Related papers: Modeling Linear Inequality Constraints in Quadrati…
Quantum Approximate Optimization Algorithm (QAOA) enables solving combinatorial optimization problems on quantum computers by optimizing variational parameters for quantum circuits. We investigate a simplified approach that combines linear…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
Optimisation algorithms designed to work on quantum computers or other specialised hardware have been of research interest in recent years. Many of these solver can only optimise problems that are in binary and quadratic form. Quadratic…
We propose an approach to solving constrained combinatorial optimization problems based on embedding the concept of Lagrangian duality into the framework of adiabatic quantum computation. Within the setting of circuit-model fault-tolerant…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
Solving hard optimization problems is one of the most promising application domains for quantum computers due to the ubiquity of such problems in industry and the availability of broadly applicable quantum speedups. However, the ability of…
Variational Quantum Algorithms (VQAs) are a class of hybrid quantum-classical algorithms that leverage on classical optimization tools to find the optimal parameters for a parameterized quantum circuit. One relevant application of VQAs is…
In variational quantum algorithms, constraints are usually added to the problem objective via penalty terms. For linear inequality constraints, this procedure requires additional slack qubits. Those extra qubits tend to blow up the search…
We revisit a formulation technique for inequality constrained optimization problems that has been known for decades: the substitution of squared variables for nonnegative variables. Using this technique, inequality constraints are converted…
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…
We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary $k$-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the…
Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…
Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
Quantum enhanced optimization of classical cost functions is a central theme of quantum computing due to its high potential value in science and technology. The variational quantum eigensolver (VQE) and the quantum approximate optimization…
Variational Quantum Algorithm (VQA) is a hybrid algorithm for noisy quantum devices. However, statistical fluctuations and physical noise degrade the solution quality, so it is difficult to maintain applicability for large-scale problems.…
To arrive at some viable product design, product development processes frequently use numerical simulations and mathematical programming techniques. Topology optimization, in particular, is one of the most promising techniques for…
Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class…
The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which…
Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a…
In black-box combinatorial optimization, objective evaluations are often expensive, so high quality solutions must be found under a limited budget. Factorization machine with quantum annealing (FMQA) builds a quadratic surrogate model from…