Courses
Structured courses in quantum computing, mathematical physics, field theory, and emerging research areas.
15 courses in the active curriculum
Looking for a particular theorem, code, algorithm or mathematical technique?
Browse all topicsMethods, geometry, topology, and symmetry language.
A complete mathematical laboratory for quantum research. Twelve sequential units develop proof literacy, complex linear algebra, spectral theory, Hilbert spaces, analytic functions, contour methods, Fourier analysis, Green operators, stochastic dynamics, distributions, and unbounded operators. Each unit includes explicit hypotheses, derivations, checked worked examples, independent exercises, computational investigations, and mastery questions. Expanded with original in-page technical chapters, mathematical proofs, independently checked calculation baselines and directly embedded credited original instructor videos where relevant.
A physics-first route through manifolds, Lie groups, representations, topology, fiber bundles, gauge connections, and Berry phase. Expanded with original in-page technical chapters, mathematical proofs, independently checked calculation baselines and directly embedded credited original instructor videos where relevant.
Core mechanics and formal reasoning for quantum systems.
A rigorous beginner-to-advanced native quantum mechanics textbook: experiments, complex amplitudes, Born probabilities, wavefunctions, operators, dynamics, measurement, bound states, spin, identical particles, approximation and decoherence. Original derivations and worked problems, with embedded MIT OpenCourseWare lectures and credited scientific diagrams.
Quantum information, algorithms, error correction, fault tolerance, and physical noise-control engineering.
Qubits, entanglement, density matrices, channels, entropy, nonlocality, teleportation, cryptography, and quantum networks. Expanded with original in-page technical chapters, mathematical proofs, independently checked calculation baselines and directly embedded credited original instructor videos where relevant.
Twelve mathematically rigorous native algorithm units covering exact circuits, reversible oracles, phase kickback, quantum Fourier transform, phase estimation, Shor, Grover, Hamiltonian simulation, variational methods, QAOA, amplitude estimation and BQP complexity. Equations, worked calculations, verified circuit figures and embedded instructor lectures are placed within QuantumSpark lessons rather than replacing the lesson with outbound links.
An independent eighteen-unit textbook on exact QEC conditions, quantum stabilizers, CSS and topological codes, noisy syndrome extraction, likelihood-based decoders, thresholds, LDPC, bosonic protection, leakage, logical gates, cellular-automaton recovery and research reproduction. Substantial original math, worked calculations, embedded original lectures and primary-source documentation are taught directly on QuantumSpark.
An independent twelve-unit research-level course on open quantum dynamics, coherent errors and leakage, microscopic system-bath models, non-Markovian processes, Ramsey and noise spectroscopy, dynamical decoupling, shaped and optimized pulses, randomized benchmarking, readout calibration, feedback and engineered reservoirs. Quantum error correction has moved into its own full specialist course.
Condensed matter, quantum materials, phases, and platforms.
Second quantization, lattice models, symmetry breaking, phase transitions, entanglement, tensor networks, topological order, and numerical methods. Expanded with original in-page technical chapters, mathematical proofs, independently checked calculation baselines and directly embedded credited original instructor videos where relevant.
Crystal and reciprocal lattices, Bloch theorem, band structure, tight binding, quasiparticles, correlated materials, topological insulators, superconductivity, 2D systems, defects, and materials for qubits. Expanded with original in-page technical chapters, mathematical proofs, independently checked calculation baselines and directly embedded credited original instructor videos where relevant.
QFT, QED, QCD, spinors, and relativistic structures.
A twelve-unit advanced QFT textbook spanning operator-valued distributions, microcausality, quantization, functional integrals, LSZ scattering, gauge fixing, renormalization and effective field theory. University videos are followed by original native explanatory chapters, six-step intermediate derivations, worked calculations, verified scientific illustrations where available and primary-source reproduction guidance.
Twelve research-grade QED units covering Dirac fields, local gauge symmetry, physical photons, amplitudes, Compton scattering, Ward identities, vacuum polarization, coupling running, anomalous moments and cavity QED. Original native mathematical derivations, explicit worked calculations, lecture resources and selected licensed figures accompany each topic.
A rigorous twelve-unit graduate QCD course developing SU(3) representation theory, gluon vertices, asymptotic freedom, confinement, Wilson loops, parton evolution, deep inelastic scattering, lattice methods, chiral physics, jets and effective theories. Detailed native calculations and directly credited human-authored source figures accompany original research-reproduction protocols.
A research-depth graduate course in Poincaré representations, Weyl and Dirac fields, Majorana systems, Clifford algebras, covariant scattering, spinor-helicity, instantons, anomalies, topological response and geometric fermions. Twelve independently authored units now combine detailed textbook exposition, two full intermediate derivations, extended worked calculations, reproducible numerical baselines, authentic credited scientific figures where available, 12 guided primary-paper reproductions, and instructor lectures from MIT and Cambridge. Students must distinguish reproducing established results from proposing and validating genuinely original research.
Paper reading, reproducibility, scientific writing, and capstone design.
Twelve deeply authored native research-methods units on claim-evidence maps, formal reading, independent proofs, computational reproducibility, discretization and extrapolation, inverse problems, uncertainty, research graphics, ethics, preprints and falsifiable proposals. Fully rendered mathematical developments and worked checks appear on QuantumSpark itself, with original instructor videos used only where relevant.
Attributed open courseware integrated into QuantumSpark with license and source metadata.
The complete attributed TU Delft TOPOCMx open course, imported natively into QuantumSpark: from toy-model topology and the Kitaev chain through Majoranas, quantum Hall effects, Chern insulators, symmetry classification, disorder, Floquet phases and topological order. Original lectures, derivations, videos, questions, Python notebook cells and source figures retained. Expanded with original in-page technical chapters, mathematical proofs, independently checked calculation baselines and directly embedded credited original instructor videos where relevant.