Fundamentals of Quantum Algorithms (IBM Learning)

The natural continuation from Basics of Quantum Information. This course steps up from quantum information formalism to the first genuinely powerful quantum algorithms, with all implementations in Qiskit using interactive notebooks.

Fundamentals of Quantum Algorithms is where the payoff from learning quantum information basics starts to become visible. The course builds from the query complexity framework through Grover’s search and into quantum phase estimation, which is the subroutine at the heart of Shor’s algorithm and many simulation algorithms.

What you’ll learn

• Quantum query complexity: the oracle model, query complexity as a measure of algorithmic efficiency, and why it is the right framework for proving quantum speedup
• The Deutsch-Jozsa and Bernstein-Vazirani algorithms: using quantum parallelism to solve problems in one query that require many classically
• Simon’s algorithm: an exponential quantum speedup for a structured problem, and the conceptual bridge to Shor’s factoring algorithm
• Grover’s search algorithm: amplitude amplification, the geometric picture of the Grover iteration as a rotation, the query count derivation, and the proof of optimality
• Quantum phase estimation: the circuit that extracts the eigenvalue of a unitary operator, the role of the quantum Fourier transform, and precision scaling with qubit count
• Introduction to quantum simulation: how quantum phase estimation underlies quantum chemistry algorithms and what problems quantum simulation targets
• Qiskit implementations for every algorithm, running interactively in the course platform

Course structure

The course opens with the query complexity model because it provides the analytical framework needed to discuss speedup rigorously. Simple algorithms establish the pattern before Grover’s algorithm takes it further.

Grover’s algorithm receives extended treatment, including the geometric picture of the Grover iteration, the optimal query count calculation, and the lower bound proof. This depth is not typical in introductory treatments and is one of the course’s stronger features.

Quantum phase estimation is built up from the quantum Fourier transform, treated as a reusable module. The final section introduces quantum simulation at a conceptual level, showing where phase estimation plugs into real-world applications.

Who is this for?

• Learners who have completed Basics of Quantum Information (IBM Learning) or equivalent
• Computer scientists and software engineers who want to understand how quantum speedup actually works rather than just hearing that it exists
• Graduate students preparing to read quantum algorithm research papers
• IBM Quantum users who want to move beyond circuit basics into algorithmic programming

Prerequisites

This course picks up where Basics of Quantum Information leaves off. Fluency with qubits, quantum gates, state vectors, and entanglement is assumed. The quantum Fourier transform is introduced within the course, so no prior knowledge of it is needed. Working Python and some Qiskit familiarity are helpful for getting the most from exercises.

Hands-on practice

All algorithms are implemented in Qiskit using the course’s interactive notebook environment:

• Build the oracle circuits for Deutsch-Jozsa and Bernstein-Vazirani problems
• Implement Simon’s algorithm and verify it finds the hidden period for small examples
• Construct the full Grover circuit with oracle and diffuser, run on the Qiskit statevector simulator, and observe amplitude amplification at each iteration
• Build the quantum Fourier transform circuit from controlled phase gates
• Implement quantum phase estimation for a simple unitary and measure the extracted phase
• Explore how output precision improves as more ancilla qubits are added to the QPE circuit

Why take this course?

The jump from understanding qubits to understanding quantum algorithms is where many learners stall. This course bridges that gap methodically: every algorithm comes with the mathematical derivation, the geometric intuition, and the working Qiskit implementation.

IBM Learning keeps the course current with the modern Qiskit API, so the code you write here is consistent with the tools you will use on real IBM Quantum hardware. The free, interactive format means there is no cost to working through it even if you already have some algorithmic background and just want to fill in gaps.

For anyone targeting quantum software development or algorithm research, this course and its predecessor form the foundation that later, more specialised study builds on.