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Noisy intermediate-scale quantum computers (NISQ computers) are now readily available, motivating many researchers to experiment with Variational Quantum Algorithms (VQAs). Among them, the Quantum Approximate Optimization Algorithm (QAOA)…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
The Vehicle Routing Problem (VRP) is a fundamental combinatorial optimization challenge with broad applications in logistics and transportation. In this work, we present a quantum-assisted framework that integrates the Quantum Approximate…
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…
The Single-Source Shortest Path (SSSP) problem is a cornerstone of computer science with vast applications, for which Dijkstra's algorithm has long been the classical baseline. While various quantum algorithms have been proposed, their…
Flexible Job Shop Scheduling (FJSSP) is a complex optimization problem crucial for real-world process scheduling in manufacturing. Efficiently solving such problems is vital for maintaining competitiveness. This paper introduces Quantum…
The search for quantum algorithms to tackle classical combinatorial optimization problems has long been one of the most attractive yet challenging research topics in quantum computing. In this context, variational quantum algorithms (VQA)…
Quantum algorithms are of great interest for their possible use in optimization problems. In particular, variational algorithms that use classical counterparts to optimize parameters hold promise for use in currently existing devices.…
Despite much recent work, the true promise and limitations of the Quantum Alternating Operator Ansatz (QAOA) are unclear. A critical question regarding QAOA is to what extent its performance scales with the input size of the problem…
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 Quantum Approximate Optimization Algorithm (QAOA) is suggested as a promising application on early quantum computers. Here, a quantum-inspired classical algorithm, the mean-field Approximate Optimization Algorithm (mean-field AOA), is…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
We present a hybrid classical/quantum algorithm for efficiently solving the eigenvalue problem of many-particle Hamiltonians on quantum computers with limited resources by splitting the workload between classical and quantum processors.…
Constrained binary optimization aims to find an optimal assignment to minimize or maximize the objective meanwhile satisfying the constraints, which is a representative NP problem in various domains, including transportation, scheduling,…
Combinatorial optimization models a vast range of industrial processes aiming at improving their efficiency. In general, solving this type of problem exactly is computationally intractable. Therefore, practitioners rely on heuristic…
The practical use of many types of near-term quantum computers requires accounting for their limited connectivity. One way of overcoming limited connectivity is to insert swaps in the circuit so that logical operations can be performed on…
Quantum Computing is an emerging paradigm which is gathering a lot of popularity in the current scientific and technological community. Widely conceived as the next frontier of computation, Quantum Computing is still at the dawn of its…
We present benchmarks of the parity transformation for the Quantum Approximate Optimization Algorithm (QAOA). We analyse the gate resources required to implement a single QAOA cycle for real-world scenarios. In particular, we consider…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…
Current hardware limitations restrict the potential when solving quadratic unconstrained binary optimization (QUBO) problems via the quantum approximate optimization algorithm (QAOA) or quantum annealing (QA). Thus, we consider training…