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quantum approximate optimization algorithm applied to multi-objective routing for large scale 6G networks

Computer Networks 2025年 267卷

作者： Oumayma Bouchmal Bruno Cimoli Ripalta Stabile Juan Jose Vegas Olmos Idelfonso Tafur Monroy Department of Electrical Engineering Eindhoven University of Technology Eindhoven Netherlands Software Architecture NVIDIA Corporation Yokneam Israel

A multi-objective optimization problem involves optimizing two or more conflicting objectives simultaneously. This type of problem arises in many scientific and industrial areas and it is classified as NP-Hard. Network routing optimization with multiple objectives falls into this category. In the context of 6G networks, solving this problem will become even more challenging due to the exponential growth of Internet of Things devices and the high quality of service requirements. Finding good quality solutions for large-scale networks will be increasingly difficult. In this paper, we introduce a quantum-inspired routing optimization scheme in which noisy-intermediate scale quantum computers (NISQ) can be used to solve the Multi-Objective Routing Problem (MORP). We evaluate the application of the proposed scheme in detail by first developing the mathematical formulas for both single-objective and multi-objective routing and mapping the problem onto gate-based models by using the quadratic unconstrained binary optimization (QUBO) approach. To validate the proposed scheme, we use the quantum approximate optimization algorithm (QAOA), the go-to approach for solving combinatorial optimization problems that are classically intractable. For the simulation, we use the IBM-Qasm simulator and Qiskit framework. Additionally, we use the Chernoff Bound as a standard technique to estimate the sample complexity of QAOA. Finally, we provide a detailed numerical and theoretical analysis of the proposed scheme, including its time complexity, resource requirements, and the challenges associated with it. Our results demonstrate that the proposed approach operates with a time complexity of O ( E 2 ) per iteration in both single and multi-objective scenarios, with an overall runtime of ( n iteration + n CB ) ⋅ O ( E 2 ) influenced by the sampling overhead, significantly outperforming Dijkstra’s algorithm in the multi-objective case, where the complexity increases to O ( 2 k ( N ( k + log N

关键词： quantum optimization Multi-objective routing quantum computing 6G quantum approximate optimization algorithm Quadratic unconstrained binary optimization

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quantum approximate optimization algorithm for Bayesian network structure learning

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quantum INFORMATION PROCESSING 2022年第1期22卷 1-28页

作者： Soloviev, Vicente P. Bielza, Concha Larranaga, Pedro Univ Politecn Madrid Computat Intelligence Grp Campus Montegancedo Madrid Spain

Bayesian network structure learning is an NP-hard problem that has been faced by a number of traditional approaches in recent decades. Currently, quantum technologies offer a wide range of advantages that can be exploited to solve optimization tasks that cannot be addressed in an efficient way when utilizing classic computing approaches. In this work, a specific type of variational quantum algorithm, the quantum approximate optimization algorithm, was used to solve the Bayesian network structure learning problem, by employing 3n(n - 1)/2 qubits, where n is the number of nodes in the Bayesian network to be learned. Our results showed that the quantum approximate optimization algorithm approach offers competitive results with stateof-the-art methods and quantitative resilience to quantum noise. The approach was applied to a cancer benchmark problem, and the results justified the use of variational quantum algorithms for solving the Bayesian network structure learning problem.

关键词： quantum approximate optimization algorithm Variational quantum algorithm quantum optimization Bayesian network structure learning

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quantum approximate optimization algorithm with Sparsified Phase Operator 3

Quantum Approximate Optimization Algorithm with Sparsified P...

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3rd IEEE International Conference on quantum Computing and Engineering (QCE)

作者： Liu, Xiaoyuan Shaydulin, Ruslan Safro, Ilya Fujitsu Res Amer Inc Sunnyvale CA 94085 USA Univ Delaware Dept Comp & Informat Sci Newark DE 19716 USA Argonne Natl Lab Math & Comp Sci Div Lemont IL USA JPMorgan Chase Future Lab Appl Res & Engn New York NY USA

ISBN: (数字)9781665491136

ISBN: (纸本)9781665491136

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 need to encode the objective function in the phase separating operator, requiring a large number of gates that potentially do not match the hardware connectivity. Using the MaxCut problem as the target, we demonstrate numerically that an easier way to implement an alternative phase operator can be used in lieu of the phase operator encoding the objective function, as long as the ground state is the same. We observe that if the ground state energy is not preserved, the approximation ratio obtained by QAOA with such a phase separating operator is likely to decrease. Moreover, we show that a better alignment of the low energy subspace of the alternative operator leads to better performance. Leveraging these observations, we propose a sparsification strategy that reduces the resource requirements of QAOA. We also compare our sparsification strategy with some other classical graph sparsification methods and demonstrate the efficacy of our approach.

