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In the past years, many quantum algorithms have been proposed to tackle hard combinatorial problems. These algorithms, which have been studied in depth in complexity theory, are at the heart of many industrial applications. In particular,…
Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary near intermediate-scale quantum (NISQ) era. The quantum approximate optimisation algorithm (QAOA)…
Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling combinatorial optimization challenges. However, their practical realization confronts a dilemma: the requisite circuit depth for…
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…
The Quantum Approximate Optimization Algorithm can be applied to search problems on graphs with a cost function that is a sum of terms corresponding to the edges. When conjugating an edge term, the QAOA unitary at depth p produces an…
In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs.…
We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific…
Combinatorial optimization is regarded as a potentially promising application of near and long-term quantum computers. The best-known heuristic quantum algorithm for combinatorial optimization on gate-based devices, the Quantum Approximate…
The quantum approximate optimization algorithm (QAOA) can require considerable processing time for developers to test and debug their codes on expensive quantum devices. One avenue to circumvent this difficulty is to use the error maps of…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
We propose and implement a quantum-informed reduction algorithm for the maximum independent set problem that integrates classical kernelization techniques with information extracted from quantum devices. Our larger framework consists of…
This work presents a graph neural network (GNN) framework for solving the maximum independent set (MIS) problem, inspired by dynamic programming (DP). Specifically, given a graph, we propose a DP-like recursive algorithm based on GNNs that…
Approximate combinatorial optimisation has emerged as one of the most promising application areas for quantum computers, particularly those in the near term. In this work, we focus on the quantum approximate optimisation algorithm (QAOA)…
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…
The Maximum Weighted Independent Set (MWIS) problem, which considers a graph with weights assigned to nodes and seeks to discover the "heaviest" independent set, that is, a set of nodes with maximum total weight so that no two nodes in the…
Variational Quantum Algorithms (VQAs), such as the Quantum Approximate Optimization Algorithm (QAOA), offer a promising route to tackling combinatorial optimization problems on near and intermediate-term quantum devices. However, their…
A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more…
We investigate the Maximum Cut (MaxCut) problem on different graph classes with the Quantum Approximate Optimization Algorithm (QAOA) using symmetries. In particular, heuristics on the relationship between graph symmetries and the…
The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization…
Variational quantum algorithms offer fascinating prospects for the solution of combinatorial optimization problems using digital quantum computers. However, the achievable performance in such algorithms and the role of quantum correlations…