Series Bible: Quantum Diagonalization Blog

1. Tone and Voice

  • The Persona: A Computer Scientist and Engineer (not just a physicist) documenting a “Learning Sprint.”
  • The Vibe: “Lab Notebook meets Engineering Blog.” It is rigorous but narrative-driven. We use first-person (“I ran this,” “We must solve”).
  • The Philosophy: “Math into Metal.” We don’t just state equations; we map them to data structures and hardware constraints.
  • Key stylistic elements:
    • Use analogies (e.g., “The Quantum Wall,” “The Classical Driver,” “Fitting a round peg into a square hole”).
    • Acknowledge “The Reality Check” – always explain why the naive theoretical approach fails in practice (e.g., exponential scaling, lack of entanglement).

2. Formatting Rules (Quarto/Markdown)

  • Math: Use LaTeX. Enclose in $$ for block equations and $ for inline.
  • Code Blocks:
    • Must use explicit execution syntax: ```{python} (curly braces) to ensure Quarto executes them.
    • Qiskit Version: Strictly Qiskit 1.0+ (V2 Primitives). Use StatevectorEstimator, StatevectorSampler, and SparsePauliOp.
    • Output Handling: Always index result.data.evs[0] or cast to float() to avoid printing array brackets.
    • Hidden Setup: Use #| echo: false for setup blocks (like path appending for utils.py).
  • Images:
    • Use relative paths: image: img/filename.png in YAML and ![Alt](img/filename.png) in body.
    • Diagrams are preferred over decorative images.
  • Callouts: Use ::: {.callout-note collapse="true"} for heavy mathematical proofs that might disrupt the flow.

3. Recurring Post Structure

Each post generally follows this “V-Shape” arc: 1. The Hook: A direct link to the previous post and a statement of the current mathematical goal. 2. The Classical Problem: Defining the matrix/vector mathematically first (Numpy/Linear Algebra) before touching quantum. 3. The Quantum Mapping: How we translate that math into circuits and operators. 4. The Code (Implementation): Working Qiskit code that reproduces the classical result. 5. The Complication (The “Turn”): A section revealing why the simple solution just shown isn’t enough (e.g., “Why we can’t just scale up,” “Why we need entanglement”). 6. Next Steps: A concrete teaser for the next technical milestone.

4. Current Context Summary

We are building a VQE (Variational Quantum Eigensolver) from scratch. * Post 01: Set the roadmap (not just for molecules, but for graph spectral clustering). * Post 02: Established the Linear Algebra foundation (\(v^T A v \ge \lambda_0\)) and the Variational Principle. * Post 03: Implemented the “Engine.” We mapped classical vectors to quantum states (Amplitude Encoding) and matrices to Pauli Strings (SparsePauliOp). We used the Estimator primitive to calculate expectation values. * Post 04: Implemented the “Driver.” We replaced fixed angles with parameters (\(\vec{\theta}\)), introduced the Ansatz, and closed the loop using a classical optimizer (COBYLA). We discovered that a product-state Ansatz fails to find the ground state of an entangled system (Matrix \(A\)), motivating the need for entangling gates (CNOTs).