The Application of Quantum Fourier Transform in Cosmic Microwave Background Data Analysis
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arXiv
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| Main Authors: | , , , , , , , , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912386440495104 |
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| author | Farsian, Farida Trombetti, Tiziana Burigana, Carlo Schilliró, Francesco Bulgarelli, Andrea Cardone, Vincenzo Cappelli, Luca Meneghetti, Massimo Murante, Giuseppe Rizzo, Alessandro Sarracino, Giuseppe Graziotti, Irene Scaramella, Roberto Testa, Vincenzo |
| author_facet | Farsian, Farida Trombetti, Tiziana Burigana, Carlo Schilliró, Francesco Bulgarelli, Andrea Cardone, Vincenzo Cappelli, Luca Meneghetti, Massimo Murante, Giuseppe Rizzo, Alessandro Sarracino, Giuseppe Graziotti, Irene Scaramella, Roberto Testa, Vincenzo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_15855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Application of Quantum Fourier Transform in Cosmic Microwave Background Data Analysis Farsian, Farida Trombetti, Tiziana Burigana, Carlo Schilliró, Francesco Bulgarelli, Andrea Cardone, Vincenzo Cappelli, Luca Meneghetti, Massimo Murante, Giuseppe Rizzo, Alessandro Sarracino, Giuseppe Graziotti, Irene Scaramella, Roberto Testa, Vincenzo Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics 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. |
| title | The Application of Quantum Fourier Transform in Cosmic Microwave Background Data Analysis |
| topic | Instrumentation and Methods for Astrophysics Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2505.15855 |