CURRICULUM / 08 MODULES
Start with states and measurement. Explore the algorithms. Then make the ideas operational in your own circuits.
FOUNDATIONS
Quantum computing starts with the quantum bit, or qubit. Unlike a classical bit that is either 0 or 1, a qubit can exist in a superposition of both states simultaneously. This property enables quantum parallelism. In this module we’ll explore the mathematics of state vectors, the Bloch sphere representation, and the practical implications of measurement.
FOUNDATIONS
Superposition is the cornerstone of quantum parallelism. We’ll learn how to construct superpositions of multiple qubits, the concept of tensor products, and why this leads to exponential state spaces.
FOUNDATIONS
Measurement is the process that converts a quantum state into a classical bit string. It is probabilistic and collapses the wavefunction. We’ll study projective measurement, basis choices, and the impact on entanglement.
FOUNDATIONS
Entanglement is a uniquely quantum correlation where the state of each particle cannot be described independently of the others. The simplest examples are the four Bell states, maximally entangled two‑qubit states. This module walks through their construction and measurement outcomes.
ALGORITHMS + SYSTEMS
The Deutsch‑Jozsa problem asks: given a black‑box function f:{0,1}ⁿ→{0,1}, determine whether f is constant (same output for all inputs) or balanced (outputs 0 for half the inputs and 1 for the other half). Classically this requires 2ⁿ evaluations in the worst case; quantumly a single query suffices.
ALGORITHMS + SYSTEMS
Grover’s algorithm provides a quadratic speed‑up for unstructured search. Given an unsorted database of N=2ⁿ items with a single marked item, a classical algorithm needs O(N) queries, while Grover finds the marked item in O(√N) queries.
ALGORITHMS + SYSTEMS
Quantum teleportation transfers the exact quantum state of a particle to a remote particle using a pair of entangled qubits and classical communication. No cloning occurs; the original state is destroyed by measurement.
ALGORITHMS + SYSTEMS
Shor’s algorithm factors integers in polynomial time using quantum period finding. It consists of reducing factoring to order‑finding, then using quantum Fourier transform to discover the period of a modular exponentiation function.