Free PDF of Quantum Algorithms Book

Derivations and Implementation Guides to Shor, Grover, Hamiltonian Simulation, Quantum Chemistry, Linear Algebra, and Block Encoding Algorithms.

Most treatments of quantum algorithms state a result and move on. This book works through the algebra. It is written for readers who want to understand why these algorithms work well enough to implement them.

What the book covers

• Foundations: the postulates, single- and multi-qubit gates, circuits, state preparation and oracles, entanglement and teleportation, Deutsch-Jozsa, Bernstein-Vazirani and Simon.

• The Fourier strand: the quantum Fourier transform, phase estimation and its iterative single-ancilla variant, period finding, Shor’s factoring algorithm, RSA, and the discrete logarithm, with the number theory developed alongside.

• The search strand: Grover search, quantum counting, amplitude amplification and estimation, and search as continuous-time evolution.

• The simulation strand: Hamiltonian simulation by Trotter-Suzuki, sparse Hamiltonians and linear combinations of unitaries; quantum chemistry through the Jordan-Wigner, parity and Bravyi-Kitaev encodings and the full pipeline from molecule to circuit; combinatorial optimization by adiabatic evolution and QAOA; and linear systems by HHL.

• The unifying view: block encodings, quantum signal processing and the quantum singular value transformation, which show that most of the preceding algorithms are the same algorithm with different polynomials, followed by three fault-tolerant applications: qubit-efficient amplitude estimation, Trotter-free simulation by qubitization, and linear solvers that improve HHL’s dependence on the condition number.

For students and for teaching

• 162 end-of-chapter problems, ordered by difficulty, with hints for the harder ones and an answer key for every problem whose answer is a number or a formula.

• Three open-ended research problems and projects at the end of every chapter, each naming a concrete deliverable, suitable as term projects or the starting point of a thesis.

• Every cost stated for what it actually counts: two-qubit gates, oracle queries, qubits, circuit depth or classical arithmetic, with every symbol defined where it is used.

• Six appendices: notation and conventions, a gate and identity reference with the Qiskit name of every gate, an algorithm resource summary, a guide to verifying an implementation, hints, and answers. A full index.

The prerequisites are linear algebra and comfort with complex numbers.