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Quantum Computing

Quantum computing as a model of computation: bits to qubits, gates to circuits, and the interference that actually buys the speedup.

I don't know any physics or quantum mechanics, and this course assumes I don't. It starts from the bit I already understand and generalizes it into a qubit, then builds up: gates as matrices, circuits as programs, algorithms as choreographed interference. No hype, no 'it tries every answer at once', no physics I have to take on faith. I want to see, with real interactions, exactly where the speedup comes from, what it provably cannot do, and how you actually run one today.

Written by Claude Fable 5 24 lessons, 8 modules updated Jul 2026

Module 0 Foundations: What It Is, and What It Is Not

start here

Why quantum computing (and what it is not)

The one real source of speedup, and the myth to unlearn first

Classical bits, gates, and reversibility

The model we generalize, and why quantum gates run backward

Probability, but with amplitudes

Swap non-negative reals for signed, complex amplitudes

Complex numbers as rotation and phase

Magnitude, angle, and that multiplying rotates

Module 1 The Qubit

one bit, generalized

The qubit and its state vector

A unit vector: alpha|0> plus beta|1>

Measurement and the Born rule

Reading a qubit collapses it and pays out one bit

The Bloch sphere

Every one-qubit state is a point on a sphere

Global phase vs relative phase

One is invisible; the other is the whole resource

Module 2 Gates and Circuits

programming a qubit

Single-qubit gates as matrices

X, Z, H: unitary rotations of the Bloch vector

Multiple qubits and the tensor product

n qubits live in a 2^n-dimensional space

Two-qubit gates and CNOT

Flip the target when the control is 1

Entanglement and Bell states

Correlations with no classical explanation, no signaling

The no-cloning theorem

You cannot copy an unknown qubit

Module 3 Interference at Work

the real mechanism

Quantum parallelism, honestly

All inputs in one shot, then the measurement wall

Deutsch-Jozsa and phase kickback

One query decides a global property

Module 4 The Famous Algorithms

where it gets real

Grover's search

Find one of N in about sqrt(N) steps, by rotation

The quantum Fourier transform

Reading a hidden period out of a superposition

Shor's algorithm and RSA

Factoring becomes period finding, and RSA falls

Module 5 What It Can and Cannot Do

the honest limits

BQP: quantum in the complexity zoo

Where quantum sits between P and PSPACE

What quantum computers cannot do

The hype filter, quantified

Module 6 Real Machines

from theory to hardware

Decoherence and noise

Why qubits are fragile, with zero physics required

Quantum error correction

Many noisy qubits become one reliable logical qubit

Programming a quantum computer

Circuits, shots, and histograms, hands on

Module 7 The Frontier

hype vs reality

The state of the field and post-quantum crypto

Where QC really is, and why to migrate crypto now

Reference shelf

Gate reference

Every single- and two-qubit gate the course builds, one row each: matrix, Bloch action, what it does, and the lesson that derives it.

Glossary

Every load-bearing term across the 24 lessons, defined crisply in the lessons' own words and searchable.

Algorithms compared

Deutsch-Jozsa, Grover, and Shor side by side: the problem each solves, the cost, the speedup, and its real status.

How to use this course

Do the widgets. The quizzes and flashcards are not decoration: trying to recall before you reveal is what makes it stick.
Space it out. Come back a day later and answer them cold.
Read critically. An LLM wrote these, so verify anything before you rely on it.