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Quantum ComputingAN INTERACTIVE OPEN TEXTBOOK
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Explore the book

The book has six complementary volumes, including an advanced algorithm atlas, plus a collection of protocol and data-tool guides. 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.

177 chapters · 112 lessons available now

  1. F01Classical Computing versus Quantum ComputingCore
  2. F02Introduction to Quantum InformationCore
  3. F03Essential Mathematics: Complex NumbersCore
  4. F04Vectors, Matrices and Linear AlgebraCore
  5. F05Dirac Notation: Kets and BrasCore
  6. F06Probability, Amplitudes and NormalisationCore
  7. F07Understanding QubitsCore
  8. F08SuperpositionCore
  9. F09Quantum MeasurementCore
  10. F10Quantum Phase and InterferenceCore
  11. F11The Bloch SphereCore
  12. F12Multiple Qubits and Tensor ProductsCore
  13. F13Entanglement and Bell StatesCore
  14. F14Quantum Reversibility and the No-Cloning PrincipleCore
  15. F15Introduction to Quantum GatesCore
  16. F16Pauli Gates and the Hadamard GateCore
  17. F17Phase and Rotation GatesCore
  18. F18Controlled Gates and CNOTCore
  19. F19Constructing Quantum CircuitsCore
  20. F20Quantum Oracles and Phase KickbackCore
  21. F21Measuring and Simulating Quantum CircuitsCore
  22. F22Quantum Noise and Hardware LimitationsCore
  23. F23Classical versus Quantum Algorithmic ComplexityCore
  24. F24Quantum Queries and OraclesCore
  25. F25How Quantum Algorithms Use InterferenceCore
  26. F26First Complete Quantum AlgorithmCore
  27. P01Programming environments: Python, notebooks, SDK choicesCore
  28. P02Quantum software architecture and clean project setupPlanned
  29. P03Toolchain reproducibility: packages, versions, environmentsPlanned
  30. P04Quantum circuits as code: qubits, registers and gatesCore
  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: inputs, outputs and assumptionsPlanned
  36. P10Classical–quantum control and workflow orchestrationPlanned
  37. P11Statevector and unitary verification techniquesUndergraduate
  38. P12Probabilistic assertions and confidence intervalsUndergraduate
  39. P13Property-based and metamorphic quantum testsUndergraduate
  40. P14Debugging quantum logic and circuit defectsUndergraduate
  41. P15Test-driven circuit development and mutation testingUndergraduate
  42. P16Backend abstraction and simulation choicesPlanned
  43. P17Compilation and transpilation fundamentalsUndergraduate
  44. P18Native gates, decomposition and qubit connectivityPlanned
  45. P19Circuit depth, width, swap overhead and resource reportsPlanned
  46. P20Noise models, backend constraints and execution budgetsUndergraduate
  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?Core
  52. A02Deutsch’s AlgorithmCore
  53. A03Deutsch–Jozsa AlgorithmCore
  54. A04Bernstein–Vazirani AlgorithmCore
  55. A05Simon’s AlgorithmUndergraduate
  56. A06Grover’s Search AlgorithmCore
  57. A07Amplitude AmplificationUndergraduate
  58. A08Quantum CountingUndergraduate
  59. A09Quantum Amplitude EstimationUndergraduate
  60. A10Quantum Walk AlgorithmsUndergraduate
  61. A11Quantum Fourier TransformUndergraduate
  62. A12Quantum Phase EstimationUndergraduate
  63. A13Order FindingUndergraduate
  64. A14Shor’s Factoring AlgorithmUndergraduate
  65. A15Hidden Subgroup ProblemsUndergraduate
  66. A16Introduction to Optimisation ProblemsCore
  67. A17QUBO and Ising ModelsUndergraduate
  68. A18Quantum Approximate Optimisation AlgorithmUndergraduate
  69. A19Variational Quantum EigensolverUndergraduate
  70. A20Quantum AnnealingUndergraduate
  71. A21Quantum Optimisation and Classical BaselinesCore
  72. A22Hamiltonian SimulationUndergraduate
  73. A23Trotter–Suzuki MethodsUndergraduate
  74. A24Linear Combination of UnitariesResearch
  75. A25QubitizationResearch
  76. A26HHL Quantum Linear Systems AlgorithmUndergraduate
  77. A27Block EncodingResearch
  78. A28Quantum Singular Value TransformationResearch
  79. A29Quantum Machine LearningUndergraduate
  80. A30Quantum KernelsUndergraduate
  81. A31Variational Quantum ClassifiersUndergraduate
  82. A32Quantum Sampling AlgorithmsUndergraduate
  83. A33Applications in Cryptography and SecurityCore
  84. A34Quantum Algorithms in Real-World OptimisationCore
  85. A35Quantum Advantage and ComplexityUndergraduate
  86. A36Noise and Resource EstimationUndergraduate
  87. A37Error Mitigation and Error CorrectionUndergraduate
  88. A38Fault-Tolerant Algorithm ConsiderationsResearch
  89. A39Quantum versus Classical BenchmarkingCore
  90. A40Open Research ChallengesResearch
  91. AA01Adiabatic quantum computation and algorithmic equivalencesResearch
  92. AA02Quantum minimum finding (Dürr–Høyer)Undergraduate
  93. AA03Amplitude estimation variants and modern iterative approachesUndergraduate
  94. AA04Quantum signal processing and polynomial transformationsResearch
  95. AA05Quantum eigenvalue transformation and spectral filteringResearch
  96. AA06Quantum singular value transformation applicationsResearch
  97. AA07Quantum linear-algebra improvements and input/output assumptionsResearch
  98. AA08Quantum principal components and spectral methodsResearch
  99. AA09Quantum recommendation and nearest-neighbour ideasResearch
  100. AA10Quantum gradient and derivative estimationResearch
  101. AA11Quantum approximate counting and mean estimationUndergraduate
  102. AA12Quantum Monte Carlo integration and risk estimationUndergraduate
  103. AA13Quantum Gibbs-state preparation and thermal samplingResearch
  104. AA14Quantum Metropolis methods and thermalisationResearch
  105. AA15Quantum walk search on graphs and spatial searchUndergraduate
  106. AA16Element distinctness and collision problemsUndergraduate
  107. AA17Quantum backtracking and tree-search methodsResearch
  108. AA18Formula evaluation and span-program viewpointsResearch
  109. AA19Quantum dynamic programming and graph problemsResearch
  110. AA20Quantum learning theory and sample complexityResearch
  111. AA21Quantum neural network models and barren plateausResearch
  112. AA22Quantum generative modelling and Born machinesUