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Expanding the horizon of automated metamaterials discovery via quantum annealing
Koki Kitai, Jiang Guo, Shenghong Ju, Shu Tanaka, Koji Tsuda, Junichiro Shiomi, Ryo Tamura
TL;DR
Complex materials discovery is limited by classical computation when design spaces become large. The paper introduces FMQA, combining a factorization machine, RCWA, and a D-Wave quantum annealer, and demonstrates it on SiO2–SiC–PMMA radiative-cooling metamaterials. The method achieves a best FOM of 0.724 and outperforms reported human-designed structures in targeted single-polarization FOM.
Problem
Complex-material discovery faces computational barriers as design spaces and degrees of freedom grow, while radiative-cooling designs can perform poorly in hot, humid areas.
Method
FMQA trains a factorization machine, converts acquisition-function optimization over binary structures into QUBO, selects candidates with a D-Wave quantum annealer, and evaluates them with RCWA.
Results
FOM = 0.724 was achieved for radiative sky cooling, and the targeted single-polarization FOM was far greater than the best reported human-designed structures.
Takeaways & Limitations
Quantum annealing enabled automated design of complex metamaterial radiators with high wavelength selectivity relative to reported human-designed alternatives.
Takeaways & Limitations
The algorithm’s computational bottleneck lies in atomistic simulation as larger-bit quantum annealers become available.
Abstract
from arXiv · showhide
Complexity of materials designed by machine learning is currently limited by the inefficiency of classical computers. We show how quantum annealing can be incorporated into automated materials discovery and conduct a proof-of-principle study on designing complex thermofunctional metamaterials consisting of SiO2, SiC, and Poly(methyl methacrylate). Empirical computing time of our quantum-classical hybrid algorithm involving a factorization machine, a rigorous coupled wave analysis, and a D-Wave 2000Q quantum annealer was insensitive to the problem size, while a classical counterpart experienced rapid increase. Our method was used to design complex structures of wavelength selective radiators showing much better concordance with the thermal atmospheric transparency window in comparison to existing human-designed alternatives. Our result shows that quantum annealing provides scientists gigantic computational power that may change how materials are designed.
Introduction
Automated materials discovery addresses enormous design spaces, but statistical and computational barriers limit complex-material optimization. The paper proposes FMQA, a quantum-classical method that uses a factorization machine and quantum annealing to search binary material structures, then demonstrates it on wavelength-selective thermal radiators.
- Motivation: Massive candidate spaces make automated discovery crucial for advancing materials with controlled energy-transport properties.The challenge grows from compounds to composites and nanostructures, while automated discovery iteratively selects candidates using machine-learned property predictions.
- Challenges: Statistical and computational barriers hinder automated discovery of complex materials.Limited training data complicate property prediction, while global optimization over large design spaces creates a computational bottleneck.
- Challenges: Heuristic local, tree, and genetic searches can find only local minima, limiting optimization quality.These methods are used instead of exhaustive search to reduce computational difficulty.
- Proposed method: FMQA converts acquisition-function optimization over binary material-structure variables into QUBO for a D-Wave quantum annealer.A factorization machine is trained on available data, the annealer selects a candidate, RCWA evaluates it, and the model is retrained iteratively.
- Application: The proof-of-principle application designs metamaterials with tailored thermal-radiation spectra for wavelength-selective radiators.The target is radiative sky cooling, where emission through the atmospheric transparency window is desirable.
Results
The study evaluates FMQA on SiO2–SiC–PMMA metamaterials for radiative cooling. FMQA reduces simulations and computational selection time while finding structures with high atmospheric-window selectivity, including a best FOM of 0.724 versus 0.250 for a five-layer multilayer structure.
- Target structures: SiO2 and SiC provide phonon-polariton resonances near 9.7 μm and 12.5 μm for atmospheric-window selectivity.The structures use SiO2 or SiC wires embedded in PMMA and are evaluated with RCWA under p-polarized normal incidence.
- FM evaluation: FM outperformed Gaussian-process and random-search regression, finding the best structure within 300 iterations.The comparison used common randomly selected initial structures and averaged FOMs across runs.
- FMQA search: 16,777,216 candidates made exhaustive classical selection impractical for the L = 6, C = 3 problem.FMQA therefore used the D-Wave quantum annealer to select candidates from the acquisition function.
