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...@@ -989,7 +989,7 @@ and building a test suite of programs \newt{for benchmarking}. ...@@ -989,7 +989,7 @@ and building a test suite of programs \newt{for benchmarking}.
\item[\ref{wp:representation}] \newt{is focussed on the further development of zx calculus, its axiomatic formulation, and its status as a theory of resources.} \item[\ref{wp:representation}] \newt{is focussed on the further development of zx calculus, its axiomatic formulation, and its status as a theory of resources.}
%is about modelling the properties of different machines in \azx, and translating \azx to hardware. %is about modelling the properties of different machines in \azx, and translating \azx to hardware.
\item[\ref{wp:theory}] \item[\ref{wp:theory}]
\newt{focusses on resource optimization, such as gate reduction in circuit representations, efficient intelligent error-correction, and other deep algorithms.} \newt{focusses on resource optimization, such as gate reduction in circuit representations, efficient intelligent error-correction, and other deep compilation algorithms.}
%develops the theory behind \azx and algorithms to realise the logical ideas. %develops the theory behind \azx and algorithms to realise the logical ideas.
\item[\ref{wp:usefulstuff}] \item[\ref{wp:usefulstuff}]
\newt{applies all the previous to specific quantum hardware.} \newt{applies all the previous to specific quantum hardware.}
...@@ -2057,9 +2057,9 @@ ICTQT will develop the foundational aspects of \zxcalculus. The expertise of Dr. ...@@ -2057,9 +2057,9 @@ ICTQT will develop the foundational aspects of \zxcalculus. The expertise of Dr.
\textbf{Dr Aleks Kissinger} is an Assistant Professor of Quantum Structures and Logic in Radboud's Institute for Quantum and Information Sciences (iCIS). For the past 10 years, he has been instrumental in the development of the diagrammatic approach to quantum theory, notably developing the theory of classical and quantum interaction for general process theories~(1), classification of strong complementarity, and the ZW calculus~(2). He also co-authored the canonical textbook for the field~(3). He also leads development on the {\tt Quantomatic}~(4) and {\tt PyZX} tools, which serve as the platform for the software and automated techniques in this proposal. \textbf{Dr Aleks Kissinger} is an Assistant Professor of Quantum Structures and Logic in Radboud's Institute for Quantum and Information Sciences (iCIS). For the past 10 years, he has been instrumental in the development of the diagrammatic approach to quantum theory, notably developing the theory of classical and quantum interaction for general process theories~(1), classification of strong complementarity, and the ZW calculus~(2). He also co-authored the canonical textbook for the field~(3). He also leads development on the {\tt Quantomatic}~(4) and {\tt PyZX} tools, which serve as the platform for the software and automated techniques in this proposal.
\textit{\color{gray} \textbf{Publications:} (1) B. Coecke, C. Heunen, and ---. Categories of quantum and classical channels. Quantum Information Processing, 15(12), 2016. (2) B. Coecke and ---. The compositional structure of multipartite quantum entanglement. In Proceedings of ICALP, 2010. Springer LNCS 6199. (3) B. Coecke and ---. Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, 2017. (4) Quantomatic: A Proof Assistant for Diagrammatic Reasoning. Proceedings of Conference on Automated Deduction (CADE) 2015. Springer LNCS 9195. \href{http://quantomatic.github.io}{\color{blue} quantomatic.github.io}.} \textit{\color{gray} \textbf{Publications:} (1) B. Coecke, C. Heunen, and ---. Categories of quantum and classical channels. Quantum Information Processing, 15(12), 2016. (2) B. Coecke and ---. The compositional structure of multipartite quantum entanglement. In Proceedings of ICALP, 2010. Springer LNCS 6199. (3) B. Coecke and ---. Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, 2017. (4) Quantomatic: A Proof Assistant for Diagrammatic Reasoning. Proceedings of Conference on Automated Deduction (CADE) 2015. Springer LNCS 9195. \href{http://quantomatic.github.io}{\color{blue} quantomatic.github.io}.}
\medskip \medskip
\textbf{Kang Feng Ng} is a postdoc working full-time on quantum circuit optimisation in the \zxcalculus. He is best known for his papers (1), (2) where he showed the \zxcalculus gives a universally complete language for quantum computation. \textit{\color{gray} \textbf{Publications:} (1) --- and Q. Wang. A universal completion of the ZX-calculus. arXiv:1706.09877, 2017. (2) A. Hadzihasanovic, ---, and Q. Wang. Two complete axiomatisations of pure-state qubit quantum computing. In Proceedings of LICS. ACM, 2018.} \textbf{(Dr) Kang Feng Ng} is a postdoc working full-time on quantum circuit optimisation in the \zxcalculus. He is best known for his papers (1), (2) where he showed the \zxcalculus gives a universally complete language for quantum computation. \textit{\color{gray} \textbf{Publications:} (1) --- and Q. Wang. A universal completion of the ZX-calculus. arXiv:1706.09877, 2017. (2) A. Hadzihasanovic, ---, and Q. Wang. Two complete axiomatisations of pure-state qubit quantum computing. In Proceedings of LICS. ACM, 2018.}
\medskip \medskip
......
