slides.tex

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\title{QuantumControl.jl: A modern framework \\for quantum optimal control}
\author[Michael Goerz~\raisebox{0.75pt}{\tikz \fill (0,0) circle (0.75pt);}~\raisebox{-1.4pt}{\includegraphics{images/mastodon}}\kern-0.5pt\href{https://qubit-social.xyz/@goerz}{goerz@qubit-social.xyz}]{
{\bf Michael~H.~Goerz}, Sebastián~C.~Carrasco, Vladimir~S.~Malinovsky}
\institute[Army Research Lab]{DEVCOM Army Research Lab}
\date{APS March Meeting 2023}

\begin{document}

{%  Title page
  \setbeamertemplate{footline}{}
  \frame{\titlepage}
}
\addtocounter{framenumber}{-1}


\begin{frame}{JuliaQuantumControl}
  \begin{textblock}{15.5}(0.25,1.00)
    \includegraphics[width=\textwidth]{images/01_01_juliaquantumcontrol}
  \end{textblock}
\end{frame}


\begin{frame}{JuliaQuantumControl}
  \begin{textblock}{15.5}(0.25,1.00)
    \includegraphics[width=\textwidth]{images/01_02_packages}
  \end{textblock}
\end{frame}


\begin{frame}{QuantumPropagators.jl}
  \begin{textblock}{15.5}(0.25,1.00)
    \includegraphics[width=\textwidth]{images/01_02_packages_hlqp}
  \end{textblock}
\end{frame}


\begin{frame}{QuantumControl.jl}
  \begin{textblock}{15.5}(0.25,1.00)
    \includegraphics[width=\textwidth]{images/01_02_packages_hlqc}
  \end{textblock}
\end{frame}


\begin{frame}{Julia}
  \begin{textblock}{15.5}(0.25,1.00)
    \includegraphics[width=\textwidth]{images/01_03_julia}
  \end{textblock}
\end{frame}


\begin{frame}
  \vfill
  \begin{center}
    \huge
    \subhead{Flexibility}
  \end{center}
  \vfill
\end{frame}


\begin{frame}{Rotating Tractor Interferometer}
  \begin{textblock}{6.5}(0.5,2.50)
    \includegraphics[width=\textwidth]{images/rottai}
    {\footnotesize
      B. Dash \emph{et al.} ``Rotation sensing using tractor atom interferometry'' (in preparation)
    }
  \end{textblock}
  \begin{textblock}{6.5}(8.0,1.50)
    \begin{equation*}
      \Op{H}_{\pm}
        = -\frac{\hbar^2}{2mR^2}\frac{\partial^2}{\partial \theta^2} +
          V_0 \cos\left[m (\theta + \phi_{\pm}(t) )\right]
    \end{equation*}
    \begin{align*}
      \onslide<2->{%
        \text{typically:}\quad
        & \Op{H} = \Op{H}_0 + \epsilon(t) \Op{H}_1 \quad \\
        & \text{with control $\epsilon(t)$}
        \\
      }
      \\
      \onslide<3->{%
        \text{here:}\quad
        & \Op{H} = \Op{T} + \Op{V}(\theta \pm \phi(t)) \\
        & \text{with control $\phi(t)$} \\
      }
    \end{align*}
  \end{textblock}
\end{frame}


\begin{frame}{Multiple Dispatch for $\Op{H} = \Op{T} + \Op{V}(\theta \pm \phi(t))$}
  \begin{textblock}{15.5}(0.25,1.00)
    \includegraphics<2->[width=\textwidth]{images/02a_splitop}
  \end{textblock}
\end{frame}


\begin{frame}{Arbitrary Functionals}
  \begin{textblock}{15}(0.5,1.30)
    \onslide<2->{%
      \subhead{Quantum Gate Concurrence}:
      Max concurrence of $\Op{U} \ket{\Psi}$ for separable input state $\ket{\Psi}$
    }
    \onslide<3->{%
      \par
      \vspace{10pt}
      \par
      Given two-qubit gate $\Op{U}$ with $U_{ij} = \Braket{\Phi_i | \Psi_j(T)}$ for $\ket{\phi_i} = \ket{00}, \ket{01}, \ket{10}, \ket{11}$
    }
    \onslide<4->{%
      \par
      \begin{enumerate}
        \item
          $\TildeOp{U} = (\Op{\sigma}_y \otimes \Op{\sigma}_y) \,\Op{U}\, (\Op{\sigma}_y \otimes \Op{\sigma}_y)$
        \item
          $
            c_1, c_2, c_3 \propto
            \text{eigvals}\left( \Op{U} \TildeOp{U} \right)
            \
          $
        \item
          $
            C(\Op{U})
              = \max \Abs{\sin(c_{1,2,3} \pm c_{3,1,2})}
          $
      \end{enumerate}
      {\footnotesize Childs \textit{et al.} Phys. Rev. A 68, 052311 (2003)}
    }
  \end{textblock}
  \begin{textblock}{7.5}(7.25,3.00)
    \onslide<5->{%
      \begin{equation*}
        \Rightarrow \quad J_T(\Op{U})
        =
        \frac{1}{2} \Big(1 - C(\Op{U})\Big) +
        \frac{1}{2} \Big(1 - \underbrace{\frac{1}{4}\tr[\Op{U}\Op{U}^\dagger]}_{\text{unitarity}}\Big)
      \end{equation*}

