Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.10952

Improving Quantum Multi-Objective Optimization with Archiving and Substitution

Linus Ekstrøm, Takafumi Hosogi, Xavier Bonet-Monroig, Hao Wang, Thomas Bäck, Sebastian Schmitt

quant-phSubmitted Feb 11, 2026• Announced Feb 12, 2026• 0 citations
arXivHTMLPDF

Abstract

Finding optimal solutions of conflicting objectives is a daily matter in many industrial applications, with multi-objective optimization trying to find the best solutions to them. The advent of quantum computing has led to researchers wondering if the promised exponential advantage can be obtained for these problems by variational quantum multi-objective optimization (QMOO) algorithm. Here, we improve it by introducing a Pareto Archive and dominated solutions substitution, clearly improving in hyper-volume convergence at additional quantum and classical cost. We propose the use of RMNK-landscapes as a unifying testbed for benchmarking QMOO, as it is common in classical multi-objective field. By devising a generic classical-to-quantum mapping of these landscapes, we perform a numerical hyperparameter tuning of QMOO, significantly enhancing its performance. Finally, we compare QMOO against well-known classical solvers for multi-objective tasks, NSGA-II/III, showing comparable results in small instances. Our results demonstrate that QMOO, when carefully tuned for the task at hand, might be advantageous on harder problems than its classical counterparts.

Comments
15 pages, 5 figures

Related papers

Variational quantum multiobjective optimization

Linus Ekstrøm, Hao Wang, Sebastian Schmitt

Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attention in recent years. Currently, most studies have focused on single-objective problems, whereas many real-world applications need to consider multiple, mostly conflicting objectives, such as cost and quality. We present a variational quantum optimization algorithm to solve discrete multiobjective optimization problems on quantum computers. The proposed quantum multiobjective optimization (QMOO) algorithm incorporates all cost Hamiltonians representing the classical objective functions in the quantum circuit and produces a quantum state consisting of Pareto-optimal solutions in superposition. From this state, we retrieve a set of solutions and utilize the widely applied hypervolume indicator to determine its quality as an approximation to the Pareto front. The variational parameters of the QMOO circuit are tuned by maximizing the hypervolume indicator in a quantum-classical hybrid fashion. We show the effectiveness of the proposed algorithm on several benchmark problems with up to five objectives. We investigate the influence of the classical optimizer and the circuit depth, and compare them to results from classical optimization algorithms. We find that the algorithm is robust to shot noise and produces good results with as few as 128 measurement shots in each iteration. These promising results open the possibility to run the algorithm on near-term quantum hardware.

arXiv:2312.14151•Physical Review Research•May 12, 2025•13 citations

Multi-objective optimization by quantum annealing

Andrew D. King

An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally intensive even for small problems, it is a natural target for quantum optimization. Indeed, this problem was recently approached using the quantum approximate optimization algorithm (QAOA) on an IBM gate-model processor. Here we compare these QAOA results with quantum annealing on the same two input problems, using the same methodology. We find that quantum annealing vastly outperforms not just QAOA run on the IBM processor, but all classical and quantum methods analyzed in the previous study. On the harder problem, quantum annealing improves upon the best known Pareto front. This small study reinforces the promise of quantum annealing in multi-objective optimization.

quant-pharXiv:2511.01762•Nov 4, 2025•0 citations

Enhanced Multi-Objective Quantum-Inspired Computing for Practical Portfolio Optimization

Yao–Hsin Chou, Yong-Feng Tong, Shu–Yu Kuo +2 more

Quantum-inspired optimization (QIO) has gained attention for leveraging both quantum and classical advantages to enhance search efficiency in solving complex optimization problems on classical computers. While most QIO approaches have shown strong potential in addressing single-objective optimization, real-world problems often involve conflicting objectives, making them inherently multi-objective and challenging to solve. Unlike single-objective optimization, which seeks a single optimal solution, multi-objective optimization aims to obtain a set of Pareto-optimal solutions. This study extends QIO to multi-objective optimization (MoQIO) by incorporating quantum-inspired characteristics and provides an in-depth analysis of its performance. It utilizes quantum superposition and Q-gates to enhance convergence efficiency toward the Pareto front, while leveraging entanglement properties to expand solution diversity. Our results demonstrate that the proposed MoQIO effectively generates a diverse set of optimal portfolio solutions.

