Learning Roadmap

A structured path from mathematical foundations to advanced quantum computing

25 modules · 185 lessons

01

00. Quantum in a Nutshell — A Gentle Introduction

No math, no prerequisites. A soft-landing introduction to quantum computing with 4 short explainer videos. Start here if you're brand new to quantum.

Lessons (4)

02

01. Mathematical Foundations I — Linear Algebra & Complex Numbers

The essential mathematical language of quantum mechanics: vector spaces, matrices, inner products, eigenvalues, tensor products, complex numbers, Hilbert spaces, and Dirac notation.

Lessons (10)

03

02. Mathematical Foundations II — Probability, Statistics & Group Theory

Probability theory, Bayes' theorem, random variables, group theory basics, Lie algebras, representation theory, Fourier analysis, and stochastic processes used in quantum mechanics.

Lessons (8)

04

03. Classical Physics — Mechanics & Electromagnetism Prerequisites

Foundational classical physics needed for quantum mechanics: Lagrangian and Hamiltonian mechanics, harmonic oscillators, wave equation, Maxwell's equations, electromagnetic waves, and classical information theory.

Lessons (6)

05

04. Quantum Mechanics I — Postulates & Wave Mechanics

The foundation of quantum theory: Stern-Gerlach experiment, wave-particle duality, the wavefunction, Schrödinger equation, potential wells, the quantum harmonic oscillator, the postulates of quantum mechanics, measurement, expectation values, and commutation relations.

Lessons (10)

06

05. Quantum Mechanics II — Operators, Spin & Angular Momentum

Linear and Hermitian operators, spin-½ systems, Pauli matrices, orbital angular momentum, addition of angular momentum, Clebsch-Gordan coefficients, and the hydrogen atom.

Lessons (8)

07

06. Quantum Mechanics III — Approximation Methods & Scattering

Time-independent and time-dependent perturbation theory, variational method, WKB approximation, scattering theory, and the physics of identical particles.

Lessons (6)

08

07. Qubits & Quantum Gates

The qubit, Bloch sphere representation, single-qubit gates (X, Y, Z, H, S, T), multi-qubit states, controlled gates (CNOT, Toffoli, SWAP), universal gate sets, gate decomposition, and the Solovay-Kitaev theorem.

Lessons (8)

09

08. Quantum Circuits & Protocols

The circuit model of computation, quantum teleportation, superdense coding, Deutsch's algorithm circuit, circuit optimization, reversible computation, measurement-based quantum computing, and cluster states.

Lessons (8)

10

09. Quantum Algorithms I — Core Algorithms

Deutsch-Jozsa, Bernstein-Vazirani, Simon's algorithm, the Quantum Fourier Transform, Quantum Phase Estimation, Grover's search, amplitude amplification, Shor's factoring algorithm, order finding, and the hidden subgroup problem.

Lessons (10)

11

10. Quantum Algorithms II — Advanced & Variational Algorithms

Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), HHL algorithm for linear systems, quantum random walks, Trotterization and Hamiltonian simulation, quantum optimization, and tensor networks.

Lessons (8)

12

11. Quantum Information Theory

Von Neumann entropy, quantum channels and Kraus operators, the Holevo bound, accessible information, quantum channel capacity, the Lloyd-Shor-Devetak theorem, the no-cloning theorem, and quantum data compression.

Lessons (8)

13

12. Quantum Error Correction I — Codes & Stabilizers

Classical error correction review, the 3-qubit bit-flip code, the Shor 9-qubit code, the Steane [[7,1,3]] code, the stabilizer formalism, the Gottesman-Knill theorem, CSS codes, and logical gate operations on encoded states.

Lessons (8)

14

13. Quantum Error Correction II — Fault-Tolerance & Surface Codes

Surface codes, toric codes, color codes, error thresholds, fault-tolerant gate design, magic state distillation, the threshold theorem, and lattice surgery for logical operations.

Lessons (8)

15

14. Quantum Complexity Theory

Complexity classes BQP and QMA, quantum query complexity, oracle separations, relation between classical and quantum complexity, quantum interactive proofs, non-locality, and Bell inequalities.

Lessons (6)

16

15. Quantum Cryptography & Communication

BB84 and E91 quantum key distribution protocols, security proofs for QKD, device-independent QKD, quantum digital signatures, quantum secret sharing, position-based quantum cryptography, and post-quantum cryptography.

Lessons (8)

17

16. Quantum Machine Learning

Quantum neural networks, variational quantum machine learning, quantum kernel methods, quantum embeddings, quantum generative models, quantum reinforcement learning, barren plateaus, and near-term QML applications.

Lessons (8)

18

17. Superconducting Qubits & Circuit QED

LC oscillators, Josephson junctions, transmon qubits, charge/flux/phase qubits, circuit quantum electrodynamics (cQED), dispersive readout, gate implementation, and coherence/decoherence mechanisms in superconducting qubits.

Lessons (8)

19

18. Trapped Ions & Photonic Qubits

Ion trap fundamentals, laser cooling, hyperfine qubits, the Mølmer-Sørensen gate, photonic qubits using polarization and time-bin encoding, linear optics quantum computing, and photonic cluster states.

Lessons (6)

20

19. Topological Quantum Computing

Anyons and braiding statistics, Fibonacci anyons, the Kitaev toric code, Majorana fermions as quasiparticles, topological qubits, Microsoft's topological approach, and measurement-only topological quantum computing.

Lessons (6)

21

20. Quantum Hardware Engineering & Noise

Noise sources and characterization, randomized benchmarking, quantum volume as a benchmark, error mitigation techniques (zero-noise extrapolation, Pauli twirling), cryogenics and control electronics, qubit fabrication, and scalability challenges.

Lessons (6)

22

21. Quantum Simulation & Quantum Chemistry

Molecular Hamiltonians for quantum chemistry, the Hartree-Fock method, Jordan-Wigner and Bravyi-Kitaev transformations for fermionic systems, VQE for chemistry, phase estimation for chemical accuracy, NISQ-era quantum chemistry, materials science applications, and quantum chemistry software.

Lessons (8)

23

22. Quantum Networks & The Quantum Internet

Quantum repeaters and entanglement distillation, quantum memory, quantum switch architectures, quantum network protocols, quantum internet architecture, and the vision of a global quantum network.

Lessons (8)

24

23. Quantum Sensing & Metrology

Quantum metrology basics, the standard quantum limit vs the Heisenberg limit, squeezed states for precision enhancement, NV centers in diamond, atomic clocks, and practical quantum sensing applications.

Lessons (7)

25

24. Research Frontiers & Open Problems

The quantum fault-tolerance roadmap, demonstrations of quantum advantage, the frontier of quantum machine learning, key open problems in quantum error correction and algorithms, and where the field is heading.

Lessons (4)