Quantum computing is not magic — it is linear algebra in complex vector spaces, running on machines cold enough to make superconductors behave. This free, open-source quantum computing textbook teaches the field the way it actually works: the mathematics first, then the physics that the mathematics describes, then the algorithms that exploit it, and finally the hardware and error correction that decide what is possible today versus what is still a promise. Quantum mechanics is not a prerequisite. The book teaches the quantum mechanics you need, from scratch, specifically for computing — you will never need a wave equation, only state vectors and operators.
Thirty-four chapters across eight parts build from the qubit to fault tolerance. Part I covers superposition and the Bloch sphere, bra-ket notation and unitary operators, the Born rule and measurement collapse, tensor products and entanglement, and the universal gate set. Part II moves to circuits and real programming in Qiskit, including quantum teleportation, superdense coding, and quantum key distribution. Part III is the canonical algorithm sequence — quantum parallelism and interference, Deutsch-Jozsa and Bernstein-Vazirani, Grover's quadratic search, the quantum Fourier transform, Shor's factoring algorithm and its consequences for RSA, phase estimation, and Hamiltonian simulation. Part IV covers the NISQ-era methods designed for imperfect hardware: VQE for ground-state chemistry, QAOA for combinatorial optimization, and quantum machine learning, including an honest treatment of barren plateaus and where claimed advantages do not survive scrutiny.
Part V builds quantum error correction from the no-cloning theorem through the Shor and Steane codes, the stabilizer formalism, surface codes, and the threshold theorem. Part VI examines the hardware itself — superconducting transmons, trapped ions, photonic and neutral-atom platforms, and the cryogenics, control electronics, and calibration that make a quantum computer run. Part VII covers post-quantum cryptography and the NIST standards, the competitive industry landscape, and a chapter devoted entirely to separating quantum hype from quantum reality. Part VIII is a capstone portfolio: eight algorithms implemented, executed on real quantum processors, and analyzed against the noise that makes real results differ from ideal ones.
Every algorithm is explained mathematically, implemented in Qiskit using current APIs, and run — with 240 exercises, a 124-term glossary, and worked derivations throughout. Written for CS students, physicists moving into quantum information, software engineers who want to program real quantum hardware for free, and cryptographers who need to understand the timeline of the quantum threat.