IEEE International Conference on Nanotechnology (IEEE-NANO)•Jul 13, 2025•1 citation

QAMOO: Quantum Approximate Multi-Objective Optimization for Portfolio Management

Jahangir Khan

We present QAMOO, a novel quantum computing framework for multi-objective portfolio optimization that simultaneously optimizes four distinct financial objectives—expected return, portfolio volatility, transaction costs, and entropy-based diversification—within a unified quantum Hamiltonian formulation. Unlike prior quantum finance approaches that treat diversification as a post-hoc penalty or encode transaction fees as scalarized weights, QAMOO embeds a Shannon entropy term directly into the quantum cost function through amplitude encoding of the portfolio weight vector. This formulation enables joint optimization over a non-convex objective landscape that cannot be faithfully reduced to a classical convex program without exponential complexity growth. The framework employs the Quantum Approximate Optimization Algorithm (QAOA) with pre-trained parameter transfer, executed on IBM Quantum hardware featuring heavy-hex topology processors with up to 156 qubits. A custom Pareto engine discovers the complete frontier of non-dominated portfolio solutions, enabling investors to select allocations matching their individual risk preferences. Empirical evaluation on a multi-asset portfolio demonstrates a 0.21% hypervolume improvement over the state-of-the-art classical multi-objective evolutionary algorithm (NSGA-III), while requiring approximately 30% fewer optimization cycles. The quantum-derived portfolios exhibit 23% lower turnover-adjusted volatility after accounting for realistic transaction fees. QAMOO establishes a new research direction at the intersection of quantum computing and quantitative finance, providing a hardware-aware optimization paradigm that integrates entropy-driven diversification directly into quantum annealing and gate-model formulations.

•Jan 23, 2026•0 citations

Quantum-Enhanced Multi-Objective Optimization

Maolin Luo, Jiapei Zhuang, Zuoheng Zou +1 more

Multi-objective combinatorial optimization requires identifying Pareto-optimal trade-off solutions among conflicting objectives, often making it more demanding than its single-objective counterpart. Although quantum multi-objective optimization methods have begun to emerge, most existing quantum optimization workflows are still built around single-objective or fixed-scalarization settings. Building on existing weighted-sum QAOA approaches to quantum multi-objective optimization, we propose QEMOO, a quantum-enhanced multi-objective optimization framework that combines Pareto-based selection and warm-started QAOA sampling in a multi-round protocol under the same total shot budget. We further introduce a PBI-inspired adaptive direction-update scheme to improve coverage in strongly conflicting benchmark regimes. Across three benchmark stages, QEMOO improves Pareto-front hypervolume over the single-pass weighted-sum QAOA baseline under matched shot budgets, suggesting a practical route toward shot-efficient quantum-assisted multi-objective optimization and its future applications.

quant-pharXiv:2607.18848•Jul 22, 2026•0 citations

Quantum approximate multi-objective optimization

Ayse Kotil, Elijah Pelofske, Stephanie Riedmüller +4 more

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches. This study explores the use of quantum computing to address multi-objective optimization challenges. By using a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of multi-objective weighted max-cut problems, the authors demonstrate promising results—both in simulation and on IBM Quantum hardware—surpassing classical approaches.

