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Quantum Information Processing

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01-02-2014

Selecting efficient phase estimation with constant-precision phase shift operators

Author: Chen-Fu Chiang

Published in: Quantum Information Processing | Issue 2/2014

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Abstract

We investigate the cost of three phase estimation procedures that require only constant-precision phase shift operators. The cost is in terms of the number of elementary gates, not just the number of measurements. Faster phase estimation requires the minimal number of measurements with a logarithmic factor of reduction when the required precision $n$ is large. The arbitrary constant-precision approach (ACPA) requires the minimal number of elementary gates with a minimal factor of 14 of reduction in comparison with Kitaev’s approach. The reduction factor increases as the precision gets higher in ACPA. Kitaev’s approach is with a reduction factor of 14 in comparison with the faster phase estimation in terms of elementary gate counts.

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In quantum computing, the quantum Fourier transform is a linear transformation on quantum bits and is the quantum analog of the discrete Fourier transform.

The iterated logarithm. It is defined as follows:

$$\begin{aligned} \log ^* n := \left\{ \begin{array}{ll} 0 &{} \quad \text {if } n \le 1 \\ 1 + \log ^*(\log n) &{} \quad \text {if } n > 1 \end{array} \right. . \end{aligned}$$

A similar analysis can be applied to $x_{j+1}$ = 1.

No matter how many rounds there are, the very last round must have $S$ of size $\log n$.

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Title: Selecting efficient phase estimation with constant-precision phase shift operators
Author: Chen-Fu Chiang
Publication date: 01-02-2014
Publisher: Springer US
Published in: Quantum Information Processing / Issue 2/2014
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-013-0659-9

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Other articles of this Issue 2/2014

The topological basis expression of Heisenberg spin chain

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Quantum discord amplification of fermionic systems in an accelerated frame

Considering nearest neighbor constraints of quantum circuits at the reversible circuit level