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Adiabatic quantum algorithms represent a promising approach to universal quantum computation. Whilst in a closed system these algorithms are limited by avoided level crossings, where the gap becomes exponentially small in the system size,…
We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…
In a previous publication we proposed discrete global optimization as a method to train a strong binary classifier constructed as a thresholded sum over weak classifiers. Our motivation was to cast the training of a classifier into a format…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
The Traveling Salesman Problem is a classical NP-hard combinatorial optimization problem that has been extensively studied in operations research. A major challenge in Traveling Salesman Problem formulations is the large number of subtour…
This paper proposes a novel multi-target tracking (MTT) algorithm for scenarios with arbitrary numbers of measurements per target. We propose the variational probabilistic multi-hypothesis tracking (VPMHT) algorithm based on the variational…
We propose digitized-counterdiabatic quantum optimization (DCQO) to achieve polynomial enhancement over adiabatic quantum optimization for the general Ising spin-glass model, which includes the whole class of combinatorial optimization…
We propose digitized counterdiabatic quantum sampling (DCQS), a hybrid quantum-classical algorithm for efficient sampling from energy-based models, such as low-temperature Boltzmann distributions. The method utilizes counterdiabatic…
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
We introduce a counter-diabatic approach for deriving Hamiltonians modeling superchargable quantum batteries (QBs). A necessary requirement for the supercharging process is the existence of multipartite interactions among the cells of the…
A promising approach to solving hard binary optimisation problems is quantum adiabatic annealing (QA) in a transverse magnetic field. An instantaneous ground state --- initially a symmetric superposition of all possible assignments of $N$…
A hybrid quantum-classical algorithm is a computational scheme in which quantum circuits are used to extract information that is then processed by a classical routine to guide subsequent quantum operations. These algorithms are especially…
Combinatorial optimization plays a crucial role in many industrial applications. While classical computing often struggles with complex instances, quantum optimization emerges as a promising alternative. Here, we present an enhanced…
The increasing scale and nonlinearity of modern energy and power system problems pose significant challenges to classical numerical solvers. In parallel, advances in quantum and quantum-inspired hardware are expected to improve scalability…
Combinatorial optimization problems are ubiquitous and computationally hard to solve in general. Quantum approximate optimization algorithm (QAOA), one of the most representative quantum-classical hybrid algorithms, is designed to solve…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum…
Numerous established machine learning models and various neural network architectures can be restructured as Quadratic Unconstrained Binary Optimization (QUBO) problems. A significant challenge in Adiabatic Quantum Machine Learning (AQML)…
We propose a general, fully gate-based quantum algorithm for counterdiabatic driving. The algorithm does not depend on heuristics as in previous variational methods, and exploits regularisation of the adiabatic gauge potential to suppress…
Quantum annealing (QA) is one of the efficient methods to calculate the ground-state energy of a problem Hamiltonian. In the absence of noise, QA can accurately estimate the ground-state energy if the adiabatic condition is satisfied.…