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arXiv:2412.17580

Quantum Time-Series Learning with Evolutionary Algorithms

Vignesh Anantharamakrishnan, Márcio M. Taddei

Published Dec 23, 2024• 0 citations
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Abstract

Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use of evolutionary algorithms for such optimization, specifically for time-series forecasting. We perform a comparison, for diverse instances of real-world data, between gradient-descent parameter optimization and covariant-matrix adaptation evolutionary strategy. We observe that gradient descent becomes permanently trapped in local minima that have been avoided by evolutionary algorithms in all tested datasets, reaching up to a six-fold decrease in prediction error. Finally, the combined use of evolutionary and gradient-based techniques is explored, aiming at retaining advantages of both. The results are particularly applicable in scenarios sensitive to gains in accuracy.

DOI
10.48550/arxiv.2412.17580

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Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use of evolutionary algorithms for such optimization, specifically for time-series forecasting. We perform a comparison, for diverse instances of real-world data, between gradient-descent parameter optimization and covariant-matrix adaptation evolutionary strategy. We observe that gradient descent becomes permanently trapped in local minima that have been avoided by evolutionary algorithms in all tested datasets, reaching up to a six-fold decrease in prediction error. Finally, the combined use of evolutionary and gradient-based techniques is explored, aiming at retaining advantages of both. The results are particularly applicable in scenarios sensitive to gains in accuracy.
Recent research has demonstrated that parametric quantum circuits (PQCs) are affected by gradients that progressively vanish to zero as a function of the number of qubits. We show that using a combination of gradient-free natural evolutionary strategy and gradient descent can mitigate the possibility of optimizing barren plateaus in the landscape. We implemented 2 specific methods: natural evolutionary strategy stochastic gradient descent (NESSGD) and natural evolutionary strategy adapting the step size according to belief in observed gradients (NESAdaBelief) to optimize PQC parameter values. They were compared with standard stochastic gradient descent, adaptive moment estimation, and a version of adaptive moment estimation adapting the step size according to belief in observed gradients in 5 classification tasks. NESSGD and NESAdaBelief demonstrated some superiority in 4 of the tasks. NESAdaBelief showed higher accuracy than AdaBelief in all 5 tasks. In addition, we investigated the applicability of NESSGD under the parameter shift rule and demonstrated that NESSGD can adapt to this rule, which means that our proposed method could also optimize the parameters of PQCs on quantum computers.
Variational Quantum Circuits (VQCs) are viable alternatives for implementing quantum circuits in current quantum processors. VQCs are reduced circuits with parameters that are trained to minimize a loss function for a given problem. In this work, we propose an approach to optimize the parameters of a VQC using Genetic Algorithms (GAs). We explored different GA configurations, on 3 databases - Sonar, Cancer and Banknotes datasets, comparing the proposed approach with 2 classical optimizers based on gradient descent. The results show that genetic algorithms can effectively optimize the weights of variational circuits to achieve high classification accuracy with convergence speed up to 7.3 times (in Sonar Database), 4.8 times (Cancer Database), and 3.7 times (Banknote Database) compared with the traditional optimizers. The experimental results indicate that the genetic algorithm achieves performance metrics that are significantly superior or at least comparable to those obtained by gradient descent-based optimizers, demonstrating the potential and robustness of evolutionary strategies in training variational quantum circuits.
Variational quantum algorithms (VQAs) employ parametrized quantum circuits optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing ``parameter shift rule'' mandates a double evaluation of the cost function for each parameter. In this paper, we introduce an optimization approach named ``learning to learn with an evolutionary strategy'' (LLES). LLES unifies ``learning to learn'' and ``evolutionary strategy'' methods. Learning to learn treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, evolutionary strategy employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. The obtained results underscore the efficacy of this approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the evolutionary strategy method.
Variational Quantum Algorithms (VQAs) employ quantum circuits parameterized by UUU, optimized using classical methods to minimize a cost function. While VQAs have found broad applications, certain challenges persist. Notably, a significant computational burden arises during parameter optimization. The prevailing ``parameter shift rule'' mandates a double evaluation of the cost function for each parameter. In this article, we introduce a novel optimization approach named ``Learning to Learn with an Evolutionary Strategy'' (LLES). LLES unifies ``Learning to Learn'' and ``Evolutionary Strategy'' methods. ``Learning to Learn'' treats optimization as a learning problem, utilizing recurrent neural networks to iteratively propose VQA parameters. Conversely, ``Evolutionary Strategy'' employs gradient searches to estimate function gradients. Our optimization method is applied to two distinct tasks: determining the ground state of an Ising Hamiltonian and training a quantum neural network. Results underscore the efficacy of this novel approach. Additionally, we identify a key hyperparameter that significantly influences gradient estimation using the ``Evolutionary Strategy'' method.
Quantum machine learning is a research area that explores the interplay of ideas from quantum computing and machine learning to speed up the time it takes to train or evaluate a machine learning model. Variational quantum classifiers are among the most widely used quantum models for supervised machine learning and base their operation on learning free parameters through conventional optimization algorithms. In spite of their potential benefits, there is a design issue making quantum variational classifiers not fully operative: the existence of exponentially vanishing gradients, known as “barren plateau landscapes”. A barren plateau is a trainability problem that occurs in optimization algorithms for quantum machine learning when the problem-solving space turns flat as the algorithm is run. In that situation, the algorithm cannot find the downward slope in what appears to be a featureless landscape and there's no clear path to the optimum of the cost function. In this challenging scenario, evolutionary optimization techniques can be a viable choice in solving the problem because of their gradient independence. This paper introduces a comparative study involving different evolutionary algorithms to assess their suitability in acting as optimizer for a specific quantum machine learning method, known as variational quantum classifier.
Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a problem-dependent cost function. Although such algorithms are powerful in principle, the non-convexity of the associated cost landscapes and the prevalence of local minima means that local optimization methods such as gradient descent typically fail to reach good solutions. In this work we suggest a method to improve gradient-based approaches to variational quantum circuit optimization, which involves coupling the output of the quantum circuit to a classical neural network. The effect of this neural network is to peturb the cost landscape as a function of its parameters, so that local minima can be escaped or avoided via a modification to the cost landscape itself. We present two algorithms within this framework and numerically benchmark them on small instances of the Max-Cut optimization problem. We show that the method is able to reach deeper minima and lower cost values than standard gradient descent based approaches. Moreover, our algorithms require essentially the same number of quantum circuit evaluations per optimization step as the standard approach since, unlike the gradient with respect to the circuit, the neural network updates can be estimated in parallel via the backpropagation method. More generally, our approach suggests that relaxing the cost landscape is a fruitful path to improving near-term quantum computing algorithms.