Began work on the simulators section
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@ -763,12 +763,65 @@
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journal = {Physical Review A}
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}
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@software{cirq2022,
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author = {{Cirq Developers}},
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title = {Cirq},
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month = dec,
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year = 2022,
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note = {{See full list of authors on Github: https://github
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.com/quantumlib/Cirq/graphs/contributors}},
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publisher = {Zenodo},
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version = {v1.1.0},
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doi = {10.5281/zenodo.7465577},
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url = {https://doi.org/10.5281/zenodo.7465577}
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}
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@manual{cirq2022simulator,
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author = {{Cirq Developers}},
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title = {cirq.Simulator},
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year = {2023},
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month = {06},
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note = {\url{https://quantumai.google/reference/python/cirq/Simulator}}
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}
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@software{qsim2020,
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author = {Quantum AI team and collaborators},
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title = {qsim},
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author = {{Quantum AI team} and collaborators},
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title = {qsim, qsimh},
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month = Sep,
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year = 2020,
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publisher = {Zenodo},
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doi = {10.5281/zenodo.4023103},
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url = {https://doi.org/10.5281/zenodo.4023103}
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}
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@article{numpy2020,
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title = {Array programming with {NumPy}},
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author = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J.
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van der Walt and Ralf Gommers and Pauli Virtanen and David
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Cournapeau and Eric Wieser and Julian Taylor and Sebastian
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Berg and Nathaniel J. Smith and Robert Kern and Matti Picus
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and Stephan Hoyer and Marten H. van Kerkwijk and Matthew
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Brett and Allan Haldane and Jaime Fern{\'{a}}ndez del
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R{\'{i}}o and Mark Wiebe and Pearu Peterson and Pierre
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G{\'{e}}rard-Marchant and Kevin Sheppard and Tyler Reddy and
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Warren Weckesser and Hameer Abbasi and Christoph Gohlke and
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Travis E. Oliphant},
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year = {2020},
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month = sep,
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journal = {Nature},
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volume = {585},
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number = {7825},
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pages = {357--362},
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doi = {10.1038/s41586-020-2649-2},
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publisher = {Springer Science and Business Media {LLC}},
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url = {https://doi.org/10.1038/s41586-020-2649-2}
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}
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@manual{microsoft2023,
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author = {Microsoft},
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title = {What are {Q\#} and the Quantum Development Kit?},
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year = {2023},
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url = {https://learn.microsoft.com/en-gb/azure/quantum/overview-what-is-qsharp-and-qdk},
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urldate = {\today},
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note = {\url{https://learn.microsoft.com/en-gb/azure/quantum/overview-what-is-qsharp-and-qdk}},
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}
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134
main.tex
134
main.tex
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@ -16,44 +16,55 @@
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\usepackage{physics}
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\usepackage{float}
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\usepackage{qcircuit}
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\usepackage{marginnote}
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\newtheorem{theorem}{Theorem}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
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\ExplSyntaxOn
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\clist_new:N \l_my_footlist
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\cs_new:Nn \my_footnotelater:n {
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\clist_gput_right:Nn \l_my_footlist {{#1}}
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}
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\cs_new:Nn \my_footnotenow: {
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\clist_gpop:NN \l_my_footlist \l_tmpa_tl
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\exp_args:Nv\footnote{l_tmpa_tl}
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}
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\NewDocumentCommand{\FootnoteLater}{m}{\my_footnotelater:n{#1}}
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\NewDocumentCommand{\FootnoteNow}{}{\my_footnotenow:}
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\ExplSyntaxOff
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\clist_new:N \l_my_footlist
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\cs_new:Nn \my_footnotelater:n {
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\clist_gput_right:Nn \l_my_footlist {{#1}}
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}
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\cs_new:Nn \my_footnotenow: {
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\clist_gpop:NN \l_my_footlist \l_tmpa_tl
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\exp_args:Nv\footnote{l_tmpa_tl}
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}
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\NewDocumentCommand{\FootnoteLater}{m}{\my_footnotelater:n{#1}}
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\NewDocumentCommand{\FootnoteNow}{}{\my_footnotenow:}
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\ExplSyntaxOn
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\cs_new:Nn \postulate:nn {
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\emph{#2}
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%\hyperlink{#1}{#2}
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}
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\NewDocumentCommand \Postulate { m }
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\cs_new:Nn \postulate:nn {
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\emph{#2}
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%\hyperlink{#1}{#2}
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}
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\NewDocumentCommand \Postulate { m }
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{
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\str_case_e:nnF { \str_foldcase:n { #1 } }
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{
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\str_case_e:nnF { \str_foldcase:n { #1 } }
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{
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{ state\space space }{\postulate:nn{postulate:state-space}{#1}}
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{ evolution }{\postulate:nn{postulate:evolution}{#1}}
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{ measurement }{\postulate:nn{postulate:measurement}{#1}}
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{ composite\space systems }{\postulate:nn{postulate:composite-systems}{#1}}
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}{
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\textbf{!!}#1\textbf{!!}
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}
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{ state\space space }{\postulate:nn{postulate:state-space}{#1}}
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{ evolution }{\postulate:nn{postulate:evolution}{#1}}
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{ measurement }{\postulate:nn{postulate:measurement}{#1}}
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{ composite\space systems }{\postulate:nn{postulate:composite-systems}{#1}}
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}{
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\textbf{!!}#1\textbf{!!}
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}
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}
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\cs_new:Nn \my_simulator_slug:Nn {
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\tl_set:Nn #1 {#2}
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\tl_set:Nx #1 {\text_lowercase:n {#2}}
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\tl_remove_all:Nn #1 { () }
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\tl_replace_all:Nnn #1 { ~_/ } { - }
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\tl_put_left:Nn #1 {sec:simulator-}
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}
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\NewDocumentCommand{\Simulator}{m}{
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\my_simulator_slug:Nn \l_tmpa_tl {#1}
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\subsubsection{#1}
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\exp_args:No \label \l_tmpa_tl
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}
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\ExplSyntaxOff
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\def\Cpp{{C\nolinebreak[4]\hspace{-.05em}\raisebox{.4ex}{\tiny\bf ++}}}
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\def\viz.{\textit{viz}.}
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\NewDocumentCommand{\Naturals}{}{\mathbb{N}}
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\let\NN\Naturals
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@ -666,7 +677,7 @@ eliminated, by giving a superclass of Clifford circuits, ``$HT$ circuits'', that
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is equivalent to classical computation and can be weakly simulated.
