Quantum Time-Series Learning with Evolutionary Algorithms

TL;DR

This paper addresses parameter optimization for variational quantum circuits used in time-series forecasting, where gradient-based methods often get trapped in local minima and struggle with barren plateaus. It compares gradient-based optimization (Adam) with CMA-ES, applied to a quantum recurrent neural network (QRNN), and introduces a hybrid approach that warms CMA-ES with gradient descent. On four univariate datasets using the first 100 points and an 80/20 split, CMA-ES surpasses gradient descent by up to six-fold in forecast error, with the hybrid method delivering further gains and often faster convergence. The results underscore the potential of evolutionary optimization to enhance accuracy in near-term quantum time-series tasks, particularly when long-horizon forecasts or limited data amplify gradient-descent weaknesses.

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.

Figures (2)

• Figure 1: Quantum recurrent neural network (QRNN) circuit used in this work, after Li2023, and its recurring ansatz.
• Figure 2: Forecast error for the gold-price, Santa Fe, Mackey-Glass, and Delhi-weather datasets, with predictions for 7, 1, 4, 9 timesteps into the future, respectively. For each dataset, three different optimization strategies are used: gradient descent (Adam), the evolutionary strategy CMA-ES, and their hybrid, which uses gradient descent as a warm start (the first point of each hybrid curve by definition coincides with the gradient-based value). The relative RMS error is shown, with points and shaded regions corresponding respectively to mean and one standard deviation after 5 runs. The x-axis values correspond to gradient-descent epochs; for CMA-ES and hybrid the points are plotted with a horizontal delay of 20 units to visually depict that they take circa 20 times longer to train, per epoch, than gradient descent.