Quadratic unconstrained binary optimization (QUBO) has gained popularity over the past ten years both for the wide range of problems that can be expressed in this form and for its compatibility with many quantum computing architectures. More recently, quantum annealers have advanced to the point where the scaling of qubits makes real-world applications increasingly feasible; however, current architectures remain restricted to solving quadratic unconstrained binary optimization problems, which can represent at most two-body interactions. Here we systematically examine the shortcomings of the QUBO framework and modern quantum annealers through the lens of the high-dimensional, exponentially scaling problem of RNA structure prediction, and find results that are generalizable to QUBO formalisms writ large. We find that using the QUBO framework to predict RNA structures results in poor accuracy, which becomes worse as system size scales. We determine that the fundamental constraint of two-body interactions prevents emergent correlations in the system, which are crucial to accurate structure prediction. Furthermore, we highlight that explicit, higher-order, empirical terms that are needed to improve structure prediction are incompatible with a QUBO framework. Finally, we show that our energy landscape has many deep local minima, which lead to local minima trapping and prevent permutation invariance. The relevance of these findings to other applications of QUBO, and therefore to modern quantum annealers more broadly, are discussed, with our work providing the first explicit explanation of why these formalisms have failed and will continue to fail in high-dimensional systems with similar constraints.
Quadratic unconstrained binary optimization (QUBO) has gained popularity over the past ten years both for the wide range of problems that can be expressed in this form and for its compatibility with many quantum computing architectures. More recently, quantum annealers have advanced to the point where the scaling of qubits makes real-world applications increasingly feasible; however, current architectures remain restricted to solving quadratic unconstrained binary optimization problems, which can represent at most two-body interactions. Here we systematically examine the shortcomings of the QUBO framework and modern quantum annealers through the lens of the high-dimensional, exponentially scaling problem of RNA structure prediction, and find results that are generalizable to QUBO formalisms writ large. We find that using the QUBO framework to predict RNA structures results in poor accuracy, which becomes worse as system size scales. We determine that the fundamental constraint of two-body interactions prevents emergent correlations in the system, which are crucial to accurate structure prediction. Furthermore, we highlight that explicit, higher-order, empirical terms that are needed to improve structure prediction are incompatible with a QUBO framework. Finally, we show that our energy landscape has many deep local minima, which lead to local minima trapping and prevent permutation invariance. The relevance of these findings to other applications of QUBO, and therefore to modern quantum annealers more broadly, are discussed, with our work providing the first explicit explanation of why these formalisms have failed and will continue to fail in high-dimensional systems with similar constraints.
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while learning-based algorithms face challenges in obtaining high-quality training data. Recently, quantum annealer has rapidly predicted the folding of the secondary structure, highlighting that quantum computing is a promising solution to this problem. However, gate model algorithms for universal quantum computing are not available. In this paper, gate-based quantum algorithms will be presented, which are highly flexible and can be applied to various physical devices. Mapped all possible secondary structure to the state of a quadratic Hamiltonian, the whole folding process is described as a quadratic unconstrained binary optimization model. Then the model can be solved through quantum approximation optimization algorithm. We demonstrate the performance with both numerical simulation and experimental realization. Throughout our benchmark dataset, simulation results suggest that our quantum approach is comparable in accuracy to classical methods. For non-nested sequences, our quantum approach outperforms classical energy-based methods. Experimental results also indicate our method is robust in current noisy devices. It is the first instance of universal quantum algorithms being employed to tackle RNA folding problems, and our work provides a valuable model for utilizing universal quantum computers in solving RNA folding problems.
