Quantum Mathematics develops the mathematical structures behind quantum theory and quantum computation, beginning with complex numbers, vectors, matrices, operators and probability and continuing into information, algorithms, many-body systems, topology and open-system dynamics.
The guide sequence is designed as a connected learning path rather than a list of isolated advanced topics. Readers can enter at the earliest secure prerequisite, move through the relevant structures, and return to the wider Mathematics system whenever a dependency needs reinforcement.
Guides 1–10
- Quantum Mathematics Learning Guide 1: Complex Numbers, State Vectors and Probability Amplitudes
- Quantum Mathematics Learning Guide 2: Matrices, Operators, Eigenvalues and Measurement
- Quantum Mathematics Learning Guide 3: Tensor Products, Qubits and Entanglement
- Quantum Mathematics Learning Guide 4: Unitary Evolution, Schrödinger’s Equation and Quantum Dynamics
- Quantum Mathematics Learning Guide 5: Density Matrices, Mixed States, Trace and Partial Trace
- Quantum Mathematics Learning Guide 6: Quantum Channels, Kraus Operators, Noise and Decoherence
- Quantum Mathematics Learning Guide 7: Generalised Measurements, POVMs, State Discrimination and Fidelity
- Quantum Mathematics Learning Guide 8: Quantum Entropy, Purity, Mutual Information and Correlations
- Quantum Mathematics Learning Guide 9: Quantum Fourier Transform, Roots of Unity and Interference
- Quantum Mathematics Learning Guide 10: Quantum Phase Estimation, Eigenphases and Controlled Powers
Guides 11–20
- Quantum Mathematics Learning Guide 11: Amplitude Amplification, Grover Rotations and Search Geometry
- Quantum Mathematics Learning Guide 12: Stabilizer Mathematics, Pauli Groups, Syndromes and Quantum Error Correction
- Quantum Mathematics Learning Guide 13: Hamiltonian Simulation, Trotter–Suzuki Product Formulas and Error Bounds
- Quantum Mathematics Learning Guide 14: Variational Quantum Eigensolvers, Rayleigh Quotients and Optimisation
- Quantum Mathematics Learning Guide 15: Quantum Metrology, Fisher Information and Precision Limits
- Quantum Mathematics Learning Guide 16: Tensor Networks, Matrix Product States and Entanglement Compression
- Quantum Mathematics Learning Guide 17: Quantum Walks, Graph Spectra and Search
- Quantum Mathematics Learning Guide 18: Block Encodings, Singular Value Transformation and Polynomial Approximation
- Quantum Mathematics Learning Guide 19: Quantum Linear Systems, HHL, Condition Numbers and Solution States
- Quantum Mathematics Learning Guide 20: Adiabatic Quantum Evolution, Spectral Gaps and Optimisation
Guides 21–30
- Quantum Mathematics Learning Guide 21: Quantum State Tomography, Informational Completeness and Physical Reconstruction
- Quantum Mathematics Learning Guide 22: Quantum Process Tomography, Choi Matrices and Channel Verification
- Quantum Mathematics Learning Guide 23: Classical Shadows, Randomised Measurements and Observable Prediction
- Quantum Mathematics Learning Guide 24: Randomised Benchmarking, Gate Fidelity and Error Budgets
- Quantum Mathematics Learning Guide 25: Fault-Tolerant Quantum Computation, Logical Qubits, Thresholds and Transversal Gates
- Quantum Mathematics Learning Guide 26: Surface Codes, Homology, Anyons, Syndromes and Topological Error Correction
- Quantum Mathematics Learning Guide 27: Magic-State Distillation, Clifford+T, T-Count and Resource States
- Quantum Mathematics Learning Guide 28: Quantum Complexity Theory, BQP, QMA, Query Complexity and Lower Bounds
- Quantum Mathematics Learning Guide 29: Bell Inequalities, CHSH, Tsirelson Bounds and No-Signalling
- Quantum Mathematics Learning Guide 30: Quantum Teleportation, Superdense Coding and Entanglement Swapping
