相关论文: A Simple QUBO Formulation of Sudoku

Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…

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…

Combinatorial optimization problems, integral to various scientific and industrial applications, often vary significantly in their complexity and computational difficulty. Transforming such problems into Quadratic Unconstrained Binary…

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…

We study a system of linear equations associated with Sudoku latin squares. The coefficient matrix $M$ of the normal system has various symmetries arising from Sudoku. From this, we find the eigenvalues and eigenvectors of $M$, and compute…

Current hardware limitations restrict the potential when solving quadratic unconstrained binary optimization (QUBO) problems via the quantum approximate optimization algorithm (QAOA) or quantum annealing (QA). Thus, we consider training…

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…

We present a heuristic algorithm designed to solve Quadratic Unconstrained Binary Optimization (QUBO) problems efficiently. The algorithm, referred to as IC-D2S, leverages a hybrid approach using Ising and classical machines to address very…

The quantum backtracking algorithm proposed by Ashley Montanaro raised considerable interest, as it provides a quantum speed-up for a large class of classical optimization algorithms. It does not suffer from Barren-Plateaus and transfers…

The prospect of quantum solutions for complicated optimization problems is contingent on mapping the original problem onto a tractable quantum energy landscape, e.g. an Ising-type Hamiltonian. Subsequently, techniques like adiabatic…

Ising machines, including quantum annealing machines, are promising next-generation computers for combinatorial optimization problems. However, due to hardware limitations, most Ising-type hardware can only solve objective functions…

Recent works on quantum algorithms for solving semidefinite optimization (SDO) problems have leveraged a quantum-mechanical interpretation of positive semidefinite matrices to develop methods that obtain quantum speedups with respect to the…

We present PyQUBO, an open-source, Python library for constructing quadratic unconstrained binary optimizations (QUBOs) from the objective functions and the constraints of optimization problems. PyQUBO enables users to prepare QUBOs or…

We propose a new Quadratic Unconstrained Binary Optimization (QUBO) formulation of the Travelling Salesman Problem (TSP), with which we overcame the best formulation of the Vehicle Routing Problem (VRP) in terms of the minimum number of…

This paper explores the applications of quantum annealing (QA) and classical simulated annealing (SA) to a suite of combinatorial optimization problems in machine learning, namely feature selection, instance selection, and clustering. We…

Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function.…

It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in…

Rubik's Cube is one of the most famous combinatorial puzzles involving nearly $4.3 \times 10^{19}$ possible configurations. Its mathematical description is expressed by the Rubik's group, whose elements define how its layers rotate. We…

The problem of selecting an appropriate number of features in supervised learning problems is investigated in this paper. Starting with common methods in machine learning, we treat the feature selection task as a quadratic unconstrained…

Many computational problems involve optimization over discrete variables with quadratic interactions. Known as discrete quadratic models (DQMs), these problems in general are NP-hard. Accordingly, there is increasing interest in encoding…