I have been using this code to implement the Solovay-Kitaev algorithm for approximating arbitrary single qubit gates. One measure of success it gives is the 'Fowler distance'. I cant find a definition for the Fowler distance anywhere, and am wondering how it relates to the approximation error 'epsilon' used in proofs of the SK theorem (such as in Appendix 3 of Nielsen&Chuang). Thanks for any help.

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    $\begingroup$ Welcome to QCSE! This paper defines Fowler distance of two single-qubit gates as $\sqrt{\frac{2 - |\mathrm{tr}(U_1U_2^\dagger)|}{2}}$, see eq $(1)$ on p.2. Is this what you have in mind? $\endgroup$ Feb 11, 2021 at 18:36
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    $\begingroup$ Thanks for your reply, that seems to be what I'm looking for. I also found it in a paper by Fowler yesterday after posting the question. Thanks again! $\endgroup$
    – shuey97
    Feb 12, 2021 at 13:37


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