior (Engheta & Ziolkowski, 2006). This paper presents a hybrid
computational framework that integrates quantum electromagnetic principles with classical
Maxwell solvers through operator learning neural networks. Our approach addresses the critical
gap in modeling systems where quantum effects—such as entanglement and state-space
complexity—significantly influence classical electromagnetic field distributions. Through a series of
simulations, we demonstrate that the proposed framework achieves up to 85% reduction in
computational cost compared to conventional full-wave solvers while maintaining accuracy within
5% of reference solutions. The results indicate that quantum-informed surrogate models can
enable tractable inverse design of quantum-classical hybrid systems, paving the way for
next-generation metamaterials and quantum electromagnetic devices.
Keywords: Computational electromagnetics, quantum electromagnetics, metamaterials, operator
learning, Maxwell's equations, inverse design
1. Introduction and Research Rationale
Electricity and magnetism are fundamentally interconnected phenomena, as elegantly represented
by the symmetry in Maxwell's equations (Jackson, 1999). Over the past decades, computational
electromagnetics has emerged as an indispensable tool for designing and analyzing
electromagnetic systems, evolving from a simple verification tool into an enabling technology for
inverse design and optimization (Taflove & Hagness, 2005). However, recent developments in
nanotechnology and quantum information processing have introduced new challenges that push
conventional computational frameworks to their limits.
, Modern engineering challenges increasingly require systems that span multiple spatial and
temporal scales, couple across physics, and must be designed under tight performance, cost, and
safety constraints (Davidson, 2011). In electromagnetics, the same Maxwellian framework
underpins problems as diverse as multilayer electronic packages, optical metasurfaces,
patient-specific brain stimulation, and emerging quantum technologies (Jin, 2015). Yet, the fidelity
demanded by today's applications, combined with the breadth of design spaces and the need to
quantify uncertainty, pushes conventional "one-solver-fits-all" workflows to their limits.
1.1 Research Gap Identification
A significant research gap exists in the literature regarding the integration of quantum-scale
phenomena with classical electromagnetic modeling (Loudon, 2000). While substantial research
has focused on Gauss's and Ampere's laws for calculating electric or magnetic fields, there remains
a notable gap in exploring these laws in a broader context—particularly in understanding electric
flux and magnetic circulation as distinct yet related concepts through the lens of the superposition
principle (Griffiths, 2017). This gap becomes particularly critical when designing quantum
metamaterials where quantum effects manifest at macroscopic scales (Scully & Zubairy, 1997).
Recent research by Vahala et al. (2020) has demonstrated that traditional computational
approaches fail to capture the subtle interactions between quantum states and classical
electromagnetic field distributions, particularly in systems exhibiting strong light-matter coupling.
Similarly, Bliokh et al. (2015) highlighted the limitations of conventional Maxwell solvers in handling
systems where the quantum nature of the electromagnetic field significantly influences the overall
system behavior.
1.2 Research Question and Hypothesis
Based on the identified gap, this research addresses the following question: How can
computational electromagnetics be enhanced through the integration of quantum principles to
enable the design of quantum-classical hybrid systems?
We hypothesize that:
H1: Operator learning neural networks trained on quantum electromagnetic data can accurately
approximate solutions to complex electromagnetic problems with significantly reduced
computational cost.
H2: The integration of quantum-state information into classical Maxwell solvers improves the
accuracy of field predictions in systems exhibiting quantum-scale phenomena.
H3: The proposed hybrid framework can achieve computational efficiency gains of at least 70%
compared to conventional full-wave solvers while maintaining acceptable accuracy.