...@@ -889,9 +889,8 @@ Provide a graphical representation of the work packages components ...@@ -889,9 +889,8 @@ Provide a graphical representation of the work packages components
showing how they inter-relate (Pert chart or similar). showing how they inter-relate (Pert chart or similar).
} }
\TODOb{Put some more here from actual WP descriptions.}
The work plan has four major scientific work packages (WPs), The work plan has four major scientific work packages (WPs),
which will proceed in parallel: which will proceed in parallel. They all contribute to the ultimate goal of providing the full theoretical underpinning as well as the actual realization of deep quantum compilation software, based on \zxcalculus. The workpackages are:
%All will have at least some activities throughout the length of the project, with the exception of \ref{wp:usefulstuff} which builds on earlier work in the other WPs and thus only begins one year into the project. (There is also a fifth %All will have at least some activities throughout the length of the project, with the exception of \ref{wp:usefulstuff} which builds on earlier work in the other WPs and thus only begins one year into the project. (There is also a fifth
%work package grouping administrative and organisational activities.) %work package grouping administrative and organisational activities.)
\begin{description} \begin{description}
...@@ -901,7 +900,7 @@ and building a test suite of programs for benchmarking. ...@@ -901,7 +900,7 @@ and building a test suite of programs for benchmarking.
\item[{\bf WP 2}] is focussed on the further development of zx calculus, its axiomatic formulation, and its status as a theory of resources. \item[{\bf WP 2}] is focussed on the further development of zx calculus, its axiomatic formulation, and its status as a theory of resources.
%is about modelling the properties of different machines in \azx, and translating \azx to hardware. %is about modelling the properties of different machines in \azx, and translating \azx to hardware.
\item[{\bf WP 3}] \item[{\bf WP 3}]
focusses on resource optimization, such as gate reduction in circuit representations, efficient intelligent error-correction, and other deep algorithms. focusses on resource optimization, such as gate reduction in circuit representations, efficient intelligent error-correction, and other deep compilation algorithms.
%develops the theory behind \azx and algorithms to realise the logical ideas. %develops the theory behind \azx and algorithms to realise the logical ideas.
\item[{\bf WP 4}] \item[{\bf WP 4}]
applies all the previous to specific quantum hardware. applies all the previous to specific quantum hardware.
...@@ -1023,7 +1022,7 @@ project event. ...@@ -1023,7 +1022,7 @@ project event.
%will be evaluated, and any new opportunities will also be discussed. These %will be evaluated, and any new opportunities will also be discussed. These
%meetings will be organised by the coordinator. %meetings will be organised by the coordinator.
To assist in monitoring and evaluating progress, as well as to collaborate on WP4, To assist in monitoring and evaluating progress, as well as to collaborate on WP4,
we have recruited Prof. ~Auffeves, Lead of the we have recruited Prof.~Auffeves, Lead of the
Grenoble Quantum Engineering project, and Prof.~Vinet, head of the silicon spin qubit experimental team, as external advisors. Grenoble Quantum Engineering project, and Prof.~Vinet, head of the silicon spin qubit experimental team, as external advisors.
%Prof. Auffeves is the , and Prof. Vinet is the head of the silicon spin qubit experimental team. %Prof. Auffeves is the , and Prof. Vinet is the head of the silicon spin qubit experimental team.
