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doc/src/week17/summary.tex renamed to doc/src/week17/LatexFiles/summary.tex

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\begin{frame}{Course Philosophy and Structure}
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\begin{columns}[T]
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\column{0.55\textwidth}
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\begin{block}{Two-Part Programme}
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\begin{block}{Two main parts}
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\begin{enumerate}
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\item \textbf{Quantum Computing} (Jan--Mar)\\
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Many-body quantum systems, VQE,\\
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\vspace{4pt}
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\begin{block}{VQE Overview}
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\[
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E(\bm\theta) = \bra{\psi(\bm\theta)}H\ket{\psi(\bm\theta)}
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E(\bm{\theta}) = \bra{\psi(\bm{\theta})}H\ket{\psi(\bm{\theta})}
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\;\geq\; E_0
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\]
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Minimise $E(\bm\theta)$ over circuit parameters $\bm\theta$.
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\end{alertblock}
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\end{frame}
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% ---- Full course map ---------------------------------------
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\begin{frame}{Course Road Map at a Glance}
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% ---- Course map: Part 1 ------------------------------------
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\begin{frame}{Course Road Map --- Part 1: Quantum Computing}
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\begin{center}
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\small
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\renewcommand{\arraystretch}{1.25}
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\begin{tabular}{@{}llp{7.2cm}@{}}
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\renewcommand{\arraystretch}{1.28}
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\begin{tabular}{@{}llp{8.0cm}@{}}
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\toprule
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\textbf{Weeks} & \textbf{Dates} & \textbf{Topics} \\
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\midrule
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1 & Jan 19--23 & Basic quantum mechanics, Hilbert spaces, qubits \\
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2--3 & Jan 26--Feb 6 & Composite systems, density matrices, entanglement \\
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4 & Feb 9--13 & Entanglement entropies, quantum gates \\
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5--6 & Feb 16--27 & VQE: algorithm, measurements, gradients (Project 1) \\
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7--8 & Mar 2--13 & VQE for Lipkin model, Jordan-Wigner transform \\
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9 & Mar 16--20 & Quantum Fourier Transform \\
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10--11 & Mar 23--Apr 10 & QPE, HHL algorithm (\textit{holiday Apr 1--3}) \\
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12 & Apr 13--17 & HHL codes and implementation \\
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13 & Apr 20--24 & QAOA algorithm \\
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14 & Apr 27--May 1 & QML foundations, Quantum Neural Networks \\
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15--16 & May 4--15 & QPINNs: solving differential equations \\
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17 & May 18--22 & Quantum Boltzmann Machines \\
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1 & Jan 19--23 & Basic quantum mechanics, Hilbert spaces, qubits \\
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2--3 & Jan 26--Feb 6 & Composite systems, density matrices, entanglement \\
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4 & Feb 9--13 & Entanglement entropies, quantum gates \\
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5--6 & Feb 16--27 & VQE: algorithm, measurements, gradients (Project 1) \\
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7--8 & Mar 2--13 & VQE for Lipkin model, Jordan-Wigner transform \\
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9 & Mar 16--20 & Quantum Fourier Transform \\
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10--11& Mar 23--Apr 10 & QPE and HHL algorithm \\
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12 & Apr 13--17 & HHL codes and implementation \\
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\bottomrule
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\end{tabular}
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\end{center}
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\end{frame}
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% ---- Course map: Part 2 ------------------------------------
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\begin{frame}{Course Road Map --- Part 2: Quantum Machine Learning}
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\begin{center}
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\small
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\renewcommand{\arraystretch}{1.28}
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\begin{tabular}{@{}llp{8.0cm}@{}}
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\toprule
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\textbf{Weeks} & \textbf{Dates} & \textbf{Topics} \\
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\midrule
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13 & Apr 20--24 & QAOA: quantum approximate optimisation \\
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14 & Apr 27--May 1 & QML foundations, Quantum Neural Networks \\
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15--16& May 4--15 & QPINNs: solving differential equations \\
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17 & May 18--22 & Quantum Boltzmann Machines and course summary \\
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\bottomrule
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\end{tabular}
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\end{center}
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\vspace{6pt}
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\begin{alertblock}{Overarching Goal}
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Equip participants with the theoretical foundations and practical
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implementation skills to design, analyse, and run quantum algorithms
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on near-term and fault-tolerant hardware.