Guides 31–40
- Quantum Mathematics Learning Guide 31: Entanglement Transformations, LOCC, Majorisation and Distillation
- Quantum Mathematics Learning Guide 32: Quantum Shannon Theory, Holevo Bounds, Channel Capacities and Coding Theorems
- Quantum Mathematics Learning Guide 33: Quantum Key Distribution, BB84, Entropic Uncertainty and Security Proofs
- Quantum Mathematics Learning Guide 34: Quantum Authentication, Private Quantum Channels and the Quantum One-Time Pad
- Quantum Mathematics Learning Guide 35: Quantum Repeaters, Network Entanglement, Swapping and End-to-End Rates
- Quantum Mathematics Learning Guide 36: Device-Independent Randomness, Self-Testing and Bell-Certified Security
- Quantum Mathematics Learning Guide 37: Bosonic Modes, Ladder Operators, Fock States and Quadratures
- Quantum Mathematics Learning Guide 38: Gaussian Quantum States, Covariance Matrices, Symplectic Transformations and Squeezing
- Quantum Mathematics Learning Guide 39: Quantum Optics, Coherent States, Beam Splitters, Interferometry and Photodetection
- Quantum Mathematics Learning Guide 40: Continuous-Variable Quantum Information, Gaussian Channels, Homodyne Detection and Teleportation
Guides 41–50
- Quantum Mathematics Learning Guide 41: GKP Oscillator Codes, Lattice States, Modular Quadratures and Displacement Errors
- Quantum Mathematics Learning Guide 42: Cat Codes, Bosonic Quantum Error Correction, Photon Loss and Parity
- Quantum Mathematics Learning Guide 43: Continuous-Variable Cluster States, Graph Nullifiers and Measurement-Based Quantum Computation
- Quantum Mathematics Learning Guide 44: Boson Sampling, Matrix Permanents, Linear Optics and Photonic Quantum Advantage
- Quantum Mathematics Learning Guide 45: Quantum Many-Body Hamiltonians, Ground States, Correlation Functions and Phase Transitions
- Quantum Mathematics Learning Guide 46: Quantum Spin Chains, Jordan–Wigner Transformation, Free Fermions and Criticality
- Quantum Mathematics Learning Guide 47: Quantum Chaos, Random Matrices, Level Statistics and Scrambling
- Quantum Mathematics Learning Guide 48: Quantum Thermodynamics, Gibbs States, Free Energy, Work and Resource Theories
- Quantum Mathematics Learning Guide 49: Berry Phases, Berry Curvature, Chern Numbers and Quantum Geometry
- Quantum Mathematics Learning Guide 50: Topological Bands, Quantum Hall Mathematics, Edge States and Bulk–Boundary Correspondence
Guides 51–60
- Quantum Mathematics Learning Guide 51: Quantum Field Theory, Second Quantisation, Fock Space, Wick’s Theorem and Propagators
- Quantum Mathematics Learning Guide 52: Lindblad Master Equations, Liouvillian Spectra, Steady States and Dissipative Quantum Dynamics
- Quantum Mathematics Learning Guide 53: Quantum Optimal Control, Lie-Algebraic Controllability, GRAPE and Pulse Engineering
- Quantum Mathematics Learning Guide 54: Continuous Quantum Measurement, Stochastic Master Equations, Quantum Filtering and Feedback
- Quantum Mathematics Learning Guide 55: Quantum Error Mitigation, Zero-Noise Extrapolation, Probabilistic Error Cancellation and Symmetry Verification
- Quantum Mathematics Learning Guide 56: Quantum Contextuality, Kochen–Specker Theorem, Compatibility Graphs and Contextual Fractions
- Quantum Mathematics Learning Guide 57: Quantum Amplitude Estimation, Approximate Counting, Monte Carlo and Quadratic Sampling Speedups
- Quantum Mathematics Learning Guide 58: Quantum Chemistry Mathematics, Electronic Structure, Fermionic Hamiltonians and Qubit Mappings
- Quantum Mathematics Learning Guide 59: Measurement-Based Quantum Computation, Qubit Graph States, Cluster States and Feed-Forward
- Quantum Mathematics Learning Guide 60: Quantum Causal Models, Process Matrices, Causal Inequalities and Indefinite Causal Order
