Algorithms Capstone: Count, Amplify, Estimate
The capstone ties the course together with three mini-projects. You can redo every number in them by hand. Project 1 counts queries for Bernstein–Vazirani. Project 2 builds a table of how Grover's chance of success grows for N = 4, 8 and 16. Project 3 shows how the precision of phase estimation depends on the number of counting qubits. Each project pairs the arithmetic with a circuit you can run, and the arithmetic predicts its exact output.
What are you building?
Why do this? Reading about algorithms is not the same as checking them. This capstone makes you the checker, which is the skill that protects you from hype.
It is a build-and-check project. What you hand in is a short report, a page or two long. In it, every number can be recomputed. Someone with your report, a calculator and the Lab should be able to check each figure without trusting you. Think of it like a math test where you must show your work, so the teacher can follow every step. There are three projects:
- Query counting. How many oracle calls does Bernstein–Vazirani cost, quantum against normal? Include the argument for why the normal count cannot be beaten. (Goes back to chapter 4.)
- Boost scaling. The Grover success-chance table for search sizes N = 4, 8 and 16. It comes from one formula and is checked against a run. (Goes back to chapter 5 and chapter 6.)
- Estimation precision. What does one extra counting qubit buy in quantum phase estimation? Include exactly what failure looks like when a phase falls between the grid lines. (Goes back to chapter 7 and chapter 8.)
A checklist for each project: the claim, the hand arithmetic, the circuit, the predicted result, and the counts you saw, with shot noise (random wobble in the counts) noted. Everything below follows that standard.
- Project 1: how many queries does a secret string cost?
- Run Bernstein–Vazirani, secret 101, one queryINTERACTIVE
- Project 2: how does Grover's success probability scale?
- Run Grover for N = 4: one iteration, certaintyINTERACTIVE
- Project 3: how much precision does a counting qubit buy?
- Run QPE on the grid: φ = 1/4 with 2 counting qubitsINTERACTIVE
- Push the phase off the gridINTERACTIVE
- What would this capstone look like on real hardware?
You’ve read the opening of chapter 12. Pro unlocks the other 8 sections — plus every chapter of every course, with circuits you can run right on the page. That’s $11.99 a month, about the price of a coffee, or $99.99 a year (save 30%). The first chapter of every course, and the whole math course, stay free.