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Journal of Advanced Research

Optimizing quantum cloning circuit parameters based on adaptive guided differential evolution algorithm

Essam Halim Houssein, Mohamed A. Mahdy, Manal G. Eldin, Doaa Shebl, Waleed M. Mohamed, Mahmoud Abdel‐Aty

Published Oct 16, 2020• 31 citations
Publisher

Abstract

Introduction: Quantum cloning operation, started with no-go theorem which proved that there is no capability to perform a cloning operation on an unknown quantum state, however, a number of trials proved that we can make approximate quantum state cloning that is still with some errors. Objectives: To the best of our knowledge, this paper is the first of its kind to attempt using meta-heuristic algorithm such as Adaptive Guided Differential Evolution (AGDE), to tackle the problem of quantum cloning circuit parameters to enhance the cloning fidelity. Methods: To investigate the effectiveness of the AGDE, the extensive experiments have demonstrated that the AGDE can achieve outstanding performance compared to other well-known meta-heuristics including; Enhanced LSHADE-SPACMA Algorithm (ELSHADE-SPACMA), Enhanced Differential Evolution algorithm with novel control parameter adaptation (PaDE), Improved Multi-operator Differential Evolution Algorithm (IMODE), Parameters with adaptive learning mechanism (PALM), QUasi-Affine TRansformation Evolutionary algorithm (QUATRE), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Cuckoo Search (CS), Bat-inspired Algorithm (BA), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA). Results: . Conclusion: Accordingly, the qualitative and quantitative measurements including average, standard deviation, convergence curves of the competitive algorithms over 30 independent runs, proved the superiority of AGDE to enhance the cloning fidelity.

