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arXiv:2407.04512 · Communications Physics

Entropy computing, a paradigm for optimization in open photonic systems

Lac Nguyen, Mohammad‐Ali Miri, R. Joseph Rupert, Wesley Dyk, Sam B. Wu, Nick Vrahoretis, Irwin Huang, Milan Begliarbekov, Nicholas Chancellor, Uchenna Chukwu, Pranav Mahamuni, Cesar Martinez-Delgado, David Haycraft, Carrie Spear, Joel Russell Huffman, Yong Meng Sua, Yu‐Ping Huang

Published Oct 24, 2025• 6 citations
arXivHTMLPDF

Abstract

Abstract Finding better solutions to combinatorial optimization problems could have a large positive impact on many real-world application areas, such as logistics. For this reason, significant efforts have been made to design novel optimization paradigms. Here we show an early instance of such paradigm in an optical setting, the entropy computing paradigm. Specifically, we experimentally demonstrate the feasibility of entropy computing by building a hybrid photonic-electronic computer that uses optical measurement and feedback to solve non-convex optimization problems. The system functions by using temporal photonic modes to create qudits in order to encode probability amplitudes in the time-frequency degree of freedom of a photon. This scheme, when coupled with with electronic interconnects, allows us to encode an arbitrary Hamiltonian into the system and solve non-convex continuous variables and combinatorial optimization problems. We show that the proposed entropy computing paradigm can act as a scalable and versatile platform for tackling a large range of NP-hard optimization problems.

