Scaling up and down of 3-D floating-point data in quantum computation

• Published in: Scientific reports 2022-02, Vol.12 (1), p.2771-2771, Article 2771
• Main Authors: Xu, Meiyu, Lu, Dayong, Sun, Xiaoyun
• Format: Article
• Language: English
• Subjects: 639/705/117; 639/766/483/481; Algorithms; Humanities and Social Sciences; Image processing; multidisciplinary; Nearest-neighbor; Scaling; Science; Science (multidisciplinary)
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-022-06756-w

In the past few decades, quantum computation has become increasingly attractive due to its remarkable performance. Quantum image scaling is considered a common geometric transformation in quantum image processing, however, the quantum floating-point data version of which does not exist. Is there a corresponding scaling for 2-D and 3-D floating-point data? The answer is yes. In this paper, we present a quantum scaling up and down scheme for floating-point data by using trilinear interpolation method in 3-D space. This scheme offers better performance (in terms of the precision of floating-point numbers) for realizing the quantum floating-point algorithms than previously classical approaches. The Converter module we proposed can solve the conversion of fixed-point numbers to floating-point numbers of arbitrary size data with p + q qubits based on IEEE-754 format, instead of 32-bit single-precision, 64-bit double-precision and 128-bit extended-precision. Usually, we use nearest-neighbor interpolation and bilinear interpolation to achieve quantum image scaling algorithms, which are not applicable in high-dimensional space. This paper proposes trilinear interpolation of floating-point data in 3-D space to achieve quantum algorithms of scaling up and down for 3-D floating-point data. Finally, the quantum scaling circuits of 3-D floating-point data are designed.