Brilliant
Vectors and Matrices
Master vectors, matrices, transformations, and eigenvalues, the essential mathematical foundation for quantum computing, machine learning, and physics.
You know the basics. Now it is time to write real quantum circuits, implement algorithms, and run on actual quantum hardware. These 26 courses are designed for learners who have completed an introductory course and are ready for the next level.
Intermediate quantum computing is the step between understanding what qubits are and being able to actually use quantum computers to solve problems. You are at the intermediate level if you can explain superposition, entanglement, and measurement without much prompting; you understand the gate model conceptually; and you are ready to write circuits rather than just read about them.
You do not need to have a physics background, and you do not need to be comfortable with all the mathematics yet. Many intermediate courses introduce linear algebra as they go. What matters is that you have enough conceptual grounding that you are not confused by the vocabulary and can focus on the new material.
If you have completed the Deutsch-Jozsa algorithm as an exercise and you understand why it demonstrates quantum advantage, even if you had to work through it carefully, you are ready for intermediate content. The algorithms you will encounter now (Grover's, Shor's, VQE, QAOA) are more involved, but the conceptual jump from Deutsch-Jozsa is manageable.
Intermediate quantum computing covers a wide range of practically important topics:
Quantum circuit design goes beyond single-qubit gates to multi-qubit operations, circuit optimization, and transpilation for specific hardware. You will learn to think about gate depth, connectivity constraints, and how to map a logical algorithm to a real device.
Algorithms at this level include Grover's search algorithm (quadratic speedup for unstructured search) and Shor's factoring algorithm (conceptually, the math is introduced step by step). You will understand what makes these algorithms work rather than just following the steps.
Variational methods such as VQE and QAOA are the most practically relevant near-term algorithms. Intermediate courses introduce these as hybrid quantum-classical optimizations and often include hands-on coding exercises using Qiskit or PennyLane.
Real hardware is a major component of intermediate courses. Running circuits on actual IBM, IonQ, or Rigetti devices means dealing with noise, error rates, and measurement statistics. Understanding the gap between simulator and hardware results is one of the most valuable practical skills at this level.
Error mitigation basics, techniques like zero-noise extrapolation and probabilistic error cancellation, are introduced at the intermediate level and prepare you for advanced fault-tolerance topics.
Before starting an intermediate course, you should ideally have:
If you are unsure whether you have the right foundation, see our prerequisites guide for a self-assessment checklist.
26 courses, ranked by rating
Brilliant
Master vectors, matrices, transformations, and eigenvalues, the essential mathematical foundation for quantum computing, machine learning, and physics.
QUANTUM ALGORITHM DESIGN
Classiq engineering and research team
Classiq's free library of hands-on quantum computing tutorials covering algorithm design, quantum machine learning, and optimization using the high-level Qmod language. No circuit assembly required.
edX
Delft University of Technology (QuTech)
Learn how a quantum computer is operated: quantum algorithms, error correction, micro-architectures, compilers, quantum programming languages, and quantum internet protocols.
Coursera
École Polytechnique / Alain Aspect, Michel Brune
École Polytechnique's acclaimed introduction to quantum optics, co-taught by Nobel laureate Alain Aspect. Learn how light is quantized, how to describe quantum states of light, and how single photons exhibit wave-particle duality in real experiments.
edX
Lieven Vandersypen and QuTech researchers (TU Delft)
Learn how a quantum computer could be physically built and controlled, covering superconducting qubits, trapped ions, and other hardware platforms from Delft University of Technology.
Austin Fowler
Google Quantum AI's free-to-audit Coursera course on quantum error correction. Covers the surface code, stabilizer formalism, and the Stim and Crumble software tools used by Google researchers, with hands-on coding labs.
edX
CertificateDelft University of Technology (QuTech)
Get hands-on with QuTech's real quantum demonstrators, Quantum Network Explorer (QNE) and Quantum Inspire (QI), programming simulations and running quantum algorithms.
edX
Delft University of Technology (QuTech)
Learn the fundamentals of quantum networks and their applications with QuTech's Quantum Network Explorer, including hands-on simulation using QNE-ADK and SquidASM.
edX
Delft University of Technology (QuTech)
Learn the fundamentals of quantum hardware and experiment with QuTech's Quantum Inspire simulators to gain hands-on experience with real quantum computing.
