An efficient quantum algorithm for spectral estimation
Abstract
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well—consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate nonHermitian matrices. Our algorithm features an efficient quantumclassical division of labor: the timecritical steps are implemented in quantum superposition, while an interjacent step, requiring much fewer parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms.
 Publication:

New Journal of Physics
 Pub Date:
 March 2017
 DOI:
 10.1088/13672630/aa5e48
 arXiv:
 arXiv:1609.08170
 Bibcode:
 2017NJPh...19c3005S
 Keywords:

 Quantum Physics
 EPrint:
 20 pages