Quantum Error Correction and Algorithms

A full-stack view of quantum algorithms and quantum error correction - essential knowledge for anyone aiming to work with fault-tolerant quantum computing. This course bridges the gap between abstract quantum algorithms and the physical realities of noisy quantum hardware, showing how error correction makes reliable large-scale quantum computation possible.

Part of the Quantum 201 professional certificate track from Delft University of Technology.

What you’ll learn

• Quantum algorithm building blocks: amplitude amplification, quantum phase estimation, and the quantum Fourier transform as general reusable subroutines
• Shor’s factoring algorithm in full: how quantum phase estimation enables efficient period finding, how period finding solves factoring, and what the classical post-processing does
• Grover’s search algorithm: the complete amplitude amplification mechanism and the proof that O(√N) queries are optimal for unstructured search
• Quantum walk algorithms: an emerging alternative to amplitude amplification for certain search and optimisation problems
• Why noise is unavoidable: gate errors, decoherence, crosstalk, and measurement errors in physical quantum hardware
• Why quantum error correction is possible: the key insight that errors can be identified (syndrome measurement) without learning the quantum information
• The stabiliser formalism: how Pauli group generators define quantum error-correcting codes and syndrome measurements efficiently
• CSS codes: the Calderbank-Shor-Steane code family and how they combine classical error-correcting codes into quantum codes
• The surface code: its planar qubit geometry, its X and Z stabiliser structure, its error threshold (~1%), and why it is the leading fault-tolerant architecture
• The overhead cost of error correction: how many physical qubits are needed per logical qubit, and what that implies for near-term hardware

Course structure

The course runs at six to eight hours per week with two parallel tracks that converge.

The algorithms track begins with quantum phase estimation, which is the subroutine at the heart of Shor’s algorithm. Phase estimation is treated in full generality before Shor’s algorithm is assembled from it. Shor’s algorithm is then worked through completely: the quantum period-finding circuit, the continued fractions post-processing, and the connection to integer factoring. This is one of the most thorough Shor’s treatments available in any online course. Grover’s algorithm and its optimality proof follow.

The error correction track begins with the noise problem: physical error rates, the types of errors that occur, and why they must be corrected rather than just tolerated. Classical error correction is briefly reviewed before quantum error correction is introduced. The three-qubit repetition code, the Steane seven-qubit code, and finally the surface code build progressively. The surface code module is the most detailed, covering stabiliser measurements, error decoding algorithms, and the error threshold.

The final modules bring the tracks together: fault-tolerant implementations of quantum algorithms, and what error correction overhead means for the timeline to useful quantum computation.

Who is this for?

• Anyone pursuing the Quantum 201 professional certificate from Delft University
• Quantum software engineers who want deep mathematical understanding of algorithms
• Hardware engineers who want to understand what fault-tolerant quantum computing demands from their systems
• Researchers in quantum information science wanting formal error correction treatment
• Anyone who wants to evaluate claims about quantum computing timelines with genuine technical understanding

Prerequisites

Quantum 201 level preparation is expected: density matrices, POVM measurements, and quantum circuits at an advanced level. The algorithms sections require familiarity with quantum Fourier transform concepts and modular arithmetic. Error correction sections require linear algebra, particularly the group theory of the Pauli group. This is one of the more mathematically demanding courses in the Delft programme.

Hands-on practice

Problem sets include:

• Working through Shor’s algorithm for small factoring examples (e.g., factoring 15)
• Constructing stabiliser code generators for the three-qubit and five-qubit codes
• Simulating error correction rounds with depolarising noise using Python
• Estimating logical error rates from physical error rates for the surface code
• Implementing quantum phase estimation in Qiskit and running on a simulator

Certificate track graded assessments are at graduate course difficulty.

Why take this course?

Quantum error correction is the critical technology separating current noisy intermediate-scale quantum devices from the fault-tolerant quantum computers needed to run Shor’s algorithm at practically relevant scales.

Understanding error correction is essential for anyone who wants to work on the path to useful quantum computing rather than just demonstrate near-term demonstrations. This course gives both the algorithms and the error correction in one coherent treatment, showing why the two subjects are inseparable: algorithms tell you what you want to compute, error correction tells you how to compute it reliably at scale.

QuTech’s instructors bring research-level depth to material that most courses only cover superficially, and the treatment of the surface code in particular is among the best available in any online course.

Related tutorials

Practise the concepts from this course with these hands-on tutorials:

• Grover’s Algorithm Explained - Step-by-step implementation of Grover’s search algorithm in Qiskit
• Shor’s Algorithm Explained - How Shor’s factoring algorithm works and why it threatens current encryption
• Getting Started with Qiskit - Installation, IBM Quantum account setup, and running circuits on real hardware