%The entire project and advisory board (see \S\ref{sec:impact-2-pages}) %The entire project and advisory board (see \S\ref{sec:impact-2-pages})
...@@ -1038,7 +1037,7 @@ The milestones are as follows: ...@@ -1038,7 +1037,7 @@ The milestones are as follows:
\begin{description} \begin{description}
\item[{\bf M1}] Minimal QASM $\to$ QASM circuit optimiser (month 12) \item[{\bf M1}] Minimal QASM $\to$ QASM circuit optimiser (month 12)
\item[{\bf M2}] Support for one HLL using parametric \zx, with 1WQC and idealized circuit output (month 18) \item[{\bf M2}] Support for one HLL using parametric \zx, with 1WQC and idealized circuit output (month 18)
\item[{\bf M3}] Architecture sensitive, fidelity aware optimiser Error correction support (month 24) \item[{\bf M3}] Architecture sensitive, fidelity aware optimiser \& error correction support (month 24)
\item[{\bf M4}] Back-end support for Oxford Ion Traps, initial back end API (month 30) \item[{\bf M4}] Back-end support for Oxford Ion Traps, initial back end API (month 30)
\item[{\bf M5}] Complete deep-\zx compiler stack with open \item[{\bf M5}] Complete deep-\zx compiler stack with open
APIs, and a target compiled protocol demonstrating explicit quantum speed-up. (month 36) APIs, and a target compiled protocol demonstrating explicit quantum speed-up. (month 36)
...@@ -1128,54 +1127,31 @@ We have sufficient proof-of concept results to guaranty that the major component ...@@ -1128,54 +1127,31 @@ We have sufficient proof-of concept results to guaranty that the major component
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
%\newpage %\newpage
\subsection{Consortium as a whole} %\REM{(1 page)} \subsection{Consortium} %\REM{(1 page)}
\label{sec:consortium-as-whole} \label{sec:consortium-as-whole}
%%\REM{The individual members are described in section 3.5, there is no The team consists of:
% need to repeat that information there. \begin{description}
%Describe the consortium. How will it match the project's objectives \item[{\bf Univ.~Grenoble (coordinator):}] Dr Dominic Horsman.
%and bring together the necessary expertise? How do the members \item[{\bf Univ.~Lorraine; LORIA; LRI:}] Dr Simon Perdrix, Prof.~Emmanuel Jeandel, Dr Beno\^it
%complement one another? Valiron.
%In what way does each of them contribute to the project? Show that \item[{\bf Univ.~Oxford:}] Prof.\ Bob Coecke, Dr Miriam Backens, Dr Niel de Beaudrap, Dr Quanlong Wang.
%each has a valid role and adequate resources in the project to fulfil \item[{\bf Cambridge Quantum Computing Ltd.:}] Dr Ross Duncan, Mr Will Simmons.
%that role. \item[{\bf Univ.~Gdansk / ICTQT:}] Dr Ana Bel\'en Sainz.
%If applicable, describe the industrial/commercial involvement in the \item[{\bf Radboud Univ.~Nijmegen:}] Dr Aleks Kissinger, (Dr) Kang Feng Ng, Mr John van de Wetering.
%project and explain why this is consistent with and will help to \end{description}
%achieve the specific measures which are proposed for exploitation of These members include the pioneers of \zxcalculus \cite{Coecke:2009aa}, those who proved its completeness \cite{1367-2630-16-9-093021,Jeandel2017A-Complete-Axio,HFW}, as well as those that proposed the exploitation of \zxcalculus in quantum technologies \cite{Duncan:2010aa, Horsman:2011lr, Chancellor2016Coherent-Parity, BH-2017, DKPdW-2019} (incl.~translations between different computational models, error-correction/lattice surgery, circuit optimisation). Hence, the consortium includes all leading researchers on \zxcalculus. CQC is moreover the world-leading quantum computing company on compiler design. Duncan and Kissinger pioneered automation of diagrammatic reasoning (cf.~{\tt quantomatic} and {\tt PyZX}), which helped in setting the state-of-the-art in circuit optimization \cite{DKPdW-2019}. We also include pioneers in quantum
%the results of the project. programming languages (Valiron), important contributors to MBQC \cite{Duncan:2010aa} and
%} quantum circuits (Jeandel).