arXiv:2503.22797•Nature Computational Science•Oct 24, 2025•24 citations
Finding optimal solutions of conflicting objectives is a daily matter in many industrial applications, with multi-objective optimization trying to find the best solutions to them. The advent of quantum computing has led to researchers wondering if the promised exponential advantage can be obtained for these problems by variational quantum multi-objective optimization (QMOO) algorithm. Here, we improve it by introducing a Pareto Archive and dominated solutions substitution, clearly improving in hyper-volume convergence at additional quantum and classical cost. We propose the use of RMNK-landscapes as a unifying testbed for benchmarking QMOO, as it is common in classical multi-objective field. By devising a generic classical-to-quantum mapping of these landscapes, we perform a numerical hyperparameter tuning of QMOO, significantly enhancing its performance. Finally, we compare QMOO against well-known classical solvers for multi-objective tasks, NSGA-II/III, showing comparable results in small instances. Our results demonstrate that QMOO, when carefully tuned for the task at hand, might be advantageous on harder problems than its classical counterparts.
Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attention in recent years. Currently, most studies have focused on single-objective problems, whereas many real-world applications need to consider multiple, mostly conflicting objectives, such as cost and quality. We present a variational quantum optimization algorithm to solve discrete multiobjective optimization problems on quantum computers. The proposed quantum multiobjective optimization (QMOO) algorithm incorporates all cost Hamiltonians representing the classical objective functions in the quantum circuit and produces a quantum state consisting of Pareto-optimal solutions in superposition. From this state, we retrieve a set of solutions and utilize the widely applied hypervolume indicator to determine its quality as an approximation to the Pareto front. The variational parameters of the QMOO circuit are tuned by maximizing the hypervolume indicator in a quantum-classical hybrid fashion. We show the effectiveness of the proposed algorithm on several benchmark problems with up to five objectives. We investigate the influence of the classical optimizer and the circuit depth, and compare them to results from classical optimization algorithms. We find that the algorithm is robust to shot noise and produces good results with as few as 128 measurement shots in each iteration. These promising results open the possibility to run the algorithm on near-term quantum hardware.
An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally intensive even for small problems, it is a natural target for quantum optimization. Indeed, this problem was recently approached using the quantum approximate optimization algorithm (QAOA) on an IBM gate-model processor. Here we compare these QAOA results with quantum annealing on the same two input problems, using the same methodology. We find that quantum annealing vastly outperforms not just QAOA run on the IBM processor, but all classical and quantum methods analyzed in the previous study. On the harder problem, quantum annealing improves upon the best known Pareto front. This small study reinforces the promise of quantum annealing in multi-objective optimization.
Quantum-inspired optimization (QIO) has gained attention for leveraging both quantum and classical advantages to enhance search efficiency in solving complex optimization problems on classical computers. While most QIO approaches have shown strong potential in addressing single-objective optimization, real-world problems often involve conflicting objectives, making them inherently multi-objective and challenging to solve. Unlike single-objective optimization, which seeks a single optimal solution, multi-objective optimization aims to obtain a set of Pareto-optimal solutions. This study extends QIO to multi-objective optimization (MoQIO) by incorporating quantum-inspired characteristics and provides an in-depth analysis of its performance. It utilizes quantum superposition and Q-gates to enhance convergence efficiency toward the Pareto front, while leveraging entanglement properties to expand solution diversity. Our results demonstrate that the proposed MoQIO effectively generates a diverse set of optimal portfolio solutions.
We present QAMOO, a novel quantum computing framework for multi-objective portfolio optimization that simultaneously optimizes four distinct financial objectives—expected return, portfolio volatility, transaction costs, and entropy-based diversification—within a unified quantum Hamiltonian formulation. Unlike prior quantum finance approaches that treat diversification as a post-hoc penalty or encode transaction fees as scalarized weights, QAMOO embeds a Shannon entropy term directly into the quantum cost function through amplitude encoding of the portfolio weight vector. This formulation enables joint optimization over a non-convex objective landscape that cannot be faithfully reduced to a classical convex program without exponential complexity growth. The framework employs the Quantum Approximate Optimization Algorithm (QAOA) with pre-trained parameter transfer, executed on IBM Quantum hardware featuring heavy-hex topology processors with up to 156 qubits. A custom Pareto engine discovers the complete frontier of non-dominated portfolio solutions, enabling investors to select allocations matching their individual risk preferences. Empirical evaluation on a multi-asset portfolio demonstrates a 0.21% hypervolume improvement over the state-of-the-art classical multi-objective evolutionary algorithm (NSGA-III), while requiring approximately 30% fewer optimization cycles. The quantum-derived portfolios exhibit 23% lower turnover-adjusted volatility after accounting for realistic transaction fees. QAMOO establishes a new research direction at the intersection of quantum computing and quantitative finance, providing a hardware-aware optimization paradigm that integrates entropy-driven diversification directly into quantum annealing and gate-model formulations.
Multi-objective combinatorial optimization requires identifying Pareto-optimal trade-off solutions among conflicting objectives, often making it more demanding than its single-objective counterpart. Although quantum multi-objective optimization methods have begun to emerge, most existing quantum optimization workflows are still built around single-objective or fixed-scalarization settings. Building on existing weighted-sum QAOA approaches to quantum multi-objective optimization, we propose QEMOO, a quantum-enhanced multi-objective optimization framework that combines Pareto-based selection and warm-started QAOA sampling in a multi-round protocol under the same total shot budget. We further introduce a PBI-inspired adaptive direction-update scheme to improve coverage in strongly conflicting benchmark regimes. Across three benchmark stages, QEMOO improves Pareto-front hypervolume over the single-pass weighted-sum QAOA baseline under matched shot budgets, suggesting a practical route toward shot-efficient quantum-assisted multi-objective optimization and its future applications.
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches. This study explores the use of quantum computing to address multi-objective optimization challenges. By using a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of multi-objective weighted max-cut problems, the authors demonstrate promising results—both in simulation and on IBM Quantum hardware—surpassing classical approaches.