Quantum Linear Prediction Using QFT

Quantum computing has the potential to significantly impact massive signal processing operations.  Research is being done in exploring ways to harness its potential for signal processing applications.  The use of quantum computing for signal processing holds great promise for improving the speed and accuracy in several signal processing applications including linear prediction of speech and other signals.

Researchers at Arizona State University have developed a quantum linear prediction algorithm for signal processing.  This algorithm uses quantum Fourier transforms (QFTs) to obtain the correlation of a signal and the modified Harrow-Hassidim-Lloyd (HHL) algorithm to solve a linear system of equations, to potentially achieve a faster computation compared to classical algorithms (e.g., classical linear prediction).  More specifically, this quantum linear prediction algorithm uses autocorrelations formed with QFTs, and a modified quantum HHL circuit that includes appropriate normalization and encoding steps.  The developed quantum linear prediction algorithm can be used for various signal processing applications such as system identification, spectral estimation, and analysis-synthesis of speech signals. 

Related publication: Quantum Linear Prediction for System Identification and Spectral Estimation Applications

Potential Applications:

• Signal Processing Algorithm (e.g., for speech signals) for:
  • System Identification
  • Spectral Estimation
  • Analysis-Synthesis

Benefits and Advantages:

• Comparing this QLP algorithm to classical linear prediction (CLP) in signal processing applications, for
  • System Identification by analyzing the frequency responses. The quantum autoregressive model (QLP-related) performs as well as the classical autoregressive model (CLP-related), with almost overlapping frequency responses.
  • Spectral Estimation by examining autoregressive spectral estimation to estimate the power spectrum of a given speech signal using the autoregressive model, the classical autoregressive spectrum obtained through CLP and the quantum autoregressive spectrum obtained through QLP closely follow the same envelope of the input signal’s spectrum.
  • Analysis-Synthesis by calculating the mean square error for quantifying the difference between the original and synthesized speech signals.  This provides a measure of reconstruction accuracy for QLP and CLP results and the QLP approach has a similar speech prediction as obtained using CLP with a similar MSE.