\newt{The members of the consortium are chosen to provide the best
combination of skills to deliver this project, including the fathers of \zxcalculus, those who established it as a universal and complete calculus, those who have developed applications of \zxcalculus to quantum technologies, and those who have outperformed all other methods using \zxcalculus.
%They also contributed greatly to community building.
\TODOb{Do we think it's really good to say we are the Oxford mafia?
Also i had two other positions between Oxford and CQC -rd}
Many members also have a long history of collaboration, and in fact have been at different consortium sites at some point of their career, for example Wang was a postdoc at Nancy before moving to Oxford and CQC. Duncan, Horsman, Kissinger and Perdrix were postdocs at Oxford before moving to CQC, Grenoble, Nijmegen and Nancy respectively. Sainz has a long-standing collaboration with members of the Oxford Group, and organised Quantum Physics and Logic X, the main conference for \zxcalculus alike research, while at Barcelona. Coecke is a member of the International Scientific Committee of ICTQT-Gdansk, the new institute that hosts Sainz' new group.
Several members have ongoing collaborations with Cambridge Quantum Computing Inc. In particular, co-inventor of \zxcalculus Ross Duncan is now the leading researcher at CQC, which clearly demonstrates CQC's commitment to \zxcalculus. Quantum compilation is moreover the key focus of CQC. Several members are part of the NQIT Quantum Technologies Hub.\footnote{nqit.ox.ac.uk}
%We now provide details on each of these.
Expertise on the
{\bf theoretical aspects} underpinning the project is provided by Oxford site leader Coecke and CQC research leader Duncan
who jointly invented the \zxcalculus\ \cite{Coecke:2009aa}. Backens, Perdrix, Jeandel and Wang are the key contributors to establishing universal completeness of \zxcalculus \cite{1367-2630-16-9-093021, Jeandel2017A-Complete-Axio, HFW}. Coecke pioneered general categorical and diagrammatic methods in quantum computing \cite{AbrCoe:CatSemQuant:2004}, and with Kissinger co-authored the textbook of the field \cite{Coecke2017Picturing-Quant}.
Expertise on {\bf quantum technology applications} is provided by those who pioneered these applications. Duncan, Perdrix and Horsman pioneered zx-based translations between different computational models \cite{Duncan:2010aa, Horsman:2011lr}, Horsman and Kissinger pioneered zx-based error-correction \cite{Chancellor2016Coherent-Parity}, and Horsman and de Beaudrap demonstrated the equivalence of zx-rules and lattice surgery \cite{BH-2017}.
Duncan and Kissinger pioneered {\bf automation} of diagrammatic reasoning (cf.~{\tt quantomatic} and {\tt PyZX}), which also will play a key role in this project, as they already have in setting the state-of-the-art in circuit optimization \cite{DKPdW-2019}. Consequently, members have a long history of collaboration. Coecke is a member of the International Scientific Committee of ICTQT-Gdansk, the new institute that hosts Sainz' new group. Several members have ongoing collaborations with Cambridge Quantum Computing Inc. In particular, co-inventor of \zxcalculus Ross Duncan is now the leading researcher at CQC, which clearly demonstrates CQC's commitment to \zxcalculus. Quantum compilation is moreover the key focus of CQC. Several members are part of the NQIT Quantum Technologies Hub.
