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The quantum approximate optimization algorithm (QAOA) is a variational method for noisy, intermediate-scale quantum computers to solve combinatorial optimization problems. Quantifying performance bounds with respect to specific problem…

Quantum Physics · Physics 2021-11-30 Phillip C. Lotshaw , Travis S. Humble , Rebekah Herrman , James Ostrowski , George Siopsis

We present benchmarking results for the non-variational Quantum Walk Optimisation Algorithm (non-variational QWOA) applied to the weighted maxcut problem, using classical simulations for problem sizes up to $n = 31$. The amplified quantum…

Quantum Physics · Physics 2025-06-02 Tavis Bennett , Aidan Smith , Edric Matwiejew , Jingbo Wang

Constructing an optimal mixer for Quantum Approximate Optimization Algorithm (QAOA) Hamiltonian is crucial for enhancing the performance of QAOA in solving combinatorial optimization problems. We present a systematic methodology for…

Quantum Physics · Physics 2024-05-14 Boris Tsvelikhovskiy , Ilya Safro , Yuri Alexeev

This paper tackles the multi-vehicle Coverage Path Planning (CPP) problem, crucial for applications like search and rescue or environmental monitoring. Due to its NP-hard nature, finding optimal solutions becomes infeasible with larger…

Quantum Physics · Physics 2024-07-15 Poojith U Rao , Florian Speelman , Balwinder Sodhi , Sachin Kinge

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…

Quantum Physics · Physics 2022-06-29 Yunlong Yu , Chenfeng Cao , Carter Dewey , Xiang-Bin Wang , Nic Shannon , Robert Joynt

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…

Quantum Physics · Physics 2024-02-29 Anthony M. Polloreno , Graeme Smith

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)…

Optimization and Control · Mathematics 2024-08-13 Camille Grange , Michael Poss , Eric Bourreau

The Tail Assignment Problem (TAP) is a critical optimization challenge in airline operations, requiring the optimal assignment of aircraft to scheduled flights to maximize efficiency and minimize costs. To address the TAP, this work applies…

Quantum Physics · Physics 2024-12-18 Marta Gili , Paul San Sebastian , Ane Blázquez-García

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…

Quantum Physics · Physics 2025-11-04 Leonardo Lavagna , Simone Piperno , Andrea Ceschini , Massimo Panella

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…

Quantum Physics · Physics 2023-07-12 Alexey Galda , Eesh Gupta , Jose Falla , Xiaoyuan Liu , Danylo Lykov , Yuri Alexeev , Ilya Safro

In wireless communication networks, it is difficult to solve many NP-hard problems owing to computational complexity and high cost. Recently, quantum annealing (QA) based on quantum physics was introduced as a key enabler for solving…

The efficient management of energy communities relies on the solution of the "prosumer problem", i.e., the problem of scheduling the household loads on the basis of the user needs, the electricity prices, and the availability of local…

Quantum Physics · Physics 2023-11-20 Carlo Mastroianni , Francesco Plastina , Luigi Scarcello , Jacopo Settino , Andrea Vinci

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…

We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study…

The classical homotopy optimization approach has the potential to deal with highly nonlinear landscape, such as the energy landscape of QAOA problems. Following this motivation, we introduce Hamiltonian-Oriented Homotopy QAOA (HOHo-QAOA),…

Quantum Physics · Physics 2023-01-31 Akash Kundu , Ludmila Botelho , Adam Glos

To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…

Quantum Physics · Physics 2025-03-13 Friedrich Wagner , Jonas Nüßlein , Frauke Liers

The Quantum Approximate Optimization Algorithm (QAOA) has been suggested as a promising candidate for the solution of combinatorial optimization problems. Yet, whether - or under what conditions - it may offer an advantage compared to…

Quantum Physics · Physics 2025-04-14 Vanessa Dehn , Martin Zaefferer , Gerhard Hellstern , Florentin Reiter , Thomas Wellens

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…

The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate algorithm for demonstrating quantum advantage in optimization using near-term quantum computers. However, QAOA has high requirements on gate fidelity due to the…

Quantum Physics · Physics 2023-03-20 Xiaoyuan Liu , Ruslan Shaydulin , Ilya Safro

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…

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