Algorithms

Deutsch-Jozsa: The First Quantum Speedup

The Deutsch-Jozsa algorithm separates constant from balanced Boolean functions in a single query, where classical deterministic algorithms need up to 2ⁿ⁻¹ + 1. This tutorial derives the algorithm from first principles, explains phase kickback, and walks through the full Qiskit implementation plus the Deutsch n=1 special case.

intermediate · ~22 min · prereq: Gates & Circuits track (Tutorials 4-7)

Bernstein-Vazirani and Simon: Learning Hidden Structure in One (or O(n)) Queries

Bernstein-Vazirani learns a hidden bit string in a single query. Simon's algorithm learns a hidden shift with O(n) queries where classical algorithms need exponentially many — and was the direct inspiration for Shor's factoring algorithm. This tutorial derives both from scratch with complete Qiskit implementations.

intermediate · ~23 min · prereq: Tutorial 8: Deutsch-Jozsa

Grover's Search and Amplitude Amplification

Grover's algorithm finds a marked element in an unstructured list of N items with O(√N) queries — a provable quadratic speedup. This tutorial derives the algorithm geometrically as a rotation in a 2D subspace, gives the exact optimal iteration count, and shows how amplitude amplification generalizes the trick far beyond search.

intermediate · ~24 min · prereq: Tutorial 9: Bernstein-Vazirani and Simon

Quantum Fourier Transform and Phase Estimation

The QFT is the quantum cousin of the classical discrete Fourier transform — but it runs in O(n²) instead of O(n·2ⁿ), which is where many quantum speedups ultimately come from. This tutorial derives the QFT circuit, explains Quantum Phase Estimation (the subroutine inside Shor, HHL, and VQE), and delivers complete Qiskit implementations.

intermediate · ~25 min · prereq: Tutorial 10: Grover and Amplitude Amplification

Shor's Algorithm: Factoring, Order-Finding, and the End of RSA

Shor's factoring algorithm reduces integer factorization to the problem of finding the multiplicative order of a random element mod N — and uses quantum phase estimation to solve that in polynomial time. This tutorial derives the full algorithm, runs a small instance in Qiskit, and honestly assesses the real-world resource requirements to break RSA-2048.

advanced · ~28 min · prereq: Tutorial 11: QFT and Phase Estimation