DOI
10.1016/j.jare.2020.10.001

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Introduction: Quantum cloning operation, started with no-go theorem which proved that there is no capability to perform a cloning operation on an unknown quantum state, however, a number of trials proved that we can make approximate quantum state cloning that is still with some errors. Objectives: To the best of our knowledge, this paper is the first of its kind to attempt using meta-heuristic algorithm such as Adaptive Guided Differential Evolution (AGDE), to tackle the problem of quantum cloning circuit parameters to enhance the cloning fidelity. Methods: To investigate the effectiveness of the AGDE, the extensive experiments have demonstrated that the AGDE can achieve outstanding performance compared to other well-known meta-heuristics including; Enhanced LSHADE-SPACMA Algorithm (ELSHADE-SPACMA), Enhanced Differential Evolution algorithm with novel control parameter adaptation (PaDE), Improved Multi-operator Differential Evolution Algorithm (IMODE), Parameters with adaptive learning mechanism (PALM), QUasi-Affine TRansformation Evolutionary algorithm (QUATRE), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Cuckoo Search (CS), Bat-inspired Algorithm (BA), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA). Results: . Conclusion: Accordingly, the qualitative and quantitative measurements including average, standard deviation, convergence curves of the competitive algorithms over 30 independent runs, proved the superiority of AGDE to enhance the cloning fidelity.
Differential evolution (DE) is a population based evolutionary algorithm widely used for solving multidimensional global optimization problems over continuous spaces. However, the design of its operators makes it unsuitable for many real-life constrained combinatorial optimization problems which operate on binary space. On the other hand, the quantum inspired evolutionary algorithm (QEA) is very well suitable for handling such problems by applying several quantum computing techniques such as Q-bit representation and rotation gate operator, etc. This paper extends the concept of differential operators with adaptive parameter control to the quantum paradigm and proposes the adaptive quantum-inspired differential evolution algorithm (AQDE). The performance of AQDE is found to be significantly superior as compared to QEA and a discrete version of DE on the standard 0–1 knapsack problem for all the considered test cases.
The use of Evolutionary Algorithms (EA) for solving Mathematical/Computational Optimization Problems is inspired by the biological processes of Evolution. Few of the primitives involved in the Evolutionary process/paradigm are selection of ’Fit’ individuals (from a population sample) for retention, cloning, mutation, discarding, breeding, crossover etc. In the Evolutionary Algorithm abstraction, the individuals are deemed to be solution candidates to an Optimization problem and additional solution(/sets) are built by applying analogies to the above primitives (cloning, mutation etc.) by means of evaluating a ’Fitness’ function/criterion. One such algorithm is Differential Evolution(DE) which can be used to compute the minima of functions such as the rastrigin function and rosenbrock function. This work is an attempt to study the result of applying the DE method on these functions with candidate individuals generated on classical Turing modeled computation and comparing the same with those on state of the art Quantum computation.The study benchmarks the convergence of these functions by varying the parameters initialized and reports timing, convergence, and resource utilization results.
This research centers on enhancing quantum circuits for Quantum Decision Trees (QDT) a highly promising algorithm in the realm of quantum machine learning aimed at classification and pattern recognition-via a hybrid metaheuristic optimization framework that integrates Golden Eagle Optimization (GEO) with Adaptive Gradient Descent (AGD). Although QDTs provide interpretability and quantum-enhanced classification capabilities for high-dimensional data sets, their effectiveness is frequently limited by subpar circuit configurations, excessive gate depth, and susceptibility to quantum noise. The suggested hybrid approach utilizes the global search capability of GEO and the local convergence accuracy of AGD to optimize QDT parameters such as entanglement structure, placement of quantum gates, and decision thresholds. Experimental findings indicate that the proposed technique achieves quicker convergence (38 iterations), superior classification accuracy (97.8 %), decreased quantum circuit complexity (39 quantum gates), and enhanced noise resilience (fidelity: 0.986), surpassing traditional methods including Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA). These results affirm the promise of hybrid metaheuristic optimizers in improving quantum circuit efficiency for real-world quantum machine learning applications.
This research endeavor centers on augmenting the quantum circuitry of the Quantum Support Vector Machine (QSVM), a pivotal algorithm in the realm of quantum machine learning, via a hybrid optimization methodology that amalgamates Quantum Natural Gradient Descent (QNGD) with the Whale Optimization Algorithm (WOA). QSVM harnesses the power of quantum computing to facilitate proficient classification within high-dimensional spaces; however, its efficacy is frequently compromised by suboptimal circuit parameters and quantum noise prevalent in near-term quantum devices. The proposed hybrid optimization paradigm integrates the global search proficiency of WOA with the effective parameter refinement capabilities of QNGD, culminating in expedited convergence (38 iterations), enhanced classification accuracy (96.8%), optimized circuit complexity (44 quantum gates), and increased resilience against noise (fidelity: 0.985). In comparison to conventional optimization techniques such as Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Firefly Algorithm (FA), our methodology demonstrates superior efficacy by refining quantum kernel computation, entanglement configurations, and circuit depth, while concurrently alleviating the impacts of quantum noise.
Intelligent optimization algorithm based on quantum behavior is the hot spot of intelligent computation. Quantum clone genetic algorithm has many shortcomings such as: low efficiency, poor population diversity, slow convergence speed, easy to trap in local minimums, blindness in global optimal searching direction and so on. An improved quantum clone genetic algorithm (IQCGA) is proposed in this paper. The algorithm have many merits: (1) Adopting the nicking probability division initialization strategy, population diversity is enhanced; (2) Introducing the quantum whole interference crossover, the information is spread in the whole population, so it helps to avoid trapping in local minimums, and accelerates convergence speed; (3) Making use of adaptation strategy in quantum rotate gate updating, searching speed for optimal solution is accelerated; (4) In order to avoid premature and evolution stagnation, the superior individual whole crossover quantum catastrophe strategy is adopted, which helps the population to search the objective solution in different directions. IQCGA is composted of initialization stage and iteration evolution stage. Furthermore, theory analysis is given to prove the convergence. Finally, Simulation results prove that the algorithms can maintain the population diversity, reduce calculation complexity, accelerate searching speed for optimal solution, and avoid trapping in local minimums. So it has the better searching optimal ability and convergence speed.
Quantum neural networks (QNNs) represent an emerging technology that uses a quantum computer for neural network computations. The QNNs have demonstrated potential advantages over classical neural networks in certain tasks. As a core component of a QNN, the parameterized quantum circuit (PQC) plays a crucial role in determining the QNN's overall performance. However, quantum circuit architectures designed manually based on experience or using specific hardware structures can suffer from inefficiency due to the introduction of redundant quantum gates, which amplifies the impact of noise on system performance. Recent studies have suggested that the advantages of quantum evolutionary algorithms (QEAs) in terms of precision and convergence speed can provide an effective solution to quantum circuit architecture-related problems. Currently, most QEAs adopt a fixed rotation mode in the evolution process, and a lack of an adaptive updating mode can cause the QEAs to fall into a local optimum and make it difficult for them to converge. To address these problems, this study proposes an adaptive quantum evolution algorithm (AQEA). First, an adaptive mechanism is introduced to the evolution process, and the strategy of combining two dynamic rotation angles is adopted. Second, to prevent the fluctuations of the population's offspring, the elite retention of the parents is used to ensure the inheritance of good genes. Finally, when the population falls into a local optimum, a quantum catastrophe mechanism is employed to break the current population state. The experimental results show that compared with the QNN structure based on manual design and QEA search, the proposed AQEA can reduce the number of network parameters by up to 20% and increase the accuracy by 7.21%. Moreover, in noisy environments, the AQEA-optimized circuit outperforms traditional circuits in maintaining high fidelity, and its excellent noise resistance provides strong support for the reliability of quantum computing.