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arXiv 1012.4727quant-ph
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基于任意常数精度相移算子的量子相位估计

Quantum Phase Estimation with Arbitrary Constant-precision Phase Shift Operators

Hamed Ahmadi, Chen-Fu Chiang

备注：
14 pages, 6 figures and 1 table
发表信息：
Quantum Information and Computation, vol.12, no.9 & 10, pp. 0864-0875, (2012)
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摘要：

虽然量子相位估计（QPE）是迄今为止已知的许多量子算法的核心，但其物理实现（基于量子傅里叶变换（QFT）的算法）受到高精度受控相移算子要求的高度约束，这仍然难以实现。在本文中，我们介绍了一种替代方法来近似实现QPE与任意恒定精度控制相移运营商。新的量子算法弥合了基于QFT的QPE算法和Kitaev原始方法之间的差距。为了近似本征相位精确到第n位，Kitaev的原始方法不需要任何受控相移算子。相比之下，基于QFT或近似QFT的QPE算法需要具有至少Pi/2n的精度的受控相移算子。新的方法填补了空白，只需要任意恒定精度的控制相移运营商。从物理实现的角度来看，新算法优于Kitaev的方法。

英文摘要：

While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In this paper, we introduce an alternative approach to approximately implement QPE with arbitrary constant-precision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase precise to the nth bit, Kitaev's original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constant-precision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev's approach.

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