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

Abstract

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.