本文证明了多种著名信号变换（如量子傅里叶变换、离散余弦/正弦变换和离散哈特利变换）在量子计算机上具有极高效实现，仅需 O(log^2 N) 个基本量子门即可处理长度为 N 的输入序列。
摘要：
我们证明许多著名的信号变换允许在量子计算机上实现极高效的计算。我们解释了一些基本量子电路，并回顾了 Quantum Fourier Transform 的构造。我们推导了 Discrete Cosine and Sine Transforms 以及 Discrete Hartley transform 的量子电路。我们证明，对于长度为 N 的输入序列，实现上述任何变换最多只需要 O(log^2 N) 个基本量子门。
英文摘要：
We show that many well-known signal transforms allow highly efficient realizations on a quantum computer. We explain some elementary quantum circuits and review the construction of the Quantum Fourier Transform. We derive quantum circuits for the Discrete Cosine and Sine Transforms, and for the Discrete Hartley transform. We show that at most O(log^2 N) elementary quantum gates are necessary to implement any of those transforms for input sequences of length N.
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Autonomous Quantum Processing Unit: An Autonomous Thermal Computing Machine & its Physical Limitations
Atominstitut, TU Wien（维也纳工业大学原子研究所）；Vienna Center for Quantum Science and Technology, TU Wien（维也纳量子科学与技术中心）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
Understanding the fundamental relationships between physics and its information-processing capability has been an active research topic for many years. Physical reservoir computing is a recently introduced framework that allows one to exploit the complex dynamics of physical systems as information-processing devices. This framework is particularly suited for edge computing devices, in which information processing is incorporated at the edge (e.g., into sensors) in a decentralized manner to reduce the adaptation delay caused by data transmission overhead. This paper aims to illustrate the poten…
A novel family of Cosine series Quantum Sampling (QCoSamp) operators appropriate for quantum computing is described. The development of quantum algorithms, analogous to classical algorithms, we apply to the harmonic analysis of signals. We show quantum sampling through measurements of a quantum system, and after operators of the family are applied, allow for input signal mapping with a Fourier series representation. Technical methodologies employed, facilitating the implementation of each QCoSamp algorithm to a quantum computer and application to the field of signal and image processing we als…
The University of Tokyo（东京大学）；Keio University（庆应义塾大学）
Quantum computing has been moving from a theoretical phase to practical one, presenting daunting challenges in implementing physical qubits, which are subjected to noises from the surrounding environment. These quantum noises are ubiquitous in quantum devices and generate adverse effects in the quantum computational model, leading to extensive research on their correction and mitigation techniques. But do these quantum noises always provide disadvantages? We tackle this issue by proposing a framework called quantum noise-induced reservoir computing and show that some abstract quantum noise mod…
Irish Centre for High-End Computing（爱尔兰高端计算中心）；National University of Ireland, Galway（爱尔兰国立大学戈尔韦分校）；Intel Deutschland GmbH（英特尔德国有限公司）
Natural language processing (NLP) problems are ubiquitous in classical computing, where they often require significant computational resources to infer sentence meanings. With the appearance of quantum computing hardware and simulators, it is worth developing methods to examine such problems on these platforms. In this manuscript we demonstrate the use of quantum computing models to perform NLP tasks, where we represent corpus meanings, and perform comparisons between sentences of a given structure. We develop a hybrid workflow for representing small and large scale corpus data sets to be enco…
