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Quadratic Unconstrained Binary Optimization (QUBO) is a combinatorial optimization to find an optimal binary solution vector that minimizes the energy value defined by a quadratic formula of binary variables in the vector. As many NP-hard…
Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that…
Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum…
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In…
Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…
In recent years, reinforcement learning has seen interest because of deep Q-Learning, where the model is a convolutional neural network. Deep Q-Learning has shown promising results in games such as Atari and AlphaGo. Instead of learning the…
We introduce SudoQ, a quantum version of the classical game Sudoku. Allowing the entries of the grid to be (non-commutative) projections instead of integers, the solution set of SudoQ puzzles can be much larger than in the classical…
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between…
Gauss proposed the problem of how to enumerate the number of solutions for placing $N$ queens on an $N\times N$ chess board, so no two queens attack each other. The N-queen problem is a classic problem in combinatorics. We describe a…
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…
The Quadratic Unconstrained Binary Optimization (QUBO) problems are NP hard; thus, so far, there are no algorithms to solve them efficiently. There are exact methods like the Branch-and-Bound algorithm for smaller problems, and for larger…
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
Practically relevant problems of quadratic optimization often contain multidimensional arrays of variables interconnected by linear constraints, such as equalities and inequalities. The values of each variable depend on its specific meaning…
This paper introduces the application of the Brain Drain Optimization algorithm -- a swarm-based metaheuristic inspired by the emigration of intellectual elites -- to the N-Queens problem. The N-Queens problem, a classic combinatorial…
This paper explores the application of Quadratic Unconstrained Binary Optimization (QUBO) models in solving the Travelling Salesman Problem (TSP) through Quantum Annealing algorithms and Graph Neural Networks. Quantum Annealing (QA), a…
Database systems encompass several performance-critical optimization tasks, such as join ordering and index tuning. As data volumes grow and workloads become more complex, these problems have become exponentially harder to solve…
The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary…
In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer…
Classical reinforcement learning (RL) aims to optimize the expected cumulative rewards. In this work, we consider the RL setting where the goal is to optimize the quantile of the cumulative rewards. We parameterize the policy controlling…