Interactive Learning

Quantum Computing From Qubits to Shor's Algorithm

A hands-on journey through quantum computation. Each module features interactive visualizations, step-by-step circuit builders, and real-time simulations.

24

Modules

7+

Chapters

100%

Interactive

        
Visual Intuition
Bloch spheres, circuit diagrams, and animated simulations bring abstract concepts to life

        
Learn by Doing
Every module has interactive widgets — tweak parameters and see quantum effects in real time

        
Structured Path
From basic qubits to Shor's algorithm — a carefully ordered progression with built-in progress tracking

Progress

0 / 24

0. Background Refresher

Mathematical prerequisites — review before diving in

Linear Algebra for QC

Vectors, matrices, eigenvalues, and unitary operators — the mathematical language of quantum mechanics.

Math Interactive

I. Foundations

Qubits, measurements, and the mathematical framework

Understanding Qubits

The building blocks of quantum computing — superposition, Bloch sphere visualization, and the quantum bit.

Interactive Bloch Sphere

Single-Qubit Measurements

Explore measurement in different bases, Born's rule, and the probabilistic nature of quantum observation.

Interactive Probabilities

Elitzur-Vaidman Bomb Tester

Interaction-free measurement — detect a bomb without detonating it using quantum interference.

Interactive Thought Experiment

Multi-Qubit Systems & Tensor Products

Combining qubits — tensor products, entanglement, Bell states, and multi-qubit gate operations.

Tensor Products Interactive

Reversible Computation

Why quantum gates must be reversible, garbage qubits, uncomputation, and the Bennett trick.

Interactive Circuits

The n-Qubit Hadamard Transform

From single-qubit H gates to full superposition — how Hadamard creates uniform quantum states.

Interactive Visualization

II. Protocols & Phenomena

Teleportation, entanglement, and Bell inequalities

Quantum Teleportation

Transfer quantum states using entanglement and classical communication — the teleportation protocol step by step.

Interactive Protocol

Bell inequalities in action — prove that quantum entanglement outperforms any classical strategy.

Game Bell Inequality

III. Quantum Algorithms

Deutsch, Simon, Grover, and computational speedups

The Deutsch Algorithm

The first quantum speedup — determine a function's global property with a single query using phase kickback.

Interactive Circuits

Simon's Algorithm

Exponential quantum speedup — find a hidden period using quantum parallelism and linear algebra.

Interactive Linear Algebra

Grover's Search Algorithm

Quadratic speedup for unstructured search — amplitude amplification and the diffusion operator.

Interactive Amplitudes

IV. The Road to Shor's Algorithm

Modular arithmetic, QFT, period finding, and factoring

Modular Arithmetic

The number theory behind Shor — modular exponentiation, Euler's theorem, and the connection to factoring.

Number Theory Interactive

Quantum Fourier Transform

The quantum analog of the DFT — exponential speedup through quantum phase estimation.

Interactive Visualization

From Factoring to Period Finding

The key reduction — how factoring integers reduces to finding the period of modular exponentiation.

Reduction Interactive

Quantum Period Finding

The quantum subroutine at the heart of Shor — using QFT to extract periods from quantum states.

Interactive Circuits

Shor's Algorithm

The crown jewel — factor large integers in polynomial time and break RSA encryption.

Interactive Full Simulation

V. Complexity Theory

BQP, lower bounds, and the limits of quantum computation

Quantum Complexity Theory

BQP, QMA, and the computational hierarchy — where quantum computers sit in the complexity landscape.

Theory Interactive

The Hybrid Method (BBBV)

Proving Grover's algorithm is optimal — the polynomial method and quantum query lower bounds.

Proof Interactive

VI. Quantum Error Correction

Protecting quantum information from decoherence

Shor's 9-Qubit Code

The first quantum error-correcting code — protect against bit-flip and phase-flip errors simultaneously.

Interactive Error Correction

Topological quantum error correction — protect qubits using the topology of a torus surface.

Interactive Topology

VII. Additional Protocols

Cryptography, state reconstruction, and practical quantum techniques

Quantum State Tomography

Reconstruct an unknown quantum state from measurement statistics across multiple bases.

Interactive Statistics

BB84 Quantum Key Distribution

Unbreakable cryptography — use quantum mechanics to securely exchange encryption keys.

Interactive Protocol

Bonus

Fun extras — test your quantum intuition

Quantum Collapse Game

Play an interactive game that builds intuition for quantum measurement, superposition, and wave function collapse.

Game Interactive

Superposition Hero

A rhythm game where you apply quantum gates in time to build target superpositions — master X, H, Z, CNOT and more!

Game Interactive