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

International Conference on Communications

Quantum Approximate Optimization Algorithm for Knapsack Resource Allocation Problems in Communication Systems

Junaid ur Rehman, Hayder Al-Hraishawi, Symeon Chatzinotas

Published May 28, 2023• 12 citations
Publisher

Abstract

Quantum technologies have recently scaled up from laboratories into commercial applications thanks to the rapid technical developments and the growing investments in quantum computing. These developments open up the way for the emergence of the so-called noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithms (QAOAs) represent a class of algorithms tailored for the NISQera computing for provisioning tangible quantum advantages. Meanwhile, wireless communications networks have become more complex over time and the pressure to conquer communications complexity is intense for both researchers and system designers. Specifically, a major optimization problem in this context is the resource allocation in modern communications where typically appears as an intricate 0/1 knapsack (0/1-KP) problem and finding its optimal solution using classical computers is prohibitively difficult. Thus, a parallel QAOA framework for optimizing the 0/1- KP problems is proposed in this paper. The proposal has the space complexity of$\mathcal{O} (n)$and pseudopolynomial time complexity of$\mathcal{O} (nW)$, where$W$is the knapsack's total capacity and$n$is the total number of items. However, the proposed QAOA solution is highly parallel and can be implemented on$M$NISQ devices of n-qubits each to obtain$\mathcal{O}(n W / M)$time complexity and$\mathcal{O} (nM)$space complexity. Numerical experiments show high approximation ratios even for shallow depth QAOA instances.

DOI
10.1109/icc45041.2023.10279239

Related papers

Quantum Computing For Combinatorial Optimization: Algorithms, Complexity Analysis, And Real-World Applications.

G. Swapna, P. Sunil

Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.

•Jan 1, 2026•0 citations

Multiscale quantum approximate optimization algorithm

Ping Zou

The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions for combinatorial optimization problems on current noisy intermediate-scale quantum (NISQ) devices. The primary focus of ongoing research is to exhibit its speed advantage over classical algorithms. However, the performance of QAOA is restricted at lower depths, while higher depths are limited by current experimental techniques. We propose an algorithm that amalgamates the capabilities of QAOA and the real-space renormalization group transformation. Numerical simulations indicate that our proposed algorithm can deliver precise solutions for specific randomly generated instances using QAOA at shallow depths, even at the lowest depth. This algorithm is particularly suitable for current NISQ devices, offering the potential to demonstrate a quantum advantage.

arXiv:2312.06181•Physical Review A•Jan 17, 2025•2 citations

Evaluating Quantum Approximate Optimization Algorithm: A Case Study

Ruslan Shaydulin, Yuri Alexeev

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We perform a large-scale numerical study of the approximation ratios attainable by QAOA is the low-to medium-depth regime. To find good QAOA parameters we perform 990 million 10-qubit QAOA circuit evaluations. We find that the approximation ratio increases only marginally as the depth is increased, and the gains are offset by the increasing complexity of optimizing variational parameters. We observe a high variation in approximation ratios attained by QAOA, including high variations within the same class of problem instances. We observe that the difference in approximation ratios between problem instances increases as the similarity between instances decreases. We find that optimal QAOA parameters concentrate for instances in out benchmark, confirming the previous findings for a different class of problems.

arXiv:1910.04881•International Green and Sustainable Computing Conference•Oct 1, 2019•55 citations

Quantum Approximate Optimization Algorithm on Different Qubit Systems

Seongmin Kim, In‐Saeng Suh, E. A. Coello Pérez +6 more

Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•0 citations

A Quantum-Inspired QAOA Solver for Knapsack Problems with 100-Qubit Scalability and 100,000x Speedup

Shan-Jung Hou, Chuan-Chi Wang, Po-Hsuan Huang +2 more

Combinatorial optimization problems play a central role in computer science and real-world decision-making, as they aim to find the optimal solution from a large set of possibilities. Among these, the Knapsack Problem is a fundamental example with many practical applications. The Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid approach designed to address such problems. However, existing simulation approaches for QAOA applied to the Knapsack Problem do not scale well because they fail to exploit the problem's structural properties. To overcome these limitations, this study exploits the entangling characteristics of circuits in the Knapsack Problem and develops an optimized solver tailored to this setting. The key technical contributions include an entanglement-free circuit simulation method that reduces complexity from exponential to linear for non-entangling circuits, enabling 24,000x speedups for QAOA ansatz circuit simulations, and a two-phase parameter selection strategy that enhances the efficiency of finding optimal Knapsack solutions. Our solver extends the scalability of QAOA simulations from the previous limit of approximately 10 qubits to 100 qubits within a system memory of 256 GB. It achieves performance gains of over 100,000x for solving Knapsack Problems while maintaining high solution quality.

