Quantum Amplitude Arithmetic
Abstract
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full use of quantum mechanical speedup, more transformation should be implemented on amplitudes. Here we propose the notion of quantum amplitude arithmetic (QAA) that intent to evolve the quantum state by performing arithmetic operations on amplitude. Based on the basic design of multiplication and addition operations, QAA can be applied to solve the black-box quantum state preparation problem and the quantum linear system problem with fairly low complexity, and evaluate nonlinear functions on amplitudes directly. QAA is expected to find applications in a variety of quantum algorithms.
Cite
@article{arxiv.2012.11056,
title = {Quantum Amplitude Arithmetic},
author = {Shengbin Wang and Zhimin Wang and Guolong Cui and Lixin Fan and Shangshang Shi and Ruimin Shang and Wendong Li and Zhiqiang Wei and Yongjian Gu},
journal= {arXiv preprint arXiv:2012.11056},
year = {2020}
}
Comments
13 pages, 7 figures