    }
  \end{textblock}
  \begin{textblock}{15}(0.5,6.00)
    \only<6>{%
      \begin{center}
        {\color{Red} \Large Not analytic!}
      \end{center}
    }
    \onslide<7->{%
      \subhead{Semi-automatic differentiation}: Calculate $\frac{\partial J_T} {\partial \bra{\Psi_k(T)}}$ via automatic differentiation.
      \vspace{4pt}
      \par
      $\Rightarrow$ automatic gradients for {\color{Red} arbitrary functionals} with {\color{Red} no numerical overhead} \\compared to analytical gradients
      \par
      {\footnotesize \color{Red} Goerz \textit{et al.} Quantum 6, 871 (2022)}
    }
  \end{textblock}
\end{frame}


\begin{frame}{Example: Gate Concurrence Maximization}
  \begin{textblock}{15.5}(0.25,1.00)
    \includegraphics<2>[width=\textwidth]{images/02b_01_pe_ham}
    \includegraphics<3>[width=\textwidth]{images/02b_02_pe_problem}
    \includegraphics<4>[width=\textwidth]{images/02b_03_pe_opt}
  \end{textblock}
\end{frame}


\begin{frame}
  \vfill
  \begin{center}
    \huge
    \subhead{Performance}
  \end{center}
  \vfill
\end{frame}

\begin{frame}{Benchmark for Chebychev Propagator -- Large Hilbert Space}
  \begin{textblock}{15.5}(0.25,1.00)
    \begin{center}%
      \includegraphics<1>{images/benchmark_cheby_dense_1000_1}%
      \includegraphics<2>{images/benchmark_cheby_dense_1000_2}%
      \includegraphics<3>{images/benchmark_cheby_dense_1000_3}%
      \includegraphics<4>{images/benchmark_cheby_dense_1000_4}%
    \end{center}
  \end{textblock}
\end{frame}


\begin{frame}{Benchmark for Chebychev Propagator -- Large Hilbert Space (sparse)}
  \begin{textblock}{15.5}(0.25,1.00)
    \begin{center}%
      \includegraphics<2>{images/benchmark_cheby_sparse_1000_2}%
      \includegraphics<3>{images/benchmark_cheby_sparse_1000_3}%
    \end{center}
  \end{textblock}
\end{frame}


\begin{frame}{Benchmark for Chebychev Propagator -- Small Hilbert Space}
  \begin{textblock}{15.5}(0.25,1.00)
    \begin{center}%
      \includegraphics<2>{images/benchmark_cheby_dense_10_3}%
      \includegraphics<3>{images/benchmark_cheby_dense_10_4}%
    \end{center}
  \end{textblock}
\end{frame}


\begin{frame}{Conclusions}
  \begin{textblock}{14.5}(1.25,1.10)
    \begin{center}
      \url{https://github.com/JuliaQuantumControl}
    \end{center}
    \vspace{8pt}
    \subhead{Flexibility:}
    \begin{itemize}
      \item Interactive usage (notebooks)
      \item Use custom project-specific data structures
      \item Tie into Julia ecosystem (e.g., automatic differentiation, GPU computing)
    \end{itemize}
    \par
    \vspace{10pt}
    \subhead{Performance:}
    \begin{itemize}
      \item Out of the Box: match Fortran (ifort + MKL)
      \item GPU, Sparse Matrices, StaticArrays: beat Fortran ($> 2\times$)
    \end{itemize}
  \end{textblock}
\end{frame}

\begin{frame}{Outlook}
  \begin{textblock}{14.5}(1.25,1.10)
    \begin{center}
      \url{https://github.com/JuliaQuantumControl}
    \end{center}
    \vspace{8pt}
    \subhead{QuantumPropagators.jl}
    \begin{itemize}
      \item Support for time-continuous controls (via DifferentialEquations.jl)
    \end{itemize}
    \vspace{10pt}
    \subhead{QuantumControl.jl}
    \begin{itemize}
      \item Optimization methods for analytical pulse shapes (CRAB, GOAT, \dots)
      \item Reinforcement learning
    \end{itemize}
    \vspace{24pt}
    \begin{center}
      {\bf \color{Red}
        Users and Contributors welcome!
      }
    \end{center}
    \vspace{5pt}
    {\footnotesize
      Please reach out by Email, GitHub, or \texttt{\#quantumcontrol} channel on the Julia Slack
    }
  \end{textblock}
\end{frame}

\end{document}