- FMQA search: FMQA reduced simulations needed to find better-FOM metamaterials and reached the highest FOM within 500 iterations.The result was obtained from averaged runs with multiple initial structures.
- Computational scaling: Quantum-annealer selection achieved overwhelming time reduction while both methods found the highest-FOM structure within 500 iterations.The comparison separated selection, FM learning, and RCWA simulation time across problem sizes.
Mechanism of high emittance in designed metamaterial
The designed metamaterial achieves high emittance through wavelength-dependent absorption and magnetic-polariton resonance. SiO2 and SiC layers distribute absorption across the atmospheric window, while confined magnetic fields coincide with high-emittance regions and remain nearly angle-insensitive.
- The analysis uses electric-power-dissipation contours and normalized magnetic-field contours to identify where absorption and resonance occur.
- SiO2 absorbs most wave energy from 8–11 μm, while SiC dominates absorption from 11–13 μm and SiO2 also contributes near 11.8 μm.
- Magnetic fields are strongly confined where emittance is high, whereas lower emittance corresponds to flatter, less centralized fields.
- The high emittance originates from magnetic-polariton resonance, whose response is almost insensitive to incident angle.
- Five-layer structures with SiC in the middle consistently show better FOM, linking material arrangement to magnetic-field confinement.
Discussion
FMQA combines a factorization machine with quantum annealing to optimize metamaterial designs, demonstrated through radiative-cooling structures computed with few RCWA simulations. The approach achieved strong cooling performance and is presented as applicable beyond this demonstration, though classical atomistic simulation remains a computational bottleneck.
- Method: FMQA represents candidate selection as a combinatorial optimization problem and solves it with a quantum annealer.The hybrid algorithm uses a factorization machine to formulate the optimization and selects the next candidate through an acquisition function.
- Demonstration: Using the D-Wave 2000Q, FMQA designed a radiative-cooling metamaterial within a small number of RCWA simulations.The target structure contains SiO2 and SiC wires placed in PMMA.
- Results: A high FOM of 0.724 was achieved for radiative sky cooling in the target metamaterial.The reported structure consists of SiO2 and SiC wires placed in PMMA.
- Results: Compared with previous human-designed structures, the targeted single-polarization FOM was far greater, while polarization- and angle-averaged cooling power was comparable.The comparison concerns both the targeted single-polarization figure of merit and averaged cooling power.
- Limitations: Fabrication is beyond this paper’s scope, although similar stratified structures have been fabricated and the authors consider the designed structure possible to fabricate.The authors state that fabrication will be discussed elsewhere.
- Scope: The algorithm applies to structural optimization of any property whose calculation is relatively fast compared with the optimization process.The authors also anticipate extensions to spectral- and angular-dependent radiative heat transfer and transport control for phonons, electrons, and magnons.
- Contribution: FMQA is described as the first black-box optimization algorithm using an Ising machine such as a quantum annealer for automated materials discovery.The passage distinguishes this use from conventional Ising-machine optimization of explicitly defined functions and machine-learning training.
- Limitations: The computational bottleneck remains the classical atomistic simulation, with resolution expected from future quantum materials simulations.The authors also anticipate larger problems as quantum annealers or other Ising machines with many bits become available.
Methods
The method combines RCWA-based thermal-emissivity evaluation with factorization-machine prediction and D-Wave quantum-annealer selection to search metamaterial structures. Candidate structures are iteratively evaluated, added to training data, and used to update subsequent selections.
- Thermal-property simulation: RCWA calculates the target metamaterials’ thermal emissivity properties by solving Maxwell’s equation with high numerical accuracy.The method decomposes the dielectric and electromagnetic fields along x and z and imposes boundary conditions.
- Thermal-property simulation: The figure of merit evaluates whether spectral emittance is concentrated in the 8–13 μm atmospheric-window region relative to the broader 1–20 μm range.The calculation uses spectral emittance and blackbody emissive power obtained by RCWA.
- Machine-learning model: A factorization machine predicts the acquisition function from binary structure variables, with its parameters trained on negative FOM values.The factorization size was fixed at K = 8, and Adam was used for training.