Biomolecules and their interactions form the material and processual basis underlying all biological phenomena, from photosynthesis to Alzheimer’s disease. Studying these systems is therefore central to the purview of all biological sciences. Computational biomolecular structure prediction (CBSP) supports this effort by leveraging computers to determine, model, and engineer biomolecular structures, properties, and processes—offering a powerful complement to laboratory-based methods. However, many core CBSP problems—such as finding minimum free energy or conformationally-stable structures given sequence information—are computationally challenging. These problems are typically NP-hard in their general form, while their corresponding decision variants are NP-complete. As a result, both formulations are resistant to efficient exact solution at large scales. Quantum computing, a developing computational paradigm leveraging quantum mechanics, offers a potential path forward, given recent evidence suggesting that certain quantum approaches may reduce resource demands for certain NP-hard problem families. Approaches include fully quantum algorithms, quantum-inspired classical heuristics, and hybrid quantum-classical frameworks, all of which may help address long-standing computational bottlenecks in CBSP. This dissertation offers a preliminary investigation of the practical potential of quantum computing for three core CBSP challenges—RNA folding, multi-body molecular docking, and protein design—that, despite their diverse applications, share structural features well suited to exploration by quantum optimization methods. Specifically, we cast each problem as a cost function network (CFN), and develop transformations of these CFNs to quadratic unconstrained binary optimization (QUBO) models in order to render them compatible with current quantum and quantum-inspired hardware. We argue that these transformations not only broaden the range of solvable CFNs across quantum platforms, but in some cases possess intrinsic features which may offer optimization advantages over native CFN formulations. Using a current‑generation superconducting flux‑qubit quantum annealer, we: (a) demonstrate its use for tuning free QUBO parameters against biomolecular structure data, and (b) benchmark solution quality and resource usage against optimized classical Monte Carlo methods, finding comparable performance. Finally, we package these methods into the Masala Quantum Computing Plugins library, an open‑source, modular CBSP platform that supports CFN construction, multiple QUBO encodings (one‑hot, domain‑wall, approximate‑binary, hybrid), and execution on both classical and quantum backends. Our contribution lays the groundwork for extensible, state‑of‑the‑art, quantum-compatible CBSP workflows.
Abstract Quantum annealing aims at solving optimization problems of practical relevance using quantum-computing hardware. Problems of interest are typically formulated in terms of quadratic unconstrained binary optimization (QUBO) Hamiltonians. However, many optimization problems are much more naturally formulated in terms of polynomial unconstrained binary optimization (PUBO) functions of higher order. As we show with various problem examples, leveraging the PUBO formulation can bring considerable savings in terms of required number of qubits. Moreover, in numerical benchmarks for the paradigmatic 3-SAT problem, we find scenarios where the scaling of the minimum energy gap during the optimization sweep differs significantly, suggesting the possibility of an exponentially faster annealing time when using the PUBO as compared to the QUBO formulation. This advantage persists even when considering the overhead caused by the higher-order interactions necessary for PUBO cost Hamiltonians. As an interesting side effect, the analysis on minimum energy gaps of different 3-SAT instance generators reveals different degrees of hardness, which will be of interest also for classical benchmark calculations. Our findings show a promising path to improving the resource efficiency and sweeping speed of quantum annealing protocols on both analog and digital platforms, which are important prerequisites when aiming at solving larger optimization problems with relevance to industry.
Molecular docking, which aims to find the most stable interacting configuration of a set of molecules, is of critical importance to drug discovery. Although a considerable number of classical algorithms have been developed to carry out molecular docking, most focus on the limiting case of docking two molecules. Since the number of possible configurations of N molecules is exponential in N, those exceptions which permit docking of more than two molecules scale poorly, requiring exponential resources to find high-quality solutions. Here, we introduce a one-hot encoded quadratic unconstrained binary optimization formulation (QUBO) of the multibody molecular docking problem, which is suitable for solution by quantum annealer. Our approach involves a classical pre-computation of pairwise interactions, which scales only quadratically in the number of bodies while permitting well-vetted scoring functions like the Rosetta REF2015 energy function to be used. In a second step, we use the quantum annealer to sample low-energy docked configurations efficiently, considering all possible docked configurations simultaneously through quantum superposition. We show that we are able to minimize the time needed to find diverse low-energy docked configurations by tuning the strength of the penalty used to enforce the one-hot encoding, demonstrating a 3-4 fold improvement in solution quality and diversity over performance achieved with conventional penalty strengths. By mapping the configurational search to a form compatible with current- and future-generation quantum annealers, this work provides an alternative means of solving multibody docking problems that may prove to have performance advantages for large problems, potentially circumventing the exponential scaling of classical approaches and permitting a much more efficient solution to a problem central to drug discovery and validation pipelines.
