<p>Right now I am going through <a href="http://arxiv.org/abs/quant-ph/0102108" rel="nofollow">Quantum Kolmogorov Complexity Based on Classical Descriptions</a> by Vitanyi.</p>

<p>In the introduction, the author assumed the primitive rotation $\theta = 53.13^\circ$ to have countably many quantum Turing machine.</p>

<p>Is this choice of angle arbitrary?</p>

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2016-09-15T07:09:29.730Z
N.B. $53.15^\circ \approx \arcsin (4/5) $. Restricting to rational amplitudes with a denominator of 5 is an old convention from the early days of quantum computing, dating back at least to Bernstein and Vazirani, for those who are looking for a special case to make comparisons between quantum complexity and counting complexity.
Niel de Beaudrap
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2016-09-15T07:47:39.010Z
I will check their paper.
Omar Shehab
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2016-11-19T22:37:31.417Z
@Niel: I am fairly sure that Bernstein and Vazirani were the first ones to use arcsin(4/5). And if it's not already clear from Niel's comment, $4/5$ is chosen because $3^2 + 4^2 = 5^2$.
Peter Shor 
<quantum-computing><turing-machines><it.information-theory><quantum-information><kolmogorov-complexity>
Why primitive rotation is $53.13^\circ$ in the quantum Turing machine used by Vitanyi for Quantum Kolmogrov Complexity?
Omar Shehab
# Why primitive rotation is $53.13^\circ$ in the quantum Turing machine used by Vitanyi for Quantum Kolmogrov Complexity?

(Asked by: username_0 on 2016-09-15)

Right now I am going through [Quantum Kolmogorov Complexity Based on Classical Descriptions](http://arxiv.org/abs/quant-ph/0102108) by Vitanyi.

In the introduction, the author assumed the primitive rotation $\theta = 53.13^\circ$ to have countably many quantum Turing machine.

Is this choice of angle arbitrary?

**Tags:** quantum-computing, turing-machines, it.information-theory, quantum-information, kolmogorov-complexity
> **Comments:**
> **username_1**: N.B. $53.15^\circ \approx \arcsin (4/5) $. Restricting to rational amplitudes with a denominator of 5 is an old convention from the early days of quantum computing, dating back at least to Bernstein and Vazirani, for those who are looking for a special case to make comparisons between quantum complexity and counting complexity.  
> **username_0**: I will check their paper.  
> **username_2**: @Niel: I am fairly sure that Bernstein and Vazirani were the first ones to use arcsin(4/5). And if it's not already clear from Niel's comment, $4/5$ is chosen because $3^2 + 4^2 = 5^2$.  

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## 0 answers

