23 lines
1.0 KiB
TeX
23 lines
1.0 KiB
TeX
% vim: ft=tex
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\section{The naive Simulator}
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A quite big part of the simulations interesting for students and researchers is not
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covered by stabilizer states and stabilizer circuits. In particular the
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phase estimation algorithm is essential for many applications. Being able to simulate
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such an algorithm is essential for education.
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\subsection{Simulator Core}
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Recalling \ref{ref:nqbitsystems} an arbitrary state $\ket{\psi}$ can be written as such:
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$$ \ket{\psi} = \sum\limits_{i = 0}^{2^N - 1} c_i \ket{i} $$
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Which yields $2^N$ coefficients $c_i = \braket{\psi}{i}$. These coefficients are used to
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store the quantum mechanical state of the simulator and are stored in numpy arrays \cite{numpy_array}.
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They can be modified and viewed without overhead
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using python and allow fast modification using so-called NumPy ufuncs\cite{numpy_ufunc}.
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A simulator state also contains a classical state which is a length $N$ integer array containing
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the measured classical bits with a default value of $-1$.
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The gates are implemented as NumPy ufuncs which allows
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