量子计算机上的离散余弦变换
Discrete Cosine Transforms on Quantum Computers
AI总结：
本文证明利用量子力学原理，量子计算机仅需O(log^2 N)次操作即可实现大小为NxN及I至IV型的离散余弦与正弦变换，突破了经典算法O(N log N)操作的限制。
摘要：
经典计算机无法在低于线性时间内计算N点的离散余弦变换。对于利用量子力学叠加、纠缠和干涉原理的计算机，这一平凡下界不再成立。事实上，我们表明，在量子计算机上仅需O(log^2 N)次操作即可实现大小为NxN且类型为I、II、III和IV的离散余弦变换与离散正弦变换，而经典计算机上已知的快速算法需要O(N log N)次操作。
英文摘要：
A classical computer does not allow to calculate a discrete cosine transform on N points in less than linear time. This trivial lower bound is no longer valid for a computer that takes advantage of quantum mechanical superposition, entanglement, and interference principles. In fact, we show that it is possible to realize the discrete cosine transforms and the discrete sine transforms of size NxN and types I,II,III, and IV with as little as O(log^2 N) operations on a quantum computer, whereas the known fast algorithms on a classical computer need O(N log N) operations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
