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Quantum ComputingAN INTERACTIVE OPEN TEXTBOOK
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The book has six complementary volumes, including an advanced algorithm atlas. Start anywhere: every route is open, and prerequisite links offer guidance rather than access restrictions.

This is a growing editorial release. Available lessons have reading content, experiments where relevant, and chapter PDFs. Planned entries show the topics being developed next. The author’s complete introduction is also available.

170 chapters · 96 lessons available now

  1. F01Classical Computing versus Quantum ComputingRead lesson
  2. F02Introduction to Quantum InformationRead lesson
  3. F03Essential Mathematics: Complex NumbersRead lesson
  4. F04Vectors, Matrices and Linear AlgebraRead lesson
  5. F05Dirac Notation: Kets and BrasRead lesson
  6. F06Probability, Amplitudes and NormalisationRead lesson
  7. F07Understanding QubitsRead lesson
  8. F08SuperpositionRead lesson
  9. F09Quantum MeasurementRead lesson
  10. F10Quantum Phase and InterferenceRead lesson
  11. F11The Bloch SphereRead lesson
  12. F12Multiple Qubits and Tensor ProductsRead lesson
  13. F13Entanglement and Bell StatesRead lesson
  14. F14Quantum Reversibility and the No-Cloning PrincipleRead lesson
  15. F15Introduction to Quantum GatesRead lesson
  16. F16Pauli Gates and the Hadamard GateRead lesson
  17. F17Phase and Rotation GatesRead lesson
  18. F18Controlled Gates and CNOTRead lesson
  19. F19Constructing Quantum CircuitsRead lesson
  20. F20Quantum Oracles and Phase KickbackRead lesson
  21. F21Measuring and Simulating Quantum CircuitsRead lesson
  22. F22Quantum Noise and Hardware LimitationsRead lesson
  23. F23Classical versus Quantum Algorithmic ComplexityRead lesson
  24. F24Quantum Queries and OraclesRead lesson
  25. F25How Quantum Algorithms Use InterferenceRead lesson
  26. F26First Complete Quantum AlgorithmRead lesson
  27. P01Programming environments: Python, notebooks, SDK choicesPlanned
  28. P02Quantum software architecture and clean project setupPlanned
  29. P03Toolchain reproducibility: packages, versions, environmentsPlanned
  30. P04Quantum circuits as code: qubits, registers and gatesPlanned
  31. P05Gate conventions, endianness and state extractionPlanned
  32. P06Parameterised circuits and reusable buildersPlanned
  33. P07Measurement pipelines and finite-shot result handlingPlanned
  34. P08Quantum functions, modules and APIsPlanned
  35. P09Supplied algorithms as executable contractsPlanned
  36. P10Classical–quantum control and workflow orchestrationPlanned
  37. P11Statevector and unitary verification techniquesPlanned
  38. P12Probabilistic assertions and confidence intervalsPlanned
  39. P13Property-based and metamorphic quantum testsPlanned
  40. P14Debugging quantum logic and circuit defectsPlanned
  41. P15Test-driven circuit development and mutation testingPlanned
  42. P16Backend abstraction and simulation choicesPlanned
  43. P17Compilation and transpilation fundamentalsPlanned
  44. P18Native gates, decomposition and qubit connectivityPlanned
  45. P19Circuit depth, width, swap overhead and resource reportsPlanned
  46. P20Noise models, backend constraints and execution budgetsPlanned
  47. P21Reproducible experiments, seeds and provenancePlanned
  48. P22Notebooks, packages, documentation and Git workflowsPlanned
  49. P23Responsible AI-assisted quantum software engineeringPlanned
  50. P24Capstone: reliable, portable quantum software componentPlanned
  51. A01What Makes a Quantum Algorithm Different?Read lesson
