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In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the…
Variational Quantum Eigensolver (VQE) algorithm is one of few approaches where the hope for near-term quantum advantage concentrates. However, they face challenges connected with measurement stochastic noise, barren plateaus, and…
Solving combinatorial optimization problems using variational quantum algorithms (VQAs) has emerged as a promising research direction. Since the introduction of the Quantum Approximate Optimization Algorithm (QAOA), numerous variants have…
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…
Traffic optimization on roads is a highly complex problem, with one important aspect being minimization of traffic congestion. By mapping to an Ising formulation of the traffic congestion problem, we benchmark solutions obtained from the…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
The ability of the Quantum Approximate Optimization Algorithm (QAOA) to deliver a quantum advantage on combinatorial optimization problems is still unclear. Recently, a scaling advantage over a classical solver was postulated to exist for…
Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications,…
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
The design of a good algorithm to solve NP-hard combinatorial approximation problems requires specific domain knowledge about the problems and often needs a trial-and-error problem solving approach. Graph coloring is one of the essential…
The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is…
Variational quantum eigensolver (VQE) is regarded as a promising candidate of hybrid quantum-classical algorithm for the near-term quantum computers. Meanwhile, VQE is confronted with a challenge that statistical error associated with the…
A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily…
We propose an Indirect Quantum Approximate Optimization Algorithm (referred to as IQAOA) where the Quantum Alternating Operator Ansatz takes into consideration a general parameterized family of unitary operators to efficiently model the…
We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
Practical applicability of quantum optimisation on near term devices is constrained by limited qubit counts and hardware noise, which restricts the scalability of quantum optimisation algorithms for combinatorial problems. The simulation of…
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…
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…
The Quantum Approximate Optimization Algorithm (QAOA) is expected to offer advantages over classical approaches when solving combinatorial optimization problems in the Noisy Intermediate-Scale Quantum (NISQ) era. In its standard…