and allowing us to leverage techniques from earlier work (cf.~\texttt{quantomatic}~\cite{Kissinger2015Quantomatic:-A-} and~\texttt{PyZX}~\cite{DKPdW-2019}). %, as well as new techniques developed as part of this project,
This denotational kernel specifies the
process to be carried out, independent of the target platform. Many
important transformations can be performed at this platform
independent level --- without recourse to matrix representations of
the operations involved --- such as simplifying the tensor network,
important transformations can be performed at this %platform independent
level,
%--- without recourse to matrix representations of the operations involved ---
such as simplifying the tensor network,
reducing Clifford fragments to minimal forms, and reducing T-count.
Development of such techniques is a low-risk extension of earlier
work, and will be done early in the project
...
...
@@ -400,64 +400,52 @@ work, and will be done early in the project
a program can be translated to a fault-tolerant equivalent with
respect to a chosen error-correcting code.
% \REM{Can do useful stuff at this level! Some optimisation; ECC
% simple generic optimisations. e.g.
% \begin{itemize}
% \item reduce T-count / gate count
% \item coalesce Cliffords
% \item Circuits: minimise depth
% \item MBQC : minimise rounds
% \end{itemize}
% }
% specifying how the tensor
% network may be realised. This consists
The annotations of the second layer provide the basis of \emph{augmented
rewrites}: program transformations which are guided by the
annotations to achieve particular goals, not expressible in the basic
tensor language. For instance, there is an efficient algorithm
rewrites}: program transformations guided by the
annotations to achieve particular goals. %, not expressible in the basic tensor language.
For instance, there is an efficient algorithm
\cite{Mhalla:2008kx} to find the \emph{gflow} of a graph state; if the
state has a gflow then it supports deterministic 1-way computation
\cite{D.E.-Browne2007Generalized-Flo}. Annotating the graph with its
gflow provides guidance for a rewrite strategy which produces an
would generalise this concept to encompass other sorts of information which would inform how to transform (i.e.,~to re-write) a generic representation of a quantum computational procedure.
generalises this concept to include other annotation information to inform re-writing.
% encompass other sorts of information which would inform how to transform (i.e.,~to re-write) a generic representation of a quantum computational procedure.
For example,
the \dzxc system could incorporate
a system which specifies both how to represent logical operations in a particular error correcting code, and how the operations are constrained in order to satisfy basic precautions to keep the realisation fault-tolerant (\ref{task:ECC}).
This would enable the \dzxc system
to re-write procedures, minimising the number of operations, subject to the constraints described by those annotations.
The \dzxc system will be modular, and allow for several different systems of annotations, for different hardware platforms or constraints one might impose on a computation.
One such system of annotations would be to describe
the constraints and the costs involved for operations within a particular hardware platform (\ref{task:runnable}).
%%For example, in
% Other
%examples of annotations might include paths in the graph corresponding
%to the trajectories of physical qubits, or subgraphs corresponding to
%the primitive hardware operations and the time required to execute
%them. For
%%hybrid architectures like NQIT, the annotations will also
%%indicate the differing behaviour of the subsystems.
Augmented
rewrites will be used to find a runnable implementation of the
abstract tensor for the target platform, and to optimise resource use.
a system which specifies both how to represent logical operations in a particular error correcting code, and how the operations are constrained in order to satisfy %basic precautions to keep the realisation
fault-tolerance (\ref{task:ECC}).
The \dzxc system will be modular, allowing for several different systems of annotations.
The \dzxc system
will re-write procedures, minimising the number of operations, subject to the constraints described by those annotations.
One such system of annotations will be to describe
the constraints and the costs of operations for particular hardware (\ref{task:runnable}).
%Augmented
%rewrites will be used to find a runnable implementation of the
%abstract tensor for the target platform, and to optimise resource use.
The development
of the general theory of annotations and augmented rewrites
(\ref{task:annotate1}, \ref{task:annotate2}), algorithms for inferring
specific annotations (\ref{wp:representation}), and rewrite strategies which exploit them
(\ref{task:opt-machine}) form a major novel component of the project.%
%
% (have I implemented
% the correct process?) and layer (is the implementation
% possible/efficient/robust?). This separation
%
(\ref{task:opt-machine}) form a major novel component of the project.
%The \dzxc system
%can therefore re-write procedures, minimising the number of operations, subject to the constraints described by those annotations.
%
%The \dzxc system will be modular, and allow for several different systems of annotations, for different hardware platforms or constraints one might impose on a computation.
% One such system of annotations would be to describe
%the constraints and the costs involved for operations within a particular hardware platform (\ref{task:runnable}).
%Augmented
%rewrites will be used to find a runnable implementation of the
%abstract tensor for the target platform, and to optimise resource use.
%The development
%of the general theory of annotations and augmented rewrites
%(\ref{task:annotate1}, \ref{task:annotate2}), algorithms for inferring
%specific annotations (\ref{wp:representation}), and rewrite strategies which exploit them
%(\ref{task:opt-machine}) form a major novel component of the project.%
Concrete tensor networks have a fixed finite size, whereas algorithms
are described in parametric fashion, \eg varying according the
...
...
@@ -466,12 +454,7 @@ To accommodate this, the \dzxc system would incorporate
a second class of annotations to represent limited forms of iteration and recursion, yielding \emph{parametric}\zx terms.
While the hardware-derived annotations are inferred in a bottom-up fashion, the parametric structure is produced top-down, based on the original
high-level quantum procedure provided as input.
% --- The following commented out as I'm not sure what it means or if it contributes to the meaning of the proposal:
% As this information is typically erased by the circuit generation phase
% \cite{Alexander-S.-Green:2013fk,Cross2017Open-Quantum-As} of
% compilation, we effectively move the boundary between \azx and the HLL
% above the circuit-level.
This is possibly the most challenging part
This is a challenging part
of the project (\ref{task:betterboxes}); however, we have experience of
