The Application of Quantum Fourier Transform in Cosmic Microwave Background Data Analysis

TL;DR

This paper explores replacing the classical FFT with the Quantum Fourier Transform in cosmic microwave background data analysis, highlighting potential speedups at high resolution and discussing current limitations due to data encoding overhead.

Contribution

It investigates the application of QFT in CMB analysis, demonstrating potential advantages and identifying data encoding as a key bottleneck for quantum speedup.

Findings

QFT shows potential advantages over FFT at high resolutions

Classical-to-quantum data encoding overhead limits current efficiency

Future improvements could enhance quantum speedup feasibility

Abstract

The Cosmic Microwave Background (CMB) data analysis and the map-making process rely heavily on the use of spherical harmonics. For suitable pixelizations of the sphere, the (forward and inverse) Fourier transform plays a crucial role in computing all-sky map from spherical harmonic expansion coefficients -- or from angular power spectrum -- and vice versa. While the Fast Fourier Transform (FFT) is traditionally employed in these computations, the Quantum Fourier Transform (QFT) offers a theoretical advantage in terms of computational efficiency and potential speedup. In this work, we study the potential advantage of using the QFT in this context by exploring the substitution of the FFT with the QFT within the \textit{healpy} package. Performance evaluations are conducted using the Aer simulator. Our results indicate that QFT exhibits potential advantages over FFT that are particularly relevant at high-resolution. However, classical-to-quantum data encoding overhead represents a limitation to current efficiency. In this work, we adopted amplitude encoding, due to its efficiency on encoding maximum data to minimum number of qubits. We identify data encoding as a potential significant bottleneck and discuss its impact on quantum speedup. Future improvements in quantum encoding strategies and algorithmic optimizations could further enhance the feasibility of QFT in CMB data analysis.