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 $$p+q$$ 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.

Impacts of metal mining on river systems: a global assessment

“…Various multilink exposure pathways exist for humans to ingest or inhale contaminant metals from mine sites and floodplain soils (6). For example, plants and crops grown domestically or commercially on contaminated soils or irrigated by water contaminated by mine waste frequently contain high concentrations of metals and metalloids (hereafter referred to as "metals") (7)(8)(9). Animals grazing on floodplains may then eat this plant material and sediment, especially after flooding, when fresh metal-rich sediment is deposited (10).…”