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Related Experiment Video

Updated: Jun 12, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Complementary Polynomials in Quantum Signal Processing.

Bjorn K Berntson^1,2, Christoph Sünderhauf²

¹Riverlane Research, Cambridge, Massachusetts, USA.

Communications in Mathematical Physics

|June 9, 2025

Summary

This summary is machine-generated.

We introduce a new method for quantum signal processing using complex analysis to find complementary polynomials. This approach offers explicit error guarantees and outperforms existing numerical techniques for quantum computing applications.

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Area of Science:

Quantum computing
Quantum signal processing

Background:

Implementing polynomial functions on quantum computers requires constructing complementary polynomials.
Current numerical methods for this task lack explicit error analysis.

Purpose of the Study:

To develop a novel approach for calculating complementary polynomials using complex analysis.
To provide explicit error guarantees for the computation of complementary polynomials.

Main Methods:

Utilizing complex analysis to derive a contour integral representation for complementary polynomials.
Developing a Fast Fourier Transform-based algorithm for efficient computation in the monomial basis.

Main Results:

A canonical complementary polynomial representation using contour integrals was established.
The Fast Fourier Transform algorithm provides explicit error bounds and demonstrates superior performance over optimization-based methods.

Conclusions:

The new complex analysis and Fast Fourier Transform-based method offers an efficient and reliable approach to quantum signal processing.
This work provides a significant advancement in the theoretical and practical aspects of implementing polynomial functions on quantum computers.