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Branch-and-bound algorithms effectively solve combinatorial optimization problems, relying on the relaxation of the objective function to obtain tight lower bounds. While this is straightforward for convex objective functions, higher-order…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
We present a novel formulation of structural design optimization problems specifically tailored to be solved by quantum annealing (QA). Structural design optimization aims to find the best, i.e., material-efficient yet high-performance,…
Quadratic Unconstrained Binary Optimization (QUBO) problems are NP-hard problems and many real-world problems can be formulated as QUBO. Currently there are no algorithms known that can solve arbitrary instances of NP-hard problems…
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
In the field of quantum computing, combinatorial optimization problems are typically addressed using QUBO (Quadratic Unconstrained Binary Optimization) solvers. However, these solvers are often insufficient for tackling higher-order…
The RSA cryptosystem, which relies on the computational difficulty of prime factorization, faces growing challenges with the advancement of quantum computing. In this study, we propose a quantum annealing based approach to integer…
Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved…
Quantum Annealing (QA) and QAOA are promising quantum optimisation algorithms used for finding approximate solutions to combinatorial problems on near-term NISQ systems. Many NP-hard problems can be reformulated as Quadratic Unconstrained…
Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical…
Linear regression is a data analysis technique, which is categorized as supervised learning. By utilizing known data, we can predict unknown data. Recently, researchers have explored the use of quantum annealing (QA) to perform linear…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
In this paper, we propose a hybrid framework to solve large-scale permutation-based combinatorial problems effectively using a high-performance quadratic unconstrained binary optimization (QUBO) solver. To do so, transformations are…
Multi-Agent Path Finding (MAPF) remains a fundamental challenge in robotics, where classical centralized approaches exhibit exponential growth in joint-state complexity as the number of agents increases. This paper investigates Quadratic…
We address the problem of unsupervised disentanglement of discrete and continuous explanatory factors of data. We first show a simple procedure for minimizing the total correlation of the continuous latent variables without having to use a…
Abstraction layers are of paramount importance in software architecture, as they shield the higher-level formulation of payload computations from lower-level details. Since quantum computing (QC) introduces many such details that are often…
Quantum Approximate Optimization Algorithm (QAOA) can be used to solve quadratic unconstrained binary optimization (QUBO) problems. However, the size of the solvable problem is limited by the number of qubits. To leverage noisy…
In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of…
There is growing interest in solving computer vision problems such as mesh or point set alignment using Adiabatic Quantum Computing (AQC). Unfortunately, modern experimental AQC devices such as D-Wave only support Quadratic Unconstrained…