80 lines
3.8 KiB
TeX
80 lines
3.8 KiB
TeX
% vim: ft=tex
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\chapter{Appendix}
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\section{Source Code for the Benchmarks}
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\label{ref:code_benchmarks}
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The benchmarks used in \ref{ref:performance} are based on this code. Note
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that the execution time is measured which is inherently noisy. To account for
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the noise several strategies are used:
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\begin{enumerate}[1.]
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\item{The same circuit is applied to the starting state several times. The
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minimal result is used as the noise must be positive}
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\item{Several circuits are applied to the starting state. The remaining
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noise is mixed with the variance due to the different circuits.}
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\item{Because the noise can be timely correlated (i.e. another process
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requires processor time for a longer period) the tests have been
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randomized such that the time correlated noise is distributed randomly over
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several uncorrelated measurements.}
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\end{enumerate}
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The code used to benchmark the three regimes is analogous and not included here.
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\lstinputlisting[title={Generating Data for the Dense State Vector vs. Graphical Simulator Benchmark}, language=Python, breaklines=true]{../performance/generate_data_scaling_qbits.py}
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\lstinputlisting[title={Code for Measuring and Computing the Execution Time and Statistics}, language=Python, breaklines=true]{../performance/measure_circuit.py}
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\section{Complete Graphical States from the Three Regimes}
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\label{ref:complete_graphs}
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Because the whole graphs are barely percetible windows have been used
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in Figure \ref{fig:graph_high_linear_regime} and Figure \ref{fig:graph_intermediate_regime}.
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For the sake of completeness the whole graphs are included here in
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Figure \ref{fig:graph_intermediate_regime_full} and Figure \ref{fig:graph_high_linear_regime_full}.
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\begin{figure}[H]
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\centering
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\includegraphics[width=\linewidth]{graphics/graph_intermediate_regime.png}
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\caption[Typical Graphical State in the Intermediate Regime]{Typical Graphical State in the Intermediate Regime}
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\label{fig:graph_intermediate_regime_full}
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\end{figure}
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\begin{figure}[H]
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\centering
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\includegraphics[width=\linewidth]{graphics/graph_high_linear_regime.png}
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\caption[Typical Graphical State in the High-Linear Regime]{Typical Graphical State in the High-Linear Regime}
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\label{fig:graph_high_linear_regime_full}
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\end{figure}
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\section{Code to Generate the Example Graphs}
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\label{ref:code_example_graphs}
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This code has been used to generate the example graphs in \ref{ref:performance}
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and \ref{ref:complete_graphs}. Note that generating the graph is done with
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a random circuit as in \ref{ref:code_benchmarks}. The generated \lstinline{dot}
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code is converted to an image using
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\lstinline{dot i_regime.dot -Tpng -o i_regime.png}.
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\lstinputlisting[title={Code used to Generate the Example Graphs}, language=Python, breaklines=true]{../performance/regimes/graph_intermediate_regime.py}
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\section{Code to Benchmark \lstinline{ufunc} Gates against Python}
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\label{ref:benchmark_ufunc_py}
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It has been mentioned several times that the implementation with
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\lstinline{ufuncs} as gates is faster than a pure \lstinline{python}
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implementation. To support this statement a simple benchmark is written. The
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relatively simple Pauli $X$ gate us implemented, more complicated gates like $CX$ or $H$
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have worse performance when written in \lstinline{python}. The performance
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improvement when in this example is a factor around $6.4$.
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One must note that the tested \lstinline{python} code is not
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realistic and in a possible application there would be a significant overhead.
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\lstinputlisting[title={Code to Benchmark \lstinline{ufunc} Gates against Python}, language=Python, breaklines=True]{extra_benchmark/benchmark.py}
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When using \lstinline{result_py[0::2] = qm_state[1::2]} the result is identical and
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the performance is only increased by a factor around $1.7$. This method is not
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applicable to general act-qbits and the bit mask has to be used.
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