Research Notes
Quantum History
Quantum computing traces its roots to the early 1980s, when Richard Feynman proposed that simulating quantum systems efficiently would require a quantum computer. David Deutsch formalised the model of a universal quantum Turing machine in 1985, and Peter Shor’s 1994 factoring algorithm demonstrated that quantum computers could solve problems believed to be classically intractable.
Key milestones:
| Year | Event |
|---|---|
| 1981 | Feynman proposes quantum simulation |
| 1985 | Deutsch defines universal quantum computation |
| 1994 | Shor’s factoring algorithm |
| 1996 | Grover’s search algorithm |
| 2019 | Google claims quantum supremacy (Sycamore) |
| 2023 | IBM reaches 1000+ qubit processor |
This section is a work in progress — more depth coming.
Important Quantum Algorithms
Quantum algorithms derive their power from superposition, entanglement, and interference. The most impactful families so far:
- Shor’s algorithm — polynomial-time integer factoring; breaks RSA.
- Grover’s algorithm — quadratic speedup for unstructured search.
- Variational Quantum Algorithms (VQAs) — hybrid classical-quantum optimisation, well-suited to near-term hardware.
For a hands-on look at variational circuits — including parameterised gates, the parameter-shift rule, and the barren plateau problem — see the full notebook: Variational Quantum Circuits →
Introductory Data Mining
Data mining extracts actionable patterns from large datasets. Core problem families:
Association rules — find items that co-occur frequently (Apriori, FP-Growth).
Clustering — group unlabelled points by similarity (k-means, DBSCAN, hierarchical).
Classification — learn a decision boundary from labelled examples (decision trees, SVMs, gradient boosting).
Dimensionality reduction — project high-dimensional data to a lower-dimensional representation that preserves structure (PCA, t-SNE, UMAP).
This section is a work in progress — code examples coming.
Introductory AI
Modern machine learning is largely the study of optimising a loss function over a parameter space. Understanding the geometry of that space — where gradients point, where local minima cluster, where saddle points trap optimisers — is central to building models that actually train.
For an interactive look at gradient descent on non-convex loss surfaces, including saddle-point escape dynamics on the Rastrigin function, see the full notebook: Gradient Descent on Loss Landscapes →