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Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function…
Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from carefully prepared Ansatz quantum circuits. However, current quantum computers are limited…
Advancements in Quantum Computing (QC) and Neural Combinatorial Optimization (NCO) represent promising steps in tackling complex computational challenges. On the one hand, Variational Quantum Algorithms such as QAOA can be used to solve a…
Benchmarking the performance of quantum optimization algorithms is crucial for identifying utility for industry-relevant use cases. Benchmarking processes vary between optimization applications and depend on user-specified goals. The…
Combinatorial optimization is widely regarded as a primary application for near-term quantum processors, although a definitive demonstration of the practical quantum advantage remains elusive. Recent studies have reported that both…
A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum…
As quantum computing advances, quantum approximate optimization algorithms (QAOA) have shown promise in addressing combinatorial optimization problems. However, the limitations of Noisy Intermediate Scale Quantum (NISQ) devices hinder the…
The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview…
Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are…
Many recent investigations conclude, based on asymptotic complexity analyses, that quantum computers could accelerate combinatorial optimization (CO) tasks relative to a purely classical computer. However, asymptotic analysis alone cannot…
Large-scale optimization problems are prevalent in several fields, including engineering, finance, and logistics. However, most optimization problems cannot be efficiently encoded onto a physical system because the existing quantum samplers…
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
Quantum Annealing (QA) and QAOA are promising quantum optimisation algorithms used for finding approximate solutions to combinatorial problems on near-term NISQ systems. Many NP-hard problems can be reformulated as Quadratic Unconstrained…
Quantum variational algorithms are one of the most promising applications of near-term quantum computers; however, recent studies have demonstrated that unless the variational quantum circuits are configured in a problem-specific manner,…
Quantum annealers aim at solving non-convex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists in designing a classical energy function whose ground states are the sought…
The Quantum Approximate Optimization Algorithm (QAOA) was originally developed to solve combinatorial optimization problems, but has become a standard for assessing the performance of quantum computers. Fully descriptive benchmarking…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attraction in recent years. Currently, most works have focused on single-objective problems, whereas many real-world applications need to consider…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…