关键词： quantum computing quantum optimization quantum approximate optimization algorithm

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quantum approximate optimization algorithm for PD-NOMA User Pairing

Quantum Approximate Optimization Algorithm for PD-NOMA User ...

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IEEE International Conference on Communications (IEEE ICC)

作者： Xiang, Qiwei Kho, Yau Hee Seah, Winston K. G. Tian, Yue Fang, Rui Huang, Peng Sichuan Agr Univ Coll Mech & Elect Engn Yaan Peoples R China Victoria Univ Wellington Sch Engn & Comp Sci Wellington 6140 New Zealand Xiamen Univ Technol Fujian Key Lab Commun Network & Informat Proc Xiamen 361024 Peoples R China

ISBN: (纸本)9781538674628

This work proposes the utilization of the quantum approximate optimization algorithm (QAOA) for user pairing in non-orthogonal multiple access (NOMA). By exploiting quantum concepts such as the quantum adiabatic theorem, a user pairing solution was derived that approximates a suboptimal sum rate. Moreover, an improved-QAOA is proposed to further enhance the performance by reducing the number of users in the cluster by dividing it into more clusters. Simulation results have demonstrated that the improved-QAOA yields a higher average achievable sum rate when compared to QAOA, and its solution is closer to the theoretical optimal value obtained by a brute-force enumeration method.

关键词： quantum approximate optimization algorithm Non-orthogonal multiple access 5G Wireless communications User pairing

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A quantum approximate optimization algorithm for solving Hamilton path problem

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JOURNAL OF SUPERCOMPUTING 2022年第13期78卷 15381-15403页

作者： Gong, Changqing Wang, Ting He, Wanying Qi, Han Shenyang Aerosp Univ Sch Comp Sci Daoyi Nan St Shenyang 110136 Liaoning Peoples R China

In recent years, combinatorial optimization has been widely studied. The existing optimization solutions are prone to fall into local optimal solutions and have a lower probability of obtaining global optimal solutions. quantum approximate optimization algorithm (QAOA) is an effective algorithm that can obtain the optimal solution with high probability. In this paper, the problem Hamiltonian is obtained by summing the problem function and the deformed constraints. Through theoretical formula derivation, the problem Hamiltonian is transformed into the Ising model. The performance of the experimental result under different optimizers and asynchronous lengths is verified on pyQPanda. The experimental results show that when using the problem Hamiltonian method set in this paper, the probability of obtaining the optimal solution is 99.59%. Compared with other methods, the proposed method can alleviate the risk of falling into local optimal solutions and obtain the global optimal solution with a higher probability.

关键词： quantum computing quantum approximate optimization algorithm Hamilton path Ising model

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quantum Linear System Solver Based on Time-optimal Adiabatic quantum Computing and quantum approximate optimization algorithm

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ACM TRANSACTIONS ON quantum COMPUTING 2022年第2期3卷 1–28页

作者： An, Dong Lin, Lin Univ Calif Berkeley Dept Math Berkeley CA 94720 USA Univ Calif Berkeley Challenge Inst Quantum Computat Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Computat Res Div Berkeley CA 94720 USA

We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with O(kappa poly(log(kappa/epsilon))) runtime, where kappa is the condition number, and epsilon is the target accuracy. This is near optimal with respect to both kappa and epsilon, and is achieved without relying on complicated amplitude amplification procedures that are difficult to implement. Our method is applicable to general non-Hermitian matrices, and the cost as well as the number of qubits can be reduced when restricted to Hermitian matrices, and further to Hermitian positive definite matrices. The success of the time-optimal AQC implies that the quantum approximate optimization algorithm (QAOA) with an optimal control protocol can also achieve the same complexity in terms of the runtime. Numerical results indicate that QAOA can yield the lowest runtime compared to the time-optimal AQC, vanilla AQC, and the recently proposed randomization method.

关键词： quantum linear system problem adiabatic quantum computing quantum approximate optimization algorithm

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Graph representation learning for parameter transferability in quantum approximate optimization algorithm

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quantum MACHINE INTELLIGENCE 2024年第2期6卷 1-16页

作者： Falla, Jose Langfitt, Quinn Alexeev, Yuri Safro, Ilya Univ Delaware Dept Phys & Astron Newark DE 19716 USA Univ Delaware Dept Comp & Informat Sci Newark DE 19716 USA Argonne Natl Lab Computat Sci Div Lemont IL 60439 USA

The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. Due to clustering of optimal QAOA parameters for MaxCut, successful parameter transferability between different MaxCut instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). In this work, we apply five different graph embedding techniques to determine good donor candidates for parameter transferability, including parameter transferability between different classes of MaxCut instances. Using this technique, we effectively reduce the number of iterations required for parameter optimization, obtaining an approximate solution to the target problem with an order of magnitude speedup. This procedure also effectively removes the problem of encountering barren plateaus during the variational optimization of parameters. Additionally, our findings demonstrate that the transferred parameters maintain effectiveness when subjected to noise, supporting their use in real-world quantum applications. This work presents a framework for identifying classes of combinatorial optimization instances for which optimal donor candidates can be predicted such that QAOA can be substantially accelerated under both ideal and noisy conditions.

