# Mainz 2017 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# Q: Fachverband Quantenoptik und Photonik

## Q 47: Quantum Computing I

### Q 47.5: Vortrag

### Donnerstag, 9. März 2017, 15:45–16:00, P 2

**An efficient quantum algorithm for spectral estimation** — •Adrian Steffens^{1,2}, Patrick Rebentrost^{2}, Iman Marvian^{2}, Jens Eisert^{1}, and Seth Lloyd^{2,3} — ^{1}Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin — ^{2}Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 — ^{3}Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139

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 non-Hermitian matrices. Our algorithm features an efficient quantumclassical division of labor: The time-critical steps are implemented in quantum superposition, while an interjacent step, requiring only exponentially few 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.