Techniques for Adapting Problems to Quantum Computing

Quantum optimization is ultimately about achieving computational advantage on hard optimization problems. Achieving that advantage may require taking a step back and asking where quantum computing offers a different lens on problem structure. This does not mean replacing classical optimization methods. It means combining quantum and classical capabilities in ways that make the best use of each.    Warm-starting quantum optimization is one example. It shows how information from one optimization method can guide another, and points toward broader workflows where quantum and classical routines inform each other across different stages of the optimization process. See, for example: https://lnkd.in/e3t6Zrgr    Another opportunity lies in problem representation. Quantum may be valuable by enabling representations that are more natural on quantum hardware and less directly accessible to classical methods. For some optimization problems, a standard formulation may appear dense or otherwise difficult to exploit, while a quantum-accessible representation may expose structure that can be used algorithmically.    Building on this idea, a recent IBM Research paper shows how Fourier-based representations can change the trade-offs in quantum optimization. The work demonstrates how certain complex interactions can be represented through simpler quantum circuits, trading circuit complexity for sampling overhead and expanding the range of interactions that may be practical to implement on quantum hardware. It provides a concrete example of how a different representation can change the algorithmic trade-offs, while fitting naturally into quantum-classical optimization workflows.    Ultimately, progress in quantum optimization may come from changing how we look at the problem: through better representations, smarter decompositions, and principled quantum-classical design. Link to paper: https://lnkd.in/eaMfc8Dg 

Getting to a reasonable quantum computing use cases is quite difficult because the path from an actual problem to something that can plausibly show exponential advantage on a quantum computer is long, technical, and full of places where the idea can fall apart. My own view is that, on today’s NISQ-era machines, the only category that still has a real chance of reaching advantage-sized problems is quantum simulation. But even there, the key requirement is often underestimated: you need a very clear-cut, simplified Hamiltonian that maps to the quantum computer without destroying the structure that made the problem interesting in the first place. If the mapping has to many uncontrolled approximations, or if the observable becomes disconnected from what a user actually wants, you are done. That is why I like to think in terms of the ITBQ scheme. Identify: If you cannot say what you compute and why it matters, nothing downstream will save it….. but purely starting from an important problem doesn’t do it either. You need a problem that is clearly defined, where an exponential speedup is at least thinkable, and where the output variables translate to a concrete gain for the user. Transform: then comes the real work. Turn that problem into a simplified Hamiltonian that still represents the relevant physics, and that fits the constraints of quantum hardware. Benchmark: and before you even start arguing about quantum advantage, you need to know what the best classical methods can do on the same task, with the same assumptions, for the same observables. Otherwise you are comparing against a strawman, and you will end up optimizing the wrong thing. If you are interested in working through these steps and then comparing them to a quantum approach, take a look at our use case examples on HQStage. They are built to make the Hamiltonians, the assumptions, and the classical baselines very clear. And we hope, quantum enthusiasts will manage the last step towards quantum advantage! Links in the comments

Happy to share that our paper “Solving mixed-integer problems as QUBO: Encodings, reformulations, and rolling-precision algorithm” has been published in Computers & Chemical Engineering. This work grew out of a simple but important modeling challenge: many optimization problems in engineering are naturally formulated as mixed-integer programs, with continuous variables, integer decisions, and explicit constraints. In contrast, QUBO-based optimization frameworks, including quantum annealing workflows, are built around binary quadratic unconstrained models. In this paper, we explore how to bridge that gap. We present a mixed-integer-to-QUBO framework that combines variable encoding, constraint reformulation, and a rolling-precision strategy for solving a sequence of QUBO problems at increasing levels of numerical refinement. The goal is not to build one very large high-precision QUBO from the start, but to refine the representation gradually and keep individual QUBO sizes more manageable. Some of the key components of the work include decimal-precision encodings for bounded continuous and slack variables, QUBO reformulations for several classes of mixed-integer optimization problems, and two rolling-precision strategies: sequential bit-growth and constant-size zoom-in. What we particularly enjoyed about this project is that it sits at the interface of mathematical programming, process systems engineering, and emerging quantum optimization methods. There are still many open questions in this area — especially around penalty selection, scalability, hardware limitations, and solver performance — but I hope this work provides a useful modeling step toward making QUBO-based optimization more accessible for realistic engineering problems. Excellent work by incredible Ashfaq Iftakher and I am grateful to Professor Metin Turkay for the wonderful collaboration and many thoughtful discussions throughout this work. Paper (free download): https://lnkd.in/gYukn9s6 Code: https://lnkd.in/giEWtT-q We would be happy to hear thoughts from colleagues working at the interface of optimization, quantum computing, process systems engineering, and related applications. #Optimization #QUBO #MixedIntegerProgramming #QuantumOptimization #ProcessSystemsEngineering #ChemicalEngineering

Harnessing Quantum Noise to Solve 3SAT on Neutral Atom Quantum Processors Introduction: A New Take on a Classic Computational Challenge Analog Physics introduces a bold methodology that embraces quantum noise instead of fighting it, using it as a computational tool for solving the notoriously difficult 3SAT problem. Implemented on neutral atom quantum processors, this noise-advantaged streaming solver reimagines how quantum systems can tackle NP-complete problems, turning a typical liability—quantum decoherence—into a strategic advantage. What is the 3SAT Problem? 3SAT (3-Satisfiability) is a classic problem in computational theory where the goal is to determine whether a Boolean formula, composed of multiple clauses each containing exactly three variables or their negations (called literals), can be made TRUE by some assignment of TRUE/FALSE values. The formula is structured as a conjunction (AND) of clauses, and each clause is a disjunction (OR) of three literals. 3SAT is NP-complete, meaning it is representative of some of the most computationally hard problems. Solving it efficiently would transform our understanding of what computers can do. Key Technological Innovations Quantum Attention Model (QAM)  QAM guides noisy quantum processes to focus on promising regions of the solution space, effectively using stochastic behavior to improve problem exploration. Hofstadter-Möbius Loop Architecture  This architectural framework enables dynamic, constraint-streaming solving of 3SAT problems, optimizing both memory use and processing efficiency with O(n·log(n)) scaling. Neutral Atom Implementation  The solver is adapted for neutral atom quantum systems, such as QuEra’s 256-qubit device, ensuring more robust performance and compatibility with a broader range of quantum platforms. Benefits of the Noise-Advantaged Approach Reduces Error Correction Needs  Instead of suppressing noise, the algorithm uses it constructively—reducing the resource overhead required for quantum error correction. Improves Exploration and Efficiency  Natural randomness in quantum behavior enhances exploration of possible solutions, leading to faster convergence in high-dimensional search spaces. Scalable to Real-World Problems  The system scales efficiently, opening the door to solving larger and more complex optimization tasks beyond small experimental benchmarks. Why This Matters: A Paradigm Shift in Quantum Optimization Analog Physics’ approach represents a fundamental rethinking of noise in quantum computing—from an error to an ally. By leveraging inherent quantum fluctuations, the team demonstrates how even notoriously hard problems like 3SAT can benefit from noisy architectures. This innovation not only advances quantum algorithm design but also strengthens the case for hybrid analog-digital computing architectures in real-world problem-solving. Analog Physics  QAI.AI