ACM Conference on Research in Adaptive and Convergent Systems (RACS)•Nov 16, 2025•0 citations

Quantum Knapsack: Optimizing Resource Allocation with QAOA

Mahfouz, Zein, Bhaskaran Potty Thulasi Lakshmi, Sreedevi

Combinatorial Optimization (CO) is one of the most important areas in the field of optimization, with practical applications found in every industry, including both the private and public sectors. In recent years, it was discovered that a mathematical formulation known as QUBO (Quadratic Unconstrained Binary Optimization) problem can embrace an exceptional variety of important CO problems found in the industry. In this work, we explore the Quantum Approximate Optimization Algorithm (QAOA) as a quantum computing approach to solve the Knapsack Problem efficiently by formulating the problem as a QUBO model. Here we implemented QAOA on a quantum emulator, leveraging quantum superposition and entanglement to explore multiple solutions simultaneously. The method offers a promising route for solving large, complex scheduling and resource allocation problems that are tough for classical algorithms, with potential applications in logistics, HPC resource scheduling, and energy optimization.

•Nov 17, 2025•0 citations
Quantum technologies have recently scaled up from laboratories into commercial applications thanks to the rapid technical developments and the growing investments in quantum computing. These developments open up the way for the emergence of the so-called noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithms (QAOAs) represent a class of algorithms tailored for the NISQera computing for provisioning tangible quantum advantages. Meanwhile, wireless communications networks have become more complex over time and the pressure to conquer communications complexity is intense for both researchers and system designers. Specifically, a major optimization problem in this context is the resource allocation in modern communications where typically appears as an intricate 0/1 knapsack (0/1-KP) problem and finding its optimal solution using classical computers is prohibitively difficult. Thus, a parallel QAOA framework for optimizing the 0/1- KP problems is proposed in this paper. The proposal has the space complexity ofO(n)\mathcal{O} (n)O(n)and pseudopolynomial time complexity ofO(nW)\mathcal{O} (nW)O(nW), whereWWWis the knapsack's total capacity andnnnis the total number of items. However, the proposed QAOA solution is highly parallel and can be implemented onMMMNISQ devices of n-qubits each to obtainO(nW/M)\mathcal{O}(n W / M)O(nW/M)time complexity andO(nM)\mathcal{O} (nM)O(nM)space complexity. Numerical experiments show high approximation ratios even for shallow depth QAOA instances.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions for combinatorial optimization problems on current noisy intermediate-scale quantum (NISQ) devices. The primary focus of ongoing research is to exhibit its speed advantage over classical algorithms. However, the performance of QAOA is restricted at lower depths, while higher depths are limited by current experimental techniques. We propose an algorithm that amalgamates the capabilities of QAOA and the real-space renormalization group transformation. Numerical simulations indicate that our proposed algorithm can deliver precise solutions for specific randomly generated instances using QAOA at shallow depths, even at the lowest depth. This algorithm is particularly suitable for current NISQ devices, offering the potential to demonstrate a quantum advantage.
Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We perform a large-scale numerical study of the approximation ratios attainable by QAOA is the low-to medium-depth regime. To find good QAOA parameters we perform 990 million 10-qubit QAOA circuit evaluations. We find that the approximation ratio increases only marginally as the depth is increased, and the gains are offset by the increasing complexity of optimizing variational parameters. We observe a high variation in approximation ratios attained by QAOA, including high variations within the same class of problem instances. We observe that the difference in approximation ratios between problem instances increases as the similarity between instances decreases. We find that optimal QAOA parameters concentrate for instances in out benchmark, confirming the previous findings for a different class of problems.
Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.
Combinatorial optimization problems play a central role in computer science and real-world decision-making, as they aim to find the optimal solution from a large set of possibilities. Among these, the Knapsack Problem is a fundamental example with many practical applications. The Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid approach designed to address such problems. However, existing simulation approaches for QAOA applied to the Knapsack Problem do not scale well because they fail to exploit the problem's structural properties. To overcome these limitations, this study exploits the entangling characteristics of circuits in the Knapsack Problem and develops an optimized solver tailored to this setting. The key technical contributions include an entanglement-free circuit simulation method that reduces complexity from exponential to linear for non-entangling circuits, enabling 24,000x speedups for QAOA ansatz circuit simulations, and a two-phase parameter selection strategy that enhances the efficiency of finding optimal Knapsack solutions. Our solver extends the scalability of QAOA simulations from the previous limit of approximately 10 qubits to 100 qubits within a system memory of 256 GB. It achieves performance gains of over 100,000x for solving Knapsack Problems while maintaining high solution quality.
Combinatorial Optimization (CO) is one of the most important areas in the field of optimization, with practical applications found in every industry, including both the private and public sectors. In recent years, it was discovered that a mathematical formulation known as QUBO (Quadratic Unconstrained Binary Optimization) problem can embrace an exceptional variety of important CO problems found in the industry. In this work, we explore the Quantum Approximate Optimization Algorithm (QAOA) as a quantum computing approach to solve the Knapsack Problem efficiently by formulating the problem as a QUBO model. Here we implemented QAOA on a quantum emulator, leveraging quantum superposition and entanglement to explore multiple solutions simultaneously. The method offers a promising route for solving large, complex scheduling and resource allocation problems that are tough for classical algorithms, with potential applications in logistics, HPC resource scheduling, and energy optimization.