Introduction

Why Quantum Computing?

Classical computers represent information as bits — 0 or 1. Quantum computers use qubits, which can exist in superpositions of 0 and 1 simultaneously, and can become entangled in ways that have no classical analogue.

This gives quantum computers extraordinary power for specific problems:

  • Grover's algorithm searches an unsorted database of N items in O(√N) steps — a quadratic speedup over classical O(N) search.
  • Shor's algorithm factors large integers in polynomial time, breaking RSA encryption.
  • Quantum simulation models molecules and materials exponentially faster than classical methods.
  • Quantum key distribution enables provably secure communication, guaranteed by the laws of physics.

The Story

The idea that quantum mechanics could enable fundamentally new kinds of computation was first articulated by Richard Feynman in 1982. In 1985, David Deutsch formalized the quantum Turing machine and published the first quantum algorithm. Peter Shor's 1994 factoring algorithm and Lov Grover's 1996 search algorithm demonstrated concrete, dramatic speedups and sparked the modern era of quantum computing research.

Today, IBM, Google, IonQ, and others operate real quantum hardware accessible over the cloud. Google claimed quantum supremacy in 2019 when their 53-qubit Sycamore processor completed a specific calculation in 200 seconds that would take a classical supercomputer approximately 10,000 years.

How This Course Works

We simulate quantum systems in Python using the mathematical formalism directly — no special libraries, just vectors and arithmetic. This lets you see exactly what quantum gates do to quantum states.

A qubit is represented as a 2-element list [alpha, beta]. Gates are functions that transform these lists. Multi-qubit systems are 4-element (or larger) lists using the tensor product.

What You Will Learn

This course contains 15 lessons organized into 4 chapters:

  1. Quantum Bits -- Qubits, normalization, and measurement probability.
  2. Single-Qubit Gates -- The Hadamard, X, and Z gates.
  3. Multi-Qubit Systems -- Tensor products, CNOT, Bell states, and entanglement.
  4. Quantum Algorithms -- The Deutsch algorithm, Grover's search, quantum error correction, and BB84 key distribution.

Let's get started.

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