Group Theory
Brilliant.org
17 courses · 6 tutorials
Brilliant.org
Prof. John Preskill, Caltech
Delft University of Technology (QuTech)
Delft University of Technology (QuTech)
Austin Fowler
Hoang Quy La
Giordano Scappucci, Menno Veldhorst, Eliška Greplová (QuTech, TU Delft)
Delft University of Technology (QuTech)
Christian Andersen (QuTech, TU Delft)
John Watrous
Microsoft Quantum
Prof. Isaac Chuang and Prof. Aram Harrow, MIT
Dr. Daniel Gottesman, Perimeter Institute
IBM Quantum / Qiskit Team
Prof. Dan Boneh and Will Zeng, Stanford
IQC Faculty, University of Waterloo
Xanadu
A practical introduction to the main quantum error models: bit flip, phase flip, depolarizing, and amplitude damping. Understand how these map onto real hardware noise and how error correction addresses each.
Learn how quantum error correction works by implementing the 3-qubit bit-flip code in Qiskit - encode a logical qubit, introduce an error, detect it with syndrome measurement, and correct it.
Implement a 3-qubit bit-flip repetition code from scratch in Qiskit: encoding, error injection, syndrome measurement with ancilla qubits, decoding logic, and fidelity benchmarking across error rates.
Simulate a distance-3 surface code using Stim and decode syndromes with PyMatching. Measure logical error rates and compute the code threshold from simulation data.
How the surface code works: the 2D lattice geometry, X and Z stabilizer measurements, logical operators, and why it's the leading candidate for fault-tolerant quantum computing.
What decoherence is physically, how T1 and T2 times characterise it, and why it is the central engineering problem of quantum computing. Includes Qiskit simulation of decoherence effects.