关键词： quantum computing quantum software quantum optimization quantum approximate optimization algorithm Parameter transferability Error mitigation

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Simulations of quantum approximate optimization algorithm on HPC-QC Integrated Systems 5

Simulations of Quantum Approximate Optimization Algorithm on...

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2024 International Conference on quantum Computing and Engineering

作者： Kim, Seongmin Suh, In-Saeng Oak Ridge Natl Lab Natl Ctr Computat Sci Oak Ridge TN 37380 USA

ISBN: (纸本)9798331541378

The quantum approximate optimization algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density_matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC integrated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM quantum simulators.

关键词： quantum approximate optimization algorithm quantum simulator HPC-QC integrated system performance analysis quadratic unconstrained binary optimization

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Noise -Aware Distributed quantum approximate optimization algorithm on Near -term quantum Hardware 5

Noise -Aware Distributed Quantum Approximate Optimization Al...

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2024 International Conference on quantum Computing and Engineering

作者： Chen, Kuan-Cheng Xu, Xiaotian Burt, Felix Liu, Chen-Yu Yu, Shang Leung, Kin K. Imperial Coll London QuEST London England Natl Taiwan Univ Grad Inst Appl Phys Taipei Taiwan Imperial Coll London Dept Phys London England Imperial Coll London Dept EEE London England

ISBN: (纸本)9798331541378

This paper introduces a noise -aware distributed quantum approximate optimization algorithm (QAOA) tailored for execution on near-term quantum hardware. Leveraging a distributed framework, we address the limitations of current Noisy Intermediate -Scale quantum (NISQ) devices, which are hindered by limited qubit counts and high error rates. Our approach decomposes large QAOA problems into smaller subproblems, distributing them across multiple quantum Processing Units (QPUs) to enhance scalability and performance. The noise -aware strategy incorporates error mitigation techniques to optimize qubit fidelity and gate operations, ensuring reliable quantum computations. We evaluate the efficacy of our framework using the HamilToniQ Benchmarking Toolkit, which quantifies the performance across various quantum hardware configurations. The results demonstrate that our distributed QAOA framework achieves significant improvements in computational speed and accuracy, showcasing its potential to solve complex optimization problems efficiently in the NISQ era. This work sets the stage for advanced algorithmic strategies and practical quantum system enhancements, contributing to the broader goal of achieving quantum advantage.

关键词： Distributed quantum Computing quantum approximate optimization algorithm optimization Compilation

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Policy Gradient based quantum approximate optimization algorithm 1

Policy Gradient based Quantum Approximate Optimization Algor...

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Conference on Mathematical and Scientific Machine Learning

作者： Yao, Jiahao Bukov, Marin Lin, Lin Univ Calif Berkeley Dept Math Berkeley CA 94720 USA Univ Calif Berkeley Dept Phys Berkeley CA 94720 USA Lawrence Berkeley Natl Lab Computat Res Div Berkeley CA 94720 USA

The quantum approximate optimization algorithm (QAOA), as a hybrid quantum/classical algorithm, has received much interest recently. QAOA can also be viewed as a variational ansatz for quantum control. However, its direct application to emergent quantum technology encounters additional physical constraints: (i) the states of the quantum system are not observable;(ii) obtaining the derivatives of the objective function can be computationally expensive or even inaccessible in experiments, and (iii) the values of the objective function may be sensitive to various sources of uncertainty, as is the case for noisy intermediate-scale quantum (NISQ) devices. Taking such constraints into account, we show that policy-gradient-based reinforcement learning (RL) algorithms are well suited for optimizing the variational parameters of QAOA in a noise-robust fashion, opening up the way for developing RL techniques for continuous quantum control. This is advantageous to help mitigate and monitor the potentially unknown sources of errors in modern quantum simulators. We analyze the performance of the algorithm for quantum state transfer problems in single- and multi-qubit systems, subject to various sources of noise such as error terms in the Hamiltonian, or quantum uncertainty in the measurement process. We show that, in noisy setups, it is capable of outperforming state-of-the-art existing optimization algorithms.

关键词： quantum approximate optimization algorithm Policy gradient Reinforcement learning Robust optimization quantum computing quantum control

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