Foundations of Quantum Algorithms

No Exponential Magic

Can we use superposition to speed up calculations?

The Magic 8-Ball

Understand the role of oracles in quantum algorithms.

Pair Programming

Learn how the oracle can be used to test solutions in pairs.

Making and Breaking Promises

Explore the role of information and promises in algorithm design.

Hadamard Transform

Understand the effect of the Hadamard transform.

Deutsch–Jozsa

Implement the Deutsch–Jozsa algorithm..

Introduction to Grover Search

Become familiar with the basic components of Grover's Algorithm.

Searching with Geometry

Study Grover's Algorithm from a geometric perspective.

Searching with Circuits

Learn the relation between phase kickback and Grover search.

Steps and Speedups

Compute the optimal number of Grover steps.

Multiple Solutions

Implement Grover to search for multiple solutions.

Changing Perspectives

A review of the classical Discrete Fourier Transform

Quantum Fourier Transform

Learn about the Quantum Fourier Transform and its properties.

Connecting the Dots

Generalize the Quantum Fourier Transform for more qubits.

Catch the Phase

Calculate phases using the phase kickback technique.

It's not Just a Phase

Derive the Quantum Phase Estimation algorithm

Let's Be Rational

Estimate phases without a t-bit binary expansion.

A Mixed Bag

Analyze the QPE output for an arbitrary input state.

Modular Arithmetic

Review the basics of modular arithmetic.

Classical Factorization

Learn how to factor integers using modular arithmetic techniques.

Period Finding

Implement the period finding routine.

Shor's Algorithm

Code Shor's algorithm in its full splendor.

The RSA System

Use Shor's algorithm to break encryption systems.