  52. A02Deutsch’s AlgorithmRead lesson
  53. A03Deutsch–Jozsa AlgorithmRead lesson
  54. A04Bernstein–Vazirani AlgorithmRead lesson
  55. A05Simon’s AlgorithmRead lesson
  56. A06Grover’s Search AlgorithmRead lesson
  57. A07Amplitude AmplificationRead lesson
  58. A08Quantum CountingRead lesson
  59. A09Quantum Amplitude EstimationRead lesson
  60. A10Quantum Walk AlgorithmsRead lesson
  61. A11Quantum Fourier TransformRead lesson
  62. A12Quantum Phase EstimationRead lesson
  63. A13Order FindingRead lesson
  64. A14Shor’s Factoring AlgorithmRead lesson
  65. A15Hidden Subgroup ProblemsRead lesson
  66. A16Introduction to Optimisation ProblemsRead lesson
  67. A17QUBO and Ising ModelsRead lesson
  68. A18Quantum Approximate Optimisation AlgorithmRead lesson
  69. A19Variational Quantum EigensolverRead lesson
  70. A20Quantum AnnealingRead lesson
  71. A21Quantum Optimisation and Classical BaselinesRead lesson
  72. A22Hamiltonian SimulationRead lesson
  73. A23Trotter–Suzuki MethodsRead lesson
  74. A24Linear Combination of UnitariesRead lesson
  75. A25QubitizationRead lesson
  76. A26HHL Quantum Linear Systems AlgorithmRead lesson
  77. A27Block EncodingRead lesson
  78. A28Quantum Singular Value TransformationRead lesson
  79. A29Quantum Machine LearningRead lesson
  80. A30Quantum KernelsRead lesson
  81. A31Variational Quantum ClassifiersRead lesson
  82. A32Quantum Sampling AlgorithmsRead lesson
  83. A33Applications in Cryptography and SecurityRead lesson
  84. A34Quantum Algorithms in Real-World OptimisationRead lesson
  85. A35Quantum Advantage and ComplexityRead lesson
  86. A36Noise and Resource EstimationRead lesson
  87. A37Error Mitigation and Error CorrectionRead lesson
  88. A38Fault-Tolerant Algorithm ConsiderationsRead lesson
  89. A39Quantum versus Classical BenchmarkingRead lesson
  90. A40Open Research ChallengesRead lesson
  91. AA01Adiabatic quantum computation and algorithmic equivalencesRead lesson
  92. AA02Quantum minimum finding (Dürr–Høyer)Read lesson
  93. AA03Amplitude estimation variants and modern iterative approachesRead lesson
  94. AA04Quantum signal processing and polynomial transformationsRead lesson
  95. AA05Quantum eigenvalue transformation and spectral filteringRead lesson
  96. AA06Quantum singular value transformation applicationsRead lesson
  97. AA07Quantum linear-algebra improvements and input/output assumptionsRead lesson
  98. AA08Quantum principal components and spectral methodsRead lesson
  99. AA09Quantum recommendation and nearest-neighbour ideasRead lesson
  100. AA10Quantum gradient and derivative estimationRead lesson
  101. AA11Quantum approximate counting and mean estimationRead lesson
  102. AA12Quantum Monte Carlo integration and risk estimationRead lesson
  103. AA13Quantum Gibbs-state preparation and thermal samplingRead lesson
  104. AA14Quantum Metropolis methods and thermalisationRead lesson
  105. AA15Quantum walk search on graphs and spatial searchRead lesson
  106. AA16Element distinctness and collision problemsRead lesson
  107. AA17Quantum backtracking and tree-search methodsRead lesson
  108. AA18Formula evaluation and span-program viewpointsRead lesson
  109. AA19Quantum dynamic programming and graph problemsRead lesson
  110. AA20Quantum learning theory and sample complexityRead lesson
  111. AA21Quantum neural network models and barren plateausRead lesson
  112. AA22Quantum generative modelling and Born machinesRead lesson
  113. AA23Quantum chemistry and electronic structure workflowsRead lesson
  114. AA24Quantum PDE/ODE ideas and differential-equation algorithmsRead lesson
  115. AA25Quantum finance and stochastic modellingRead lesson
