Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

A. Gilyén, Y. Su, G. H. Low, N. Wiebe · 2019 · Proc. 51st ACM STOC

| 编号 QC017 | 主题 量子算法工具箱 | 链接 10.1145/3313276.3316366 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new “Singular value transformation” algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang [LC17a]. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while typically only use a constant number of ancilla qubits.

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