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Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…
Simulated annealing (SA) is a key algorithm for solving combinatorial optimization problems, which model numerous real-world systems. While SA is commonly used to solve quadratic unconstrained binary optimization (QUBO) problems, many…
In experimental High-Energy Physics, unfolding refers to the problem of estimating the underlying distribution of a physical observable from detector-level data, in the presence of statistical fluctuations and systematic uncertainties.…
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…
We demonstrate that the search space of the quadratic assignment problem (QAP), known as an NP-hard combinatorial optimization problem, can be reduced using Grover adaptive search (GAS) with permutation preparation operator (PPO). To that…
Leveraging quantum computers for optimization problems holds promise across various application domains. Nevertheless, utilizing respective quantum computing solvers requires describing the optimization problem according to the Quadratic…
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…
Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the…
Variational Quantum Algorithms (VQAs) provide a promising framework for tackling complex optimization problems on near-term quantum hardware. Here, we demonstrate that hybrid qubit--qumode quantum devices offer an efficient route to solving…
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…
Ising machines are next-generation computers expected to efficiently sample near-optimal solutions of combinatorial optimization problems. Combinatorial optimization problems are modeled as quadratic unconstrained binary optimization (QUBO)…
In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a…
This article describes how to solve Sudoku puzzles using Quadratic Unconstrained Binary Optimization (QUBO). To this end, a QUBO instance with 729 variables is constructed, encoding a Sudoku grid with all constraints in place, which is then…
This work presents a novel tensor network algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, Quadratic Unconstrained Discrete Optimization (QUDO) problems, and Tensor Quadratic Unconstrained Discrete…
The quantum approximate optimization algorithm (QAOA) is designed to determine optimum and near optimum solutions of quadratic (and higher order) unconstrained binary optimization (QUBO or HUBO) problems, which in turn accurately model…
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 introduce a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation method for spanning tree problems. Instead of encoding the presence of edges in the tree individually, we opt to encode spanning trees as a permutation…
We introduce a novel approach to translate arbitrary 3-SAT instances to Quadratic Unconstrained Binary Optimization (QUBO) as they are used by quantum annealing (QA) or the quantum approximate optimization algorithm (QAOA). Our approach…
Many artificial intelligence (AI) problems naturally map to NP-hard optimization problems. This has the interesting consequence that enabling human-level capability in machines often requires systems that can handle formally intractable…