We also include pioneers in {\bf quantum
programming languages} (Valiron), important contributors to the
theory of {\bf MBQC} (Perdrix, de Beaudrap, and Duncan) and
{\bf quantum circuits} (Jeandel). }
The consortium has also been instrumental in community building, for example with the QPL conference series which now attracts well over 100 participants every year and approx.~75 paper submissions on foundational and structural research in the area of quantum computing. It also has organised several schools e.g.~the QiCS School\footnote{www.cs.ox.ac.uk/people/bob.coecke/QICS$\underline{\ }$School.html} and the CAP Spring School,\footnote{www.cs.ox.ac.uk/ss2014/} and a substantial talks archive is maintained.\footnote{www.youtube.com/user/OxfordQuantumVideo} \newt{More recently, the several members are %The consortium has also been instrumental in community building, for example with the QPL conference series which now attracts well over 100 participants every year and approx.~75 paper submissions on foundational and structural research in the area of quantum computing. It also has organised several schools e.g.~the QiCS School\footnote{www.cs.ox.ac.uk/people/bob.coecke/QICS$\underline{\ }$School.html} and the CAP Spring School,\footnote{www.cs.ox.ac.uk/ss2014/} and a substantial talks archive is maintained.\footnote{www.youtube.com/user/OxfordQuantumVideo} \newt{More recently, the several members are
involved in the Compositionality community, which has diagrammatic/categorical reasoning as its core focus, with a new journal, a new conference series, and a new workshop series.} %involved in the Compositionality community, which has diagrammatic/categorical reasoning as its core focus, with a new journal, a new conference series, and a new workshop series.}
\TODOb{Keeping any of this? Introducing anything else?} %\TODOb{Keeping any of this? Introducing anything else?}
\bR Of utter importance is the alignment with Networked Quantum Information Technologies Hub (NQIT) at the Oxford site, which means that several members of the consortium have already direct expertise with interacting with quantum hardware (de Beaudrap, Horsman). The NQIT is the largest of the four Hubs in the UK National Quantum Technology Programme, a 270 GBP million investment by the UK government to establish a quantum technology industry in the UK. %We are working towards building a quantum computer demonstrator, the Q20:20 engine, which demonstrates a networked, hybrid light-matter approach to quantum information processing. %\bR Of utter importance is the alignment with Networked Quantum Information Technologies Hub (NQIT) at the Oxford site, which means that several members of the consortium have already direct expertise with interacting with quantum hardware (de Beaudrap, Horsman). The NQIT is the largest of the four Hubs in the UK National Quantum Technology Programme, a 270 GBP million investment by the UK government to establish a quantum technology industry in the UK. %We are working towards building a quantum computer demonstrator, the Q20:20 engine, which demonstrates a networked, hybrid light-matter approach to quantum information processing.
Concretely, the most important aspect is the fact that the modular architecture motivated using lattice surgery on surface codes for the logical operations, and that these are in effect \zx-operations \cite{{BH-2017}}. This will certainly make the ambition here much more achievable. \e %Concretely, the most important aspect is the fact that the modular architecture motivated using lattice surgery on surface codes for the logical operations, and that these are in effect \zx-operations \cite{{BH-2017}}. This will certainly make the ambition here much more achievable. \e
%\REM{From cyril to address industrial/commericial} %\REM{From cyril to address industrial/commericial}
%Bull brings expertise in high performance simulation as well as %Bull brings expertise in high performance simulation as well as
...@@ -1183,7 +1159,7 @@ Concretely, the most important aspect is the fact that the modular architecture ...@@ -1183,7 +1159,7 @@ Concretely, the most important aspect is the fact that the modular architecture
\newpage%\TODOb{This needs to be done urgently} %\newpage%\TODOb{This needs to be done urgently}
\subsection{Financial plan} \subsection{Financial plan}
\label{sec:financial-plan} \label{sec:financial-plan}
...@@ -1194,18 +1170,7 @@ Concretely, the most important aspect is the fact that the modular architecture ...@@ -1194,18 +1170,7 @@ Concretely, the most important aspect is the fact that the modular architecture
other. Justify them here. Both the justification and the information other. Justify them here. Both the justification and the information
in the system will be communicated to the Evaluation Panel.} in the system will be communicated to the Evaluation Panel.}
\paragraph{Personnel} We request 30 months of salary
\label{sec:personnel}
This is a large and multifaceted project, which will require
significant work to deliver. A full-time post doc at each contributing academic
site is needed, under supervision of the site lead. In addition, At
all the academic sites there is a large amount of time donated to the
project by senior scientists with relevant expertise. At CQC, our
industrial partner, a Senior Scientist and a Research Software Developer will contribute to the project.
\begin{itemize}
\item \emph{Post-doctoral researchers}: We request 30 months of salary
for post-docs at Oxford, 36+18 months at Gdansk, and 18 months at each of Grenoble and LORIA. The Oxford post-doc will also engage in co-operation with industrial partners at CQC. The post-docs for post-docs at Oxford, 36+18 months at Gdansk, and 18 months at each of Grenoble and LORIA. The Oxford post-doc will also engage in co-operation with industrial partners at CQC. The post-docs
will be hired as soon as possible by the site leads at each site. will be hired as soon as possible by the site leads at each site.