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Finally, note also that certain classes of efficiently simulatable circuits not
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discussed here, such as \emph{matchgate} circuits, may relate non-trivially
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discussed here, such as \emph{matchgate circuits}, may relate non-trivially
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with Clifford circuits \cite{Valiant2002,Jozsa2008,Brod2016}.
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\subsection{Schr\"{o}dinger simulation}
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@ -925,21 +936,74 @@ exhaustive in the number of simulators considered, nor on the benchmarking the
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considered solutions. The large and growing number of quantum circuit
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simulators available, and the different possible goals for such software (e.g.,
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small-scale \textit{vs.}~supremacy-scale simulation), would make it impossible
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for a complete and even comparison. Thus, we focused on offline, small-scale,
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industry-recognized simulators, such as those that a researcher might use to
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validate their algorithms in toy-settings using their laptop.
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for a complete and even comparison. Thus, we focused on a subset of offline,
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small-scale, industry-recognized simulators, such as those that a researcher
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might use to validate their algorithms in toy-settings using their laptop.
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\subsection{Methodology}
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\FootnoteLater{As of July $16$, $2023$, the Github repositories for the Cirq,
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the Microsoft Quantum, and the Qiskit simulators have, respectively,
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$3,\!823$, $3,\!737$, and $3,\!678$, ``stars''.}
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$3,\!823$, $3,\!737$, and $3,\!678$ ``stars''.}
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We began with the $3$ most popular (at the time of writing) quantum circuit
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simulators under the Github ``quantum-computing'' tag\FootnoteNow. Then, we
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considered every quantum circuit simulator for which Qiskit provided a backend
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interface. For providers of quantum hardware interfacing with Qiskit, we
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considered the provider's simulation solution, if it existed.
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considered simulators for which Qiskit or Cirq provided backend interface. For
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providers of quantum hardware interfacing with Qiskit, we considered the
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provider's simulation solution, if it existed. We then proceeded to traverse
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the reference graph of the simulator's reference publications, gathering a
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total of $20$ simulators. A graph outlining the citation chains followed is
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given in figure \ref{fig:citation-graph}.
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\begin{figure}[thb]
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\includegraphics[page=2]{assets/reference_spider.pdf}
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\caption{Graph illustrating the citation chains followed to enumerate the
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simulators considered.}
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\label{fig:citation-graph}
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\end{figure}
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\subsection{Simulators}
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\Simulator{Cirq (internal/qsim/qsimh simulators)}
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Cirq \cite{cirq2022} is Google's solution for quantum circuit related tasks,
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from design to real-world execution. Besides third-party backends (see sections
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\ref{sec:simulator-qflex},\ref{sec:simulator-quimb}), Cirq contains three
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separate simulators: the built-in Python simulator \cite{cirq2022simulator},
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qsim, and qsimh \cite{qsim2020}. The built-in Python simulator performs
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\Schrodinger-based simulation (thus, maintains the state vector) using a Numpy
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\cite{numpy2020} sparse-matrix representation, and is meant for testing small
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circuits. qsim and qsimh, in contrast, are Google's optimized and
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high-performance simulation solutions. Both are written in \Cpp, and are,
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respectively, a \Schrodinger\ and a \Schrodinger-Feynman simulator (\viz.\
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sections
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\ref{sec:schrodinger-simulation},\ref{sec:schrodinger-feynman-simulation}).
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qsim and qsimh employ gate fusion, vectorized instructions and multi-threading
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for computational speed-up. qsimh supports trading computational time by
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lower-fidelity simulation, as outlined in section \ref{sec:feynman-simulation}.
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Both qsim and qsimh integrate with Cirq's Python interface.
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\Simulator{Microsoft Quantum}
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Microsoft's ``Quantum Development Kit'' is a tool-kit for quantum computation,
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including quantum circuit simulation \cite{microsoft2023}. It is integrated with
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\Simulator{Qiskit}
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\Simulator{qFlex}
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\Simulator{quimb}
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\Simulator{Rigetti Forest}
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\Simulator{NVIDIA cuStateVec}
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\Simulator{NVIDIA cuTensorNet}
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\Simulator{Amazon SV1}
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\Simulator{Amazon TN1}
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\Simulator{Amazon DM1}
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\Simulator{MQT/DDSIM}
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\Simulator{Intel Quantum Simulator}
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\Simulator{Xanadu's Strawberry Fields}
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\Simulator{Pennylane Lightning}
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\Simulator{Qibo}
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\Simulator{QCGPU}
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\Simulator{Quantum++}
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\appendix
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