Quantum Computing:
From Mathematics to Algorithms
A concept-first journey through quantum states, circuits, interference, landmark algorithms, noise and practical Qiskit simulations. Independently authored educational text; no reproduced textbook pages.
Browse the 20 chapters
The quantum computing landscape
What quantum computers compute, what they do not, and why amplitudes matter.
CHAPTER 02Complex numbers and probability amplitudes
Magnitude, phase, normalization, and interference.
CHAPTER 03Vectors, matrices and Hilbert spaces
The mathematical language of finite quantum systems.
CHAPTER 04Single-qubit states and the Bloch sphere
Geometric understanding of two-level systems.
CHAPTER 05Quantum gates and circuit composition
Build reversible transformations with a small gate vocabulary.
CHAPTER 06Tensor products and entanglement
What changes when registers contain multiple qubits.
CHAPTER 07Measurement and information
Projective measurement, expectation and repeated sampling.
CHAPTER 08Interference and phase kickback
How reversible operations move information into phase.
CHAPTER 09Deutsch–Jozsa algorithm
Detect constant versus balanced Boolean functions under a promise.
CHAPTER 10Bernstein–Vazirani algorithm
Recover a hidden bit string from a parity oracle.
CHAPTER 11Quantum Fourier transform
Fourier analysis of discrete amplitudes.
CHAPTER 12Quantum phase estimation
Read an eigenphase using controlled powers.
CHAPTER 13Grover search and amplitude amplification
Increase the probability of marked outcomes.
CHAPTER 14Quantum teleportation
Transfer an unknown qubit using entanglement and classical bits.
CHAPTER 15Superdense coding
Send two classical bits using one transmitted qubit and shared entanglement.
CHAPTER 16Shor and order finding
Why factoring is linked to periodicity.
CHAPTER 17Quantum noise and density matrices
Model open systems beyond ideal state vectors.
CHAPTER 18Quantum error correction
Encode logical information into a larger physical system.
CHAPTER 19Variational quantum algorithms
Combine parameterized circuits with classical optimization.
CHAPTER 20Quantum complexity and realistic advantage
Evaluate resources, oracle assumptions and verification.