- Iterative optimization: After selection, RCWA evaluates the candidate FOM, the result enlarges the FM training set, and the procedure repeats to find high-FOM structures with few evaluations.The implementation used 50 output states and selected the minimum-energy state, while already observed structures could also be selected.
Supplementary information for Expanding the horizon of automated materials discovery via quantum annealing
The supplementary information identifies the paper’s research team and describes a computing-time comparison for 500 automated-discovery iterations. The comparison varies encoding bits and contrasts quantum-classical selection with classical exhaustive search while keeping learning and simulation on the same classical computer.
- Authors and affiliations: The paper’s authors are affiliated with the University of Tokyo, NIMS, Waseda University, JST PRESTO, and RIKEN.The listed affiliations span materials science, mechanical engineering, green computing, and advanced intelligence research.
- Computing-time comparison: Supplementary Table I measures empirical computing time for 500 automated-materials-discovery iterations as the number of encoding bits changes.The table concerns the selection part of the workflow.
- Computing-time comparison: The comparison uses a quantum-annealer quantum-classical hybrid or classical exhaustive search for selection, with FM learning and RCWA simulation performed on the same classical computer.The classical selection baseline uses an Intel Xeon E5-2690 v3 @ 2.6 GHz.
Supplementary Note A. Comparison between a global search and a local search
The supplementary notes compare global quantum-annealer search with local search and examine selected multilayer and angular-emittance properties. The comparisons address optimization behavior, multilayer candidates, and the radiator’s angle-dependent response.
- Global versus local search: The global-search comparison averages best FOM over 20 trials from common random initial states for a target structure with L = 4 and C = 3.Figure A-1 compares D-Wave global search with local search for the selection step.
- Global versus local search: The local greedy search restricts candidates to single-bit flips, reducing the search space but risking entrapment in a local optimum.The supplementary note describes global D-Wave search as recommended for avoiding this trap.
- Multilayer comparison: For five-layer SiO2–SiC–PMMA structures with 1 μm layers, all 3^5 = 243 candidates were evaluated by RCWA for comparison.The top five structures are shown in Figure B-1, while the designed radiator had FOM = 0.724 and the comparison FOMs were much smaller.
- Angular response: The designed radiator’s p-wave emittance is almost angle-independent between 769 and 1250 cm^-1, corresponding to 8–13 μm.The dispersion indicates magnetic polariton excitation in this range, alongside weaker surface-phonon-polariton and coupling resonances.
Supplementary Note D. Comparison of performance with previous works
The designed radiator outperforms prior designs in wavelength selectivity and delivers substantial cooling power under modeled atmospheric, conductive, convective, and solar conditions. The supplementary validation also establishes RCWA accuracy and identifies a convergence tradeoff for Fourier-term selection.
- Performance comparison: The designed metamaterial has the highest FOM among compared radiators, indicating the closest match to an ideal wavelength-selective radiator.The comparison uses emittance data from previous works under normal incidence.
- Cooling performance: The normalized emitted radiation exceeds absorbed atmospheric radiation in the modeled spectrum, supporting a large positive net cooling power.Atmospheric transmittance is calculated with MODTRAN and the 1976 US standard atmosphere model.
- Cooling performance: 100.36 W m-2 is the ideal emitter’s cooling power at 303 K with no conductive or convective heat transfer, versus 60.62 W m-2 for the designed structure.The ideal emitter’s equilibrium temperature is more than 50 K below ambient, while the designed structure’s temperature difference depends on hcond+conv.
- Cooling performance: 42 W m-2 cooling power and a stagnation temperature near 253 K are achieved by the designed device at 293 K, compared with 62 W m-2 for Ref. 2.The lower cooling power than Ref. 2 is attributed in the passage to the design’s lower s-wave emittance.
- RCWA validation: The homemade RCWA code agrees relatively well with FDTD and reproduces exactly the same result as S4 for the tested structure.RCWA is used to calculate radiative-cooling properties and diffraction efficiency in sub-wavelength periodic structures.
- RCWA validation: N_Fourier = 40 is sufficient for convergent results for 99.1% of 200,000 structures, balancing simulation accuracy against time and memory demands.The convergence study varies Fourier-term counts across randomly generated metamaterial structures.