%\item \emph{Coordinator}: We request 10\% contribution the %\item \emph{Coordinator}: We request 10\% contribution the
...@@ -1213,49 +1178,30 @@ industrial partner, a Senior Scientist and a Research Software Developer will co ...@@ -1213,49 +1178,30 @@ industrial partner, a Senior Scientist and a Research Software Developer will co
% the project. This is reduced from 20\% upon negotiation with % the project. This is reduced from 20\% upon negotiation with
% Stratclyde. (Duncan will contribute an additional 8.4 months of % Stratclyde. (Duncan will contribute an additional 8.4 months of
% time as a researcher, see below.) % time as a researcher, see below.)
\item \emph{Principle investigators and other named staff}: Spread
Spread
across the sites, more than 110 person-months of time across the sites, more than 110 person-months of time
will be contributed by the named staff on the project, all of which will be contributed by the named staff on the project, all of which
is supported by other sources. This means that almost 40\% of the is supported by other sources.
research effort of the project is funded from elsewhere.
\item \emph{PhD Students}: at LORIA, Titouan Carette will contribute
approx 9 months to the project; this is funded from other sources.
At Grenoble, Richard East will contribute
approx 9 months to the project; this is funded from other sources.
At Gdansk, a PhD student will contribute
approx 12 months to the project; this is funded from other sources. \newt{At Oxford, at least two PhD students will contribute to the project, as well as several MSc students}.
\item \emph{Engineers}: At CQC, a Senior Scientist and a Research Software Developer will contribute, funded from other sources.
\end{itemize}
\paragraph{Workshops} At LORIA and Grenoble, one PhD student will contribute
\label{sec:workshops} approx 9 months to the project, at Gdansk, one will contribute 12 months, and at Oxford, two PhD students will be fully dedicated, all funded from other sources.
Project workshops serve a key role in intra-project communication, At CQC, a Senior Scientist and a Research Software Developer will contribute, funded from elsewhere.
dissemination, and outreach. We plan one workshop each year, in
Oxford, Nijmegen, and Grenoble. We plan to invite significant figures from the experimental and software industrial communities to supplement the project reach and expertise, which increases the cost beyond We plan one workshop each year, in
the usual expenses of venue hire and speakers' expenses. We have Oxford, Nijmegen, and Grenoble. We plan to invite significant figures from the experimental and software industrial communities to supplement the project reach and expertise. We have
budgeted budgeted
\euro 15k for each, through the co-ordinating site budget. \euro 15k for each, through the co-ordinating site budget.
\paragraph{Travel and subsistence} We request substantial budget for travel, for quantERA
\label{sec:travel-subsistence}
Since many of the personnel have expertise relevant to more than one
work package, we request substantial budget for travel, for quantERA
reporting meetings, for formal project meetings, smaller more frequent reporting meetings, for formal project meetings, smaller more frequent
WP meetings, and also to present our work at conferences. WP meetings, and also to present our work at conferences.
\paragraph{Equipment} We request laptop computers for each of the postdocs, and
\label{sec:equipment} replacement laptops for some staff.
\begin{itemize} \newpage\section{ETHICAL ISSUES \REM{1/2 page}}
\item We request laptop computers for each of the postdocs, and
replacement laptops for some staff. These are necessary
because of the frequent need to travel and work at another site
and/or present work at conferences or workshops.
\end{itemize}
\section{ETHICAL ISSUES \REM{1/2 page}}
\label{sec:ethical-issues} \label{sec:ethical-issues}
\REM{Describe any foreseeable ethical issue that may arise during the \REM{Describe any foreseeable ethical issue that may arise during the
......
...@@ -3807,7 +3807,7 @@ well.}, ...@@ -3807,7 +3807,7 @@ well.},
} }
   
@article{DKPdW-2019, @article{DKPdW-2019,
author={Ross Duncan and Aleks Kissinger and Simon Pedrix and John van de Wetering}, author={Ross Duncan and Aleks Kissinger and Simon Perdrix and John van de Wetering},
title={Graph-theoretic Simplification of Quantum Circuits with the {ZX}-calculus}, title={Graph-theoretic Simplification of Quantum Circuits with the {ZX}-calculus},
Journal = {arXiv.org}, Journal = {arXiv.org},
Number = {1902.03178}, Number = {1902.03178},
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