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We present a detailed study of portfolio optimization using different versions of the quantum approximate optimization algorithm (QAOA). For a given list of assets, the portfolio optimization problem is formulated as quadratic binary…

MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…

Quantum Physics · Physics 2023-11-27 Yovav Tene-Cohen , Tomer Kelman , Ohad Lev , Adi Makmal

Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum heuristic with empirical evidence of speedup over classical state-of-the-art for some problems. QAOA uses a parameterized circuit with $p$ layers, where higher $p$…

Variational Quantum Algorithm (VQA) is a hybrid algorithm for noisy quantum devices. However, statistical fluctuations and physical noise degrade the solution quality, so it is difficult to maintain applicability for large-scale problems.…

Quantum Physics · Physics 2025-04-18 Hiromichi Matsuyama , Yu Yamashiro

The Quantum Approximate Optimization Algorithm (QAOA) is designed to maximize a cost function over bit strings. While the initial state is traditionally a uniform superposition over all strings, it is natural to try expediting the QAOA:…

Quantum Physics · Physics 2023-07-10 Madelyn Cain , Edward Farhi , Sam Gutmann , Daniel Ranard , Eugene Tang

We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At…

Quantum Physics · Physics 2021-12-21 Pietro Torta , Glen B. Mbeng , Carlo Baldassi , Riccardo Zecchina , Giuseppe E. Santoro

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 Physics · Physics 2024-05-09 Boy Choy , David J. Wales

We propose and study Th-QAOA (pronounced Threshold QAOA), a variation of the Quantum Alternating Operator Ansatz (QAOA) that replaces the standard phase separator operator, which encodes the objective function, with a threshold function…

Quantum Physics · Physics 2022-06-06 John Golden , Andreas Bärtschi , Daniel O'Malley , Stephan Eidenbenz

Quantum computing holds promise for outperforming classical computing in specialized applications such as optimization. With current Noisy Intermediate Scale Quantum (NISQ) devices, only variational quantum algorithms like the Quantum…

Quantum Physics · Physics 2024-07-08 Daniel Müssig , Markus Wappler , Steve Lenk , Jörg Lässig

The quantum approximate optimization algorithm (QAOA) is a near-term hybrid algorithm intended to solve combinatorial optimization problems, such as MaxCut. QAOA can be made to mimic an adiabatic schedule, and in the $p\to\infty$ limit the…

Quantum Physics · Physics 2022-02-02 Jonathan Wurtz , Peter J. Love

Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate algorithm for solving combinatorial optimization problems on quantum computers. However, in many cases QAOA requires computationally intensive parameter optimization.…

Variational quantum algorithms, which consist of optimal parameterized quantum circuits, are promising for demonstrating quantum advantages in the noisy intermediate-scale quantum (NISQ) era. Apart from classical computational resources,…

Quantum Physics · Physics 2024-12-30 Chen Qian , Wei-Feng Zhuang , Rui-Cheng Guo , Meng-Jun Hu , Dong E. Liu

Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class…

Quantum Physics · Physics 2025-10-15 Teemu Pihkakoski , Aravind Plathanam Babu , Pauli Taipale , Petri Liimatta , Matti Silveri

Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has…

Quantum Physics · Physics 2023-02-16 Marko J. Rančić

We propose a technique for optimizing parameterized circuits in variational quantum algorithms based on the probabilistic tensor sampling optimization. This method allows one to relax random initialization issues or heuristics for…

Quantum Physics · Physics 2024-02-01 G. V. Paradezhenko , A. A. Pervishko , D. Yudin

The quantum approximate optimisation ansatz (QAOA) is one of the flagship algorithms used to tackle combinatorial optimisation on graphs problems using a quantum computer, and is considered a strong candidate for early fault-tolerant…

Quantum Physics · Physics 2025-06-24 Yann Beaujeault-Taudière

One of the central goals of the DARPA Optimization with Noisy Intermediate-Scale Quantum (ONISQ) program is to implement a hybrid quantum/classical optimization algorithm with high $N\cdot p$, where $N$ is the number of qubits and $p$ is…

Quantum Physics · Physics 2026-02-23 Ruslan Shaydulin , Marco Pistoia

Quantum approximate optimization algorithm (QAOA) has attracted much attention as an algorithm that has the potential to efficiently solve combinatorial optimization problems. Among them, a fermionic QAOA (FQAOA) for solving constrained…

Quantum Physics · Physics 2023-12-11 Takuya Yoshioka , Keita Sasada , Yuichiro Nakano , Keisuke Fujii

In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…

Hybrid quantum-classical variational algorithms such as the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) are promising applications for noisy, intermediate-scale quantum (NISQ) computers.…

Quantum Physics · Physics 2021-09-13 William M. Kirby , Peter J. Love
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