Algorithms Capstone: Count, Amplify, Estimate
The capstone ties the course together with three mini-projects whose every number you can recompute by hand: query counting for Bernstein–Vazirani, a Grover iteration-scaling table for N = 4, 8, and 16, and phase-estimation precision as a function of counting qubits. Each project pairs the arithmetic with a runnable circuit whose exact output distribution the arithmetic predicts.
What are you building?
This capstone is a build-and-verify project. The deliverable is a short report — a page or two — in which every number is recomputable: someone with your report, a calculator, and the Lab should be able to check each figure without trusting you. Three projects:
- Query counting — how many oracle calls Bernstein–Vazirani costs, quantum vs classical, with the argument for why the classical count cannot be beaten. (Revisits chapter 4.)
- Amplification scaling — the Grover success-probability table for search spaces N = 4, 8, 16, derived from one formula and checked against a run. (Revisits chapter 5 and chapter 6.)
- Estimation precision — what one extra counting qubit buys in quantum phase estimation, including exactly what failure looks like when a phase falls off the grid. (Revisits chapter 7 and chapter 8.)
Report checklist, per project: the claim, the hand arithmetic, the circuit, the predicted distribution, and the observed counts with shot noise acknowledged. Everything below models that standard.
You’ve read the opening of chapter 12 — 8 more sections follow, with worked examples and circuits you can run on the page. A free account unlocks every chapter of every course (paid plans aren’t live yet — early readers get everything free).