Guides 61–70
- Quantum Mathematics Learning Guide 61: Quantum Approximate Optimisation Algorithm, MaxCut, Cost Hamiltonians and Alternating Operators
- Quantum Mathematics Learning Guide 62: Quantum Machine Learning, Feature Maps, Quantum Kernels and Variational Classifiers
- Quantum Mathematics Learning Guide 63: Quantum Differential Equations, Linear ODEs, PDEs, Spectral Methods and Solution States
- Quantum Mathematics Learning Guide 64: Quantum Simulation of Lattice Gauge Theories, Gauge Constraints, Wilson Loops and Kogut–Susskind Hamiltonians
- Quantum Mathematics Learning Guide 65: Shor’s Algorithm, Order Finding, Period Finding, Modular Exponentiation and Integer Factoring
- Quantum Mathematics Learning Guide 66: Hidden Subgroup Problems, Simon’s Algorithm, Fourier Sampling and Abelian Quantum Algorithms
- Quantum Mathematics Learning Guide 67: Quantum Gibbs-State Preparation, Thermal Sampling, Partition Functions and Quantum Metropolis Methods
- Quantum Mathematics Learning Guide 68: Quantum Semidefinite Programming, Matrix Multiplicative Weights, Convex Optimisation and Quantum SDP Solvers
- Quantum Mathematics Learning Guide 69: Quantum State Preparation, Amplitude Encoding, QROM, Data Loading and State-Synthesis Algorithms
- Quantum Mathematics Learning Guide 70: Quantum Hamiltonian Learning, System Identification, Bayesian Estimation and Spectroscopy
Guides 71–80
- Quantum Mathematics Learning Guide 71: Quantum Graph Algorithms, Connectivity, Triangle Finding, Shortest Paths and Quantum-Walk Search
- Quantum Mathematics Learning Guide 72: Quantum Reference Frames, Superselection Rules, Asymmetry and Relational Quantum States
- Quantum Mathematics Learning Guide 73: Quantum Floquet Systems, Periodic Driving, Quasienergies, Magnus Expansion and Floquet Engineering
- Quantum Mathematics Learning Guide 74: Non-Hermitian Quantum Mechanics, PT Symmetry, Exceptional Points and Biorthogonal Spectra
- Quantum Mathematics Learning Guide 75: Many-Body Localization, Anderson Localization, l-Bits, Entanglement Growth and Thermalisation Breakdown
- Quantum Mathematics Learning Guide 76: Non-Markovian Quantum Dynamics, Memory Kernels, Nakajima–Zwanzig Equations and Information Backflow
- Quantum Mathematics Learning Guide 77: Quantum Zeno Effect, Anti-Zeno Effect, Survival Probabilities and Zeno Subspaces
- Quantum Mathematics Learning Guide 78: Quantum Speed Limits, Mandelstam–Tamm, Margolus–Levitin, Bures Geometry and Control Times
- Quantum Mathematics Learning Guide 79: Quantum Quasiprobabilities, Wigner Functions, Negativity and Discrete Phase Space
- Quantum Mathematics Learning Guide 80: Quantum Trajectories, Monte Carlo Wave Functions, Quantum Jumps and Diffusive Unravellings
Guides 81–90
- Quantum Mathematics Learning Guide 81: Quantum Darwinism, Pointer States, Environment as Witness, Redundancy and Decoherence
- Quantum Mathematics Learning Guide 82: Quantum Discord, Classical–Quantum States, Conditional Entropy and Measurement Disturbance
- Quantum Mathematics Learning Guide 83: Weak Measurements, Weak Values, Postselection and Pointer Shifts
- Quantum Mathematics Learning Guide 84: Leggett–Garg Inequalities, Macrorealism and Temporal Quantum Correlations
Live series search: show the latest related pages. Newly published pages can appear here before the static directory is refreshed.
Return to the relevant BTT owner or the complete Mathematics directory.
Mathematics system route: Mathematics Hub · Knowledge Warehouse · Real-World Mathematics · World Mathematics Atlas.
Mathematics progression: Knowledge Warehouse → University Mathematics → Quantum Mathematics → World Mathematics Atlas.