Quantum Linear Prediction for System Identification and Spectral Estimation Applications

This paper presents the design and implementation of quantum algorithms and circuits for linear prediction. The intended applications are system identification, spectral estimation, and speech processing. A frequency-domain method that uses the quantum Fourier transform is developed to estimate the autocorrelation sequence of the signal and a quantum circuit is designed to estimate the linear prediction parameters. The quantum linear prediction performance is evaluated in system identification, autoregressive (AR) spectral estimation, and speech analysis applications. More specifically, we evaluate the performance of the quantum linear predictor in terms of quantum noise effects, qubit precision, and overall computational requirements. Comparisons of quantum versus classical linear prediction are presented.