Learning Path¶
A guided route through the Circuit Bench, from zero to quantum algorithms. Follow this if you're new and want a structured progression.
Stage 1: The basics¶
What's a qubit? What's a gate? What does measurement mean?
These circuit notes build your intuition for the machinery behind quantum computing: gates, measurement bases, superposition, entanglement, and measurement.
| Order | Circuit note | Key concept |
|---|---|---|
| 0 | Reading a Quantum Circuit | Gates, Bloch sphere, unitary rotation, and measurement bases |
| 1 | Bell State | Entanglement — two qubits, perfectly correlated |
| 2 | Teleportation | Using entanglement as a resource to transmit quantum information |
| 3 | Deutsch-Jozsa | Your first quantum speedup — interference as computation |
After Stage 1 you'll understand
- What qubits, gates, unitary rotations, and measurement bases actually do
- Why entanglement is useful, not just spooky
- How interference lets quantum computers answer questions in fewer steps
Stage 2: Querying and searching¶
How do you extract information from a quantum system?
| Order | Circuit note | Key concept |
|---|---|---|
| 4 | Bernstein-Vazirani | Querying a hidden structure with one question |
| 5 | Simon's Problem | Exponential speedup from structure in a function |
| 6 | Grover's Search | Amplitude amplification — boosting the right answer |
After Stage 2 you'll understand
- How oracles encode problems into quantum circuits
- Why quantum speedups come from structure, not magic
- The difference between quadratic and exponential advantage
Stage 3: Real applications¶
What can you actually compute?
| Order | Circuit note | Key concept |
|---|---|---|
| 7 | QAOA for MaxCut | Variational optimization on a graph |
| 8 | VQE for H₂ | Finding the ground-state energy of a molecule |
| 9 | Quantum Fourier Transform | The engine behind phase estimation and Shor's algorithm |
After Stage 3 you'll understand
- How hybrid classical-quantum algorithms work
- How quantum simulation connects to chemistry
- What the QFT actually does and why it matters
Stage 4: Deep cuts¶
Advanced techniques for when you want the full picture.
| Order | Circuit note | Key concept |
|---|---|---|
| 10 | Quantum Phase Estimation | Precision measurement of eigenvalues |
| 11 | Error Mitigation (ZNE) | Making noisy results useful |
| 12 | Quantum Counting | Combining Grover with QPE |
Philosophy¶
Each stage builds on the previous one, but every circuit note is self-contained. If you already understand entanglement, skip to Stage 2. If you're here for VQE, jump straight to Stage 3 — links to prerequisite concepts are built into each note.
The goal is understanding, not coverage. We'd rather you deeply grasp six circuits than skim twenty.