  116. AA26Quantum methods for scientific optimisation and energy systemsRead lesson
  117. AA27Query adversary and lower-bound techniquesRead lesson
  118. AA28Hamiltonian simulation algorithms beyond product formulasRead lesson
  119. AA29Precision, condition-number and fault-tolerance costsRead lesson
  120. AA30Dequantisation, quantum-inspired classical algorithms and honest baselinesRead lesson
  121. S01Classical cryptography refresher: symmetric keys and hashesPlanned
  122. S02Public-key cryptography: RSA, ECC and finite groupsPlanned
  123. S03Key exchange, KEMs, certificates and digital signaturesPlanned
  124. S04Security notions, threat modelling and threat timelinesPlanned
  125. S05Quantum computing threat to RSA and ECCPlanned
  126. S06Shor’s algorithm as a cryptanalytic threatPlanned
  127. S07Grover search and symmetric-key security marginsPlanned
  128. S08Harvest-now-decrypt-later and information lifetimePlanned
  129. S09Introduction to quantum communicationPlanned
  130. S10Measurement bases, no-cloning and channel modelsPlanned
  131. S11QKD versus post-quantum cryptographyPlanned
  132. S12BB84: states, bases and siftingPlanned
  133. S13BB84: error rates, intercept–resend and noisePlanned
  134. S14Finite-key statistics, confidence and leakagePlanned
  135. S15Error reconciliation and privacy amplificationPlanned
  136. S16Authentication, side channels and QKD operational limitsPlanned
  137. S17E91, entanglement-based QKD and CHSH contextPlanned
  138. S18Decoy-state and measurement-device-independent QKDPlanned
  139. S19Security evaluation of QKD simulationsPlanned
  140. S20PQC design goals and underlying hard problemsPlanned
  141. S21ML-KEM and FIPS 203: learning and safe librariesPlanned
  142. S22ML-DSA and FIPS 204: signature verificationPlanned
  143. S23SLH-DSA and FIPS 205: hash-based signaturesPlanned
  144. S24PQC integration, hybrid key establishment and interoperabilityPlanned
  145. S25Cryptographic inventories, crypto-agility and migration planningPlanned
  146. S26Migration capstone: standards, risk and technical assurancePlanned
  147. X01Quantum channels, density matrices and mixed statesPlanned
  148. X02Noise representations: Kraus maps and CPTP channelsPlanned
  149. X03Quantum process tomography and state estimationPlanned
  150. X04Information measures and quantum entropyPlanned
  151. X05Bell inequalities, nonlocal games and contextualityPlanned
  152. X06Fault-tolerant thresholds and logical qubitsPlanned
  153. X07Stabilizer formalism and Clifford circuitsPlanned
  154. X08Quantum error correction: repetition and surface codesPlanned
  155. X09Syndrome extraction and decoding basicsPlanned
  156. X10Logical gates, transversal gates and magic statesPlanned
  157. X11Error mitigation: ZNE, PEC and measurement mitigationPlanned
  158. X12Randomised benchmarking and device characterisationPlanned
  159. X13Hamiltonian complexity and simulation limitsPlanned
  160. X14Resource estimation and space–time costPlanned
  161. X15Distributed quantum computing and quantum networksPlanned
  162. X16Quantum communications protocols beyond QKDPlanned
  163. X17Quantum sensing and metrologyPlanned
  164. X18Quantum machine learning research directionsPlanned
  165. X19AI workloads and quantum algorithm mappingsPlanned
  166. X20Quantum-inspired classical optimisationPlanned
  167. X21Applications: energy, logistics and schedulingPlanned
  168. X22Quantum software and research reproducibilityPlanned
  169. X23Research methodology: falsifiable advantage claimsPlanned
  170. X24Open challenges, literature reading and reproducible projectsPlanned