DOI
10.1038/s42005-025-02324-6

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Abstract Finding better solutions to combinatorial optimization problems could have a large positive impact on many real-world application areas, such as logistics. For this reason, significant efforts have been made to design novel optimization paradigms. Here we show an early instance of such paradigm in an optical setting, the entropy computing paradigm. Specifically, we experimentally demonstrate the feasibility of entropy computing by building a hybrid photonic-electronic computer that uses optical measurement and feedback to solve non-convex optimization problems. The system functions by using temporal photonic modes to create qudits in order to encode probability amplitudes in the time-frequency degree of freedom of a photon. This scheme, when coupled with with electronic interconnects, allows us to encode an arbitrary Hamiltonian into the system and solve non-convex continuous variables and combinatorial optimization problems. We show that the proposed entropy computing paradigm can act as a scalable and versatile platform for tackling a large range of NP-hard optimization problems.
The demand for efficient solvers of complicated combinatorial optimization problems, especially those classified as NP-complete or NP-hard, has recently led to increased exploration of novel computing architectures. One prominent collective state computing paradigm embodied in the so-called Ising machines has recently attracted considerable research attention due to its ability to optimize complex problems with large numbers of interacting variables. Ising model-inspired solvers, thus named due to mathematical similarities to the well-known model from solid-state physics, represent a promising alternative to traditional von Neumann computer architectures due to their high degree of inherent parallelism. While there are many possible physical realizations of Ising solvers, just as there are many possible implementations of any binary computer, photonic Ising machines (PIMs) use primarily optical components for computation, taking advantage of features like lower power consumption, fast calculation speeds, the leveraging of physical optics to perform the calculations themselves, possessing decent scalability and noise tolerance. Photonic computing in the form of PIMs may offer certain computational advantages that are not easily achieved with non-photonic approaches and is nonetheless an altogether fascinating application of photonics to computing. In this review, we provide an overview of Ising machines generally, introducing why they are useful, what types of problems they can tackle, and how different Ising solvers can be compared and benchmarked. We delineate their various operational mechanisms, advantages, and limitations vis-à-vis non-photonic Ising machines. We describe their scalability, interconnectivity, performance, and physical dimensions. As research in PIMs continues to progress, there is a potential that photonic computing could well emerge as a way to handle large and challenging optimization problems across diverse domains. This review serves as a comprehensive resource for researchers and practitioners interested in understanding capabilities and potential of PIMs in addressing such complex optimization problems.
We introduce a framework for combinatorial optimization using sum-constrained continuous quadratic programs solvable by QCi's Dirac-3S photonic entropy computer. This is enabled by the Motzkin-Straus theorem which provides a powerful bridge between discrete clique problems and optimization over the probability simplex. We demonstrate this framework's versatility by solving constraint satisfaction problems, providing extensive benchmarks on the DIMACS suite. The Dirac-3S platform matches or outright leads two independently implemented classical baselines on more than four-fifths of the benchmark instances, reaching the best known solution on nearly all structured graph families, even outperforming both classical solvers on several of the largest instances tested. On the other hand, well-tuned classical continuous optimizers retain an edge only on the hardest planted-clique instances. This work establishes a viable pathway for solving combinatorial optimization problems using natively analog unconventional computing platforms, while positioning entropy computing as a competitive approach for navigating non-convex landscapes and providing rigorous baselines for an emerging computational paradigm.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
One of the key applications of near-term quantum computers has been the development of quantum optimization algorithms. However, these algorithms have largely been focused on qubit-based technologies. Here, we propose a hybrid quantum-classical approximate optimization algorithm for photonic quantum computing, specifically tailored for addressing continuous-variable optimization problems. Inspired by counterdiabatic protocols, our algorithm reduces the required quantum operations for optimization compared to adiabatic protocols. This reduction enables us to tackle non-convex continuous optimization within the near-term era of quantum computing. Through illustrative benchmarking, we show that our approach can outperform existing state-of-the-art hybrid adiabatic quantum algorithms in terms of convergence and implementability. Our algorithm offers a practical and accessible experimental realization, bypassing the need for high-order operations and overcoming experimental constraints. We conduct a proof-of-principle demonstration on Xanadu’s eight-mode nanophotonic quantum chip, successfully showcasing the feasibility and potential impact of the algorithm. The authors introduce a hybrid quantum-classical algorithm for photonic quantum computing that focuses on tackling continuous-variable optimization problems using fewer quantum operations than existing methods. The approach shows better performance and practical implementation potential, demonstrated on Xanadu’s quantum chip.
A study published on bioRxiv successfully formulated the complex combinatorial problem of fixed-backbone computational protein design as a quadratic Hamiltonian, naturally mapping it onto the hybrid photonic entropy computing platform, Dirac-3. Benchmarking results on protein instances ranging from 493 to 943 variables confirmed that the photonic solver derives high-precision solutions, reaching within 0.16–2.47% of optimal energies. By overcoming the sharp super-polynomial runtime growth of existing classical solvers and implementing near-linear polynomial scaling, it established a scalable framework capable of integrating quantum-inspired hardware into practical protein engineering pipelines. [Quantum Biology Society] Customized computational protein design is considered a core challenge in next-generation drug discovery and biotechnology. However, due to the enormous combinatorial complexity of amino acid sequence combinations, existing classical optimization methods have faced fatal computational bottlenecks. Recently, a groundbreaking study breaking through this massive computational barrier using quantum-inspired hardware based on the physics of light has been published, drawing significant attention. The paper "Entropy Quantum Computing for Fixed-Backbone Protein Design," published on the preprint repository bioRxiv, presents a pioneering demonstration of applying photon-based entropy computing to biotechnology. A joint research team led by Babak Emami from Quantum Computing Inc. (QCi) and Professor David J. Huggins from Weill Cornell Medicine spearheaded this innovative study. ■ Mapping Protein Design to a Physical Model of Light The research team newly formulated the amino acid rotamer variables of a protein with a fixed backbone into a physical energy function known as a quadratic Hamiltonian. This transformed optimization problem maps naturally onto Dirac-3, a hybrid photonic entropy computing platform. Instead of existing computers repeating complex numerical calculations via transistors, this is an innovative approach where an optical system utilizes thermodynamic entropy to guide itself toward the most stable ground energy state (the optimal solution). ■ Overwhelming Scalability Beyond Classical Limits The true value of this photonic solver was clearly revealed in benchmarking experiments on large protein instances ranging from 493 to 943 variables. While the existing classical solver (CFN-based) reached a practical operational limit with a sharp super-polynomial runtime growth beyond approximately 1,000 variables, the Dirac-3 platform firmly maintained a near-linear polynomial scaling. What is even more surprising is that while enjoying this computational speed advantage, the final derived solutions recorded a highly precise level, within 0.16–2.47% of the perfect optimal energy. ■ A Quantum Framework for Next-Generation Protein Engineering This demonstration proves the overwhelming viability that entropy-based quantum optimization can surpass the limits of existing supercomputers in highly dense sequence spaces. The framework established by the research team lays a physical foundation to seamlessly integrate quantum-inspired hardware into practical protein engineering and large-scale screening pipelines, dramatically eliminating the massive friction of conventional computational processes. In the near future, utilizing light and entropy computing, humanity may witness a revolutionary leap in designing novel enzymes and therapeutic antibodies—which do not exist in nature—in real time. https://www.biorxiv.org/content/10.64898/2026.02.20.706589v1
In this article, we take a close look at Entropy Quantum Computing (EQC), a computational paradigm developed by Quantum Computing Inc. (QCi), which deviates from mainstream quantum computing by embracing rather than battling environmental noise and decoherence arXiv:2407.04512 . In their words this approach purports EQC as an open quantum system that turns "entropy into super-power fuels of its computing engine". We show that some of the claims in the main article can be made more rigorous, and yet these are still not good enough to beat state of the art classical algorithms on conventional classical computers. Note that these conclusions reflect the technology's current early stage of development and are not meant to discourage its pursuit. Continued rigorous exploration is necessary to fully assess the long-term viability and potential advantages of this distinct computational approach.