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\end{alertblock}
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\end{frame}
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% ---- Closing -----------------------------------------------
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\begin{frame}{Summary: What You Will Learn}
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\begin{frame}{Summary: What we have done}
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\begin{columns}[T]
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\column{0.48\textwidth}
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\begin{block}{Part 1 -- Quantum Computing}
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\item Variational algorithms (VQE)
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\item Fault-tolerant algorithms:\\
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QFT, QPE, HHL
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\item Physical models: Lipkin,\\
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fermionic Hamiltonians
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\item Physical models: Lipkin, Pairing
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\end{itemize}
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\end{block}
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\column{0.48\textwidth}
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\end{alertblock}
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\end{frame}
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% ============================================================
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% PERSPECTIVES — QUANTUM COMPUTING: FUTURE DIRECTIONS
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% ============================================================
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% ---- Perspectives: section divider -------------------------
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\begin{frame}[plain]
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\begin{center}
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\vspace{1.4cm}
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{\Huge\bfseries\color{qblue} Perspectives}\\[0.5em]
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{\Large\color{black} Future Directions in Quantum Computing}\\[0.3em]
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{\normalsize\color{gray} Algorithms, Hardware, and Scientific Applications}
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\end{center}
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\end{frame}
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% ---- Perspectives 1: NISQ & fault-tolerant algorithms ------
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\begin{frame}{Perspectives --- Algorithms: NISQ and Fault-Tolerant}
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\begin{columns}[T]
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\column{0.48\textwidth}
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\begin{block}{Near-Term (NISQ) Algorithms}
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\begin{itemize}\small\itemsep1pt
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\item \textbf{Improved VQE ans\"{a}tze:}
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hardware-efficient, UCC and ADAPT-VQE,
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symmetry-preserving circuits
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\item \textbf{Quantum error mitigation:}
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zero-noise extrapolation,
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probabilistic error cancellation
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\item \textbf{Barren plateau remedies:}
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layerwise training, local cost
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functions, better initialisation
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\item \textbf{Quantum advantage benchmarks:}
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tasks where NISQ devices
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outperform classical methods
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\end{itemize}
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\end{block}
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\column{0.48\textwidth}
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\begin{block}{Fault-Tolerant Algorithms}
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\begin{itemize}\small\itemsep1pt
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\item \textbf{Quantum simulation:}
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Trotterisation, qubitisation,
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linear combination of unitaries (LCU)
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\item \textbf{Improved QPE:}
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randomised and Bayesian phase
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estimation with fewer qubits
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\item \textbf{Beyond HHL:}
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quantum linear algebra (QSVM,
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quantum PCA), dequantisation
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\item \textbf{Quantum walks and search:}
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Grover speedups, walk-based
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graph algorithms, Monte Carlo
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\end{itemize}
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\end{block}
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\end{columns}
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\end{frame}
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% ---- Perspectives 2: Physical sciences applications --------
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\begin{frame}{Perspectives --- Applications in the Physical Sciences}
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\begin{columns}[T]
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\column{0.48\textwidth}
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\begin{block}{Quantum Chemistry and Nuclear Physics}
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\begin{itemize}\small\itemsep1pt
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\item \textbf{Electronic structure:}
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VQE and QPE for ground and excited
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states beyond coupled-cluster reach
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\item \textbf{Nuclear structure:}
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ab initio calculations using Lipkin,
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pairing, and shell-model Hamiltonians
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\item \textbf{Quantum advantage:}
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fault-tolerant simulation of strongly
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correlated systems (e.g.\ FeMoco)
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\item \textbf{Imaginary-time evolution:}
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thermal states and finite-temperature
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properties on quantum hardware
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\end{itemize}
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\end{block}
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\column{0.48\textwidth}
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\begin{block}{Condensed Matter and High-Energy Physics}
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\begin{itemize}\small\itemsep1pt
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\item \textbf{Lattice gauge theories:}
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quantum simulation of QED, QCD,
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and the Hubbard model
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\item \textbf{Topological phases:}
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preparation and detection of
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topological order and anyons
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\item \textbf{Quantum gravity:}
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holographic duality (AdS/CFT)
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encoded on quantum circuits
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\item \textbf{Quantum sensing:}
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Heisenberg-limited parameter
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estimation, magnetometry,
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gravimetry
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\end{itemize}
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\end{block}
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\end{columns}
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\end{frame}
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% ---- Perspectives 3: QML, hardware, open challenges --------
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\begin{frame}{Perspectives --- Quantum ML, Hardware, and Open Challenges}
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\begin{columns}[T]
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\column{0.54\textwidth}
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\begin{block}{Quantum Machine Learning Frontiers}
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\begin{itemize}\small\itemsep1pt
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\item \textbf{Quantum generative models:}
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quantum GANs, quantum diffusion,
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and QBMs beyond the RQBM
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\item \textbf{Quantum reinforcement learning:}
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RL on quantum hardware for
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quantum control and
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agentic scientific workflows
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\item \textbf{Classical--quantum hybrid:}
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tensor networks and classical
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circuit simulation as a
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guide for algorithm design
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\item \textbf{Certification:}
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classical shadow tomography
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and cross-entropy benchmarking
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\end{itemize}
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\end{block}
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\column{0.43\textwidth}
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\begin{block}{Hardware and Open Challenges}
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\begin{itemize}\small\itemsep1pt
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\item \textbf{Qubit platforms:}
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superconducting, trapped-ion,
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photonic, neutral-atom arrays
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\item \textbf{Error correction:}
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surface and color codes;
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logical fault-tolerant qubits
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\item \textbf{Scalability:}
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how many logical qubits for
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quantum advantage on
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real-world problems?
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\end{itemize}
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\end{block}
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\begin{alertblock}{Key Insight}
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Quantum advantage requires both
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better algorithms \emph{and}
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better hardware in tandem.
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\end{alertblock}
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\end{columns}
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\end{frame}
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\end{document}

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