The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also being used heav...
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ISBN:
(纸本)9798350311990
The Traveling Salesman Problem (TSP) is one of the most often-used NP-Hard problems in computer science to study the effectiveness of computing models and hardware platforms. In this regard, it is also being used heavily as a vehicle to study the feasibility of the quantum computing paradigm for this class of problems. In this work, we formulate the symmetric TSP as an optimization problem, which we solve using the quantum approximate optimization algorithm (QAOA) approach. By adopting an improved qubit encoding strategy and a layerwise learning optimization protocol, we obtain numerical results on the gate-based digital quantum simulator for the 3-, 4-, and 5city TSPs. Specifically, we focus on three QAOA mixer designs to evaluate their performances in terms of numerical accuracy and optimization cost. Based on our results, we propose that a well-balanced QAOA mixer design is more prominent on gatebased simulators or realistic quantum devices in the near future. In addition, we study the sensitivity of TSP graph properties such as graph skewness and penalty weight in the TSP-QAOA simulation. Overall, our results prove digital quantum simulation is a powerful candidate for obtaining the optimal solution to the TSP.
The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential...
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The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantumclassical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. We numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.
The intermittent nature of wind speed poses challenges for its widespread utilization as an electrical power generation source. As the integration of wind energy into the power system increases, accurate wind speed fo...
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The intermittent nature of wind speed poses challenges for its widespread utilization as an electrical power generation source. As the integration of wind energy into the power system increases, accurate wind speed forecasting becomes crucial. The reliable scheduling of wind power generation heavily relies on precise wind speed forecasts. This paper presents an extended work that focuses on a hybrid model for 24 h ahead wind speed forecasting. The proposed model combines residual Long Short-Term Memory (LSTM) and a quantum neural network that is studied by a quantum simulator, leveraging the support of NVIDIA Compute Unified Device Architecture (CUDA). To ensure the desired accuracy, a comparative analysis is conducted, examining the qubit count and quantum circuit depth of the proposed model. The execution time required for the model is significantly reduced when the GPU incorporates CUDA, accounting for only 8.29% of the time required by a classical CPU. In addition, different quantum embedding layers with various entangler layers in the quantum neural network are explored. The simulation results utilizing an offshore wind farm dataset demonstrate that the proper number of qubits and embedding layer can achieve favorable 24 h ahead wind speed forecasts.
This study explores the application of quantum computing in asset management, focusing on the use of the quantum approximate optimization algorithm (QAOA) to solve specific classes of financial asset recommendation pr...
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This study explores the application of quantum computing in asset management, focusing on the use of the quantum approximate optimization algorithm (QAOA) to solve specific classes of financial asset recommendation problems. While quantum computing holds promise for combinatorial optimization tasks, its application to portfolio management faces significant challenges in scalability for practical implementations. In this work, we model the problem using a graph representation where nodes represent investors, and edges reflect significant similarities in asset choices. We test the proposed method using quantum simulators, including cuquantum, Cirq-GPU, and Cirq with IonQ, and compare the performance of quantumoptimization against classical brute-force methods. Our results suggest that quantumalgorithms may offer computational advantages for certain use cases, though classical heuristics also provide competitive performance for smaller datasets. This study contributes to the ongoing investigation into the potential of quantum computing for real-time financial decision-making, providing insights into both its applicability and limitations in asset management for larger and more complex investor datasets.
The researched data shows that quantumalgorithms have been mostly used for battery’s chemistry and conventional grid systems. These algorithms have proved to be computationally cheaper as a common meritorious aspect...
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quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the...
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quantum variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate optimization algorithm (QAOA), which can be used to solve certain quantum control problems, state preparation problems, and combinatorial optimization problems. We demonstrate that the error of QAOA simulation can be significantly reduced by robust control optimization techniques, specifically, by sequential convex programming (SCP), to ensure error suppression in situations where the source of the error is known but not necessarily its magnitude. We show that robust optimization improves both the objective landscape of QAOA as well as overall circuit fidelity in the presence of coherent errors and errors in initial state preparation.
The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently, a quantumapproximate Bayesian optimizationalgorithm (QABOA)...
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The searching efficiency of the quantum approximate optimization algorithm is dependent on both the classical and quantum sides of the algorithm. Recently, a quantumapproximate Bayesian optimizationalgorithm (QABOA) that includes two mixers was developed, where surrogate-based Bayesian optimization is applied to improve the sampling efficiency of the classical optimizer. A continuous-time quantum walk mixer is used to enhance exploration, and the generalized Grover mixer is also applied to improve exploitation. In this article, an extension of the QABOA is proposed to further improve its searching efficiency. The searching efficiency is enhanced through two aspects. First, two mixers, including one for exploration and the other for exploitation, are applied in an alternating fashion. Second, uncertainty of the quantum circuit is quantified with a new quantum Mat & eacute;rn kernel based on the kurtosis of the basis state distribution, which increases the chance of obtaining the optimum. The proposed new two-mixer QABOA's with and without uncertainty quantification are compared with three single-mixer QABOA's on five discrete and four mixed-integer problems. The results show that the proposed two-mixer QABOA with uncertainty quantification has the best performance in efficiency and consistency for five out of the nine tested problems. The results also show that QABOA with the generalized Grover mixer performs the best among the single-mixer algorithms, thereby demonstrating the benefit of exploitation and the importance of dynamic exploration-exploitation balance in improving searching efficiency.
quantum computing is a promising technology that may provide breakthrough solutions to today's difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. A class of...
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ISBN:
(纸本)9781728186832
quantum computing is a promising technology that may provide breakthrough solutions to today's difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. A class of algorithms referred to as quantum approximate optimization algorithm (QAOA) have been recently proposed. QAOA attempts to approximately solve hard problems using a protocol know as bang-bang. The technique is based on the unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. QAOA has been explored in the context of several optimization problems such as Max-Cut problem, variational Eigenvalue problem etc. Recently, attempts have been made to create QAOA for the Traveling Salesman Problem (TSP). Due to small node size and limited solution capability of the currently available quantum computers and/or simulators, we develop a hybrid approach where subgraphs of a TSP tour are executed on a quantum computer and the results from the quantumoptimization are combined in further optimization of the whole tour. Since the local optimization of a subgraph is prone to getting stuck in a local minima, we overcome this problem by using a parallel Ant Colony optimizationalgorithm with periodic pheromone exchange between colonies. Our results are encouraging and yield optimum results for benchmarks with less than 50 nodes, and usually within 1% of the optimal solution for benchmarks with around 200 nodes.
The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systemat...
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The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger-Horne-Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressed atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.
Mobile edge computing is a promising paradigm that provides edge users with dependable computing services. However, due to the dynamic nature of mobile users and the limited resources of edge servers, it is essential ...
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Mobile edge computing is a promising paradigm that provides edge users with dependable computing services. However, due to the dynamic nature of mobile users and the limited resources of edge servers, it is essential to emphasize the load balancing of edge servers and the cooperation of heterogeneous computing resources. This paper proposes a Dynamic Resource Allocation (DRA) scheme based on a quantum approximate optimization algorithm (QAOA). The DRA is composed of the two components listed below. Firstly, we apply generative adversarial network to predict the future user density in various regions, which is an effective resource allocation aid. Secondly, QAOA is utilized to pre-allocate edge servers resources based on an advanced model of user density. The simulation results demonstrate that the efficient application of DRA ensures the load balancing of edge servers and simultaneously alleviates communication latency.
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