D-Wave
D-Wave's flagship developer training: 35 hours of hands-on instruction covering QUBO formulation, Ising models, Ocean SDK, hybrid solvers, and real-world portfolio optimization. Includes virtual office hours with D-Wave experts. Multiple 2026 sessions available.
D-Wave
D-Wave's bundle combining Quantum Programming Core with one additional month of unlimited Leap Quantum Cloud access. 35 hours of developer training plus hands-on QPU access for first-time Leap users. Approximately 6 weeks total.
edX
Purdue University / Pramey Upadhyaya
The first course in Purdue University's Applied Quantum Computing series. Teaches the postulates of quantum mechanics and how they map onto present-day quantum information processing models including computation, simulation, optimization, and machine learning.
Coursera
SpecialisationUniversity of Colorado Boulder / Wounjhang Park
University of Colorado Boulder's three-course specialization giving engineers the quantum mechanics foundation behind modern electrical, mechanical, and quantum engineering. Covers superposition, entanglement, measurement, the uncertainty principle, angular momentum, and approximation methods.
IBM Quantum
Max Rossmannek, Julian Schuhmacher, Alexander Miessen, and Laurin Fischer, IBM Quantum
Free openHPI course on quantum simulation for chemistry and materials science, developed with IBM Quantum. Covers the second quantization, molecular Hamiltonians, VQE for molecular ground states, and Qiskit Nature.
QUANTUM COMPUTING
CertificateMIT xPRO / Isaac Chuang, William Oliver, Peter Shor, Aram Harrow
MIT xPRO's professional certificate program in quantum computing, taught by Isaac Chuang, William Oliver, Peter Shor, and Aram Harrow. A two-course program covering quantum computing fundamentals, algorithms for cybersecurity and chemistry, and the business implications of the technology.
Udemy
Hoang Quy La
A hands-on Udemy course by Hoang Quy La covering qubits, quantum gates, and quantum circuits in Python with Cirq and Qiskit, plus the Deutsch-Jozsa algorithm, Grover's algorithm, the quantum Fourier transform, quantum phase estimation, variational quantum circuits, and an introduction to quantum error correction.
Google Quantum AI
Google Quantum AI's free self-paced tutorial series for the Cirq quantum programming framework. Covers circuit construction, noise models, algorithm implementation, and access to Google's Quantum Virtual Machine via Google Colab.
IBM Quantum
Free intermediate course from IBM covering Grover's search, quantum phase estimation, and the fundamentals of quantum algorithm design.
IBM Quantum
IBM's free course on utility-scale quantum computing. Covers running large circuits on real IBM hardware, error mitigation, and near-term application areas using Qiskit Runtime.
IBM Quantum
John Watrous
John Watrous's four-course video lecture series covering quantum information theory, algorithms, error correction, and the general formulation of quantum operations. Graduate-level rigor, freely available.
QUANTUM INFORMATION
Prof. Isaac Chuang and Prof. Peter Shor, MIT
MIT's three-part interactive course on quantum information science covering quantum mechanics, protocols, algorithms, and communication. Fully free with graded exercises on the Open Learning Library.
PennyLane
Xanadu / Community
Xanadu's collection of hundreds of interactive PennyLane tutorials, including 50+ quantum machine learning demos covering VQE, QAOA, quantum kernels, quantum neural networks, and more.
QUANTUM ALGORITHMS
Dr. Donovan
The sequel to Quantum Computing 101. Eight modules on how quantum algorithms actually get their speedup, why real hardware fights you, and what a transpiler does to your circuit before it ever runs. Free and self-paced.
QUANTUM ML
Xanadu
Annual quantum hackathon run by Xanadu, the team behind PennyLane, with coding challenges covering PennyLane, hybrid algorithms, and quantum kernels. Talk recordings and challenge write-ups remain available online after each event.
QUANTUM FOURIER TRANSFORM
QWorld volunteer instructors
QWorld's free intermediate quantum programming workshop covering complex numbers, the quantum Fourier transform, and Shor's algorithm. The follow-on to QBronze, run as mentored online sessions through QWorld's global network.
QUANTUM MECHANICS
Prof. R. Shankar, Yale University
R. Shankar's celebrated Yale Open Courses lectures for PHYS 201, covering electromagnetism and optics before closing with a seven-lecture introduction to quantum mechanics: wave-particle duality, the Schrodinger equation, and quantum measurement.