Lattice-based post-quantum cryptography relies on the hardness of the Learning With Errors (LWE) and Module Learning With Errors (MLWE) problems. This work introduces a constructive framework for encoding small MLWE instances as Quadratic Unconstrained Binary Optimization (QUBO) models suitable for quantum annealing. The formulation jointly represents secret coefficients and explicit error variables within a unified binary optimization structure, enabling their simultaneous recovery from the ground-state solution. Beyond the encoding, we develop a stability analysis of the resulting optimization landscape under additive perturbations. We show that the admissible noise region forms a convex polytope defined by competing candidate secrets, and establish an equivalent characterization in terms of the QUBO energy gap between the optimal and second-best solutions. Numerical experiments on low-dimensional benchmark instances using exact simulation demonstrate correct recovery of both secret and discretized error vectors, and confirm consistency between geometric stability regions and energy-gap behavior. We further quantify the scaling of logical variables and embedding overhead with increasing MLWE dimensions to assess feasibility on quantum annealing architectures. The results establish a systematic connection between MLWE problems and quantum optimization while providing a framework for analyzing robustness properties of QUBO formulations. Although current quantum annealing hardware remains insufficient for cryptographically relevant parameters, the proposed methodology offers a structured basis for studying lattice-based problems in quantum optimization settings without implying a practical threat to standardized post-quantum schemes.
Quantum Optimization (QO) is emerging as a promising approach to tackle hard combinatorial optimization problems by leveraging the unique computational properties of quantum hardware. In recent years, QO has gained traction in Machine Learning (ML), where problems such as clustering and vector quantization can be naturally expressed as Quadratic Unconstrained Binary Optimization (QUBO) problems. These ML applications often involve complex, high-dimensional data, which directly influences both the structure and scale of the resulting QUBO formulations. However, current quantum devices fall under the category of Noisy Intermediate-Scale Quantum (NISQ) hardware, which imposes significant limitations on qubit counts and small error rates. This dissertation investigates the impact of data complexity and data scale—as encountered in ML settings—on the effectiveness and feasibility of QO on NISQ devices. We propose novel, hardware-aware methods to overcome these challenges. The first part of this thesis focuses on the effect of data complexity for QO. We analyze how problem structure—particularly when QUBO formulations are derived from ML tasks—affects quantum solvability. We identify the spectral gap as a key factor in the success of adiabatic quantum algorithms and provide a theoretical and empirical analysis linking data-induced complexity to optimization performance.To address noise sensitivity and limited precision, we introduce a preprocessing framework based on a principled Branch-and-Bound algorithm that reduces dynamic range while preserving global optima. This improves robustness on both quantum annealers and classical solvers. In the second part, the thesis addresses challenges introduced by data scale. First, we propose a recursive Divide-and-Conquer strategy that breaks down large QUBO problems into tractable subproblems, demonstrated through an application to Bundle Adjustment in 3D scene reconstruction. Second, we introduce a variable and constraint generation method inspired by column generation for Integer Linear Programming, enabling dynamic QUBO size growth. This technique is successfully applied to Multi-Agent Pathfinding, where it scales well on NISQ devices while maintaining compatibility with classical solvers. Finally, we explore QUBO reformulations that reduce problem size through compact encodings and cyclic expansion, enabling the use of quantum hardware for tasks such as FPGA placement in chip design. Across all contributions, the developed algorithms are evaluated both theoretically and empirically, with experiments conducted on real quantum and quantum-inspired hardware. These methods significantly improve solution quality, scalability, and hardware compatibility, paving the way for more effective use of QO in practical settings. While tailored for NISQ era constraints, the results remain relevant for fault-tolerant quantum computing, offering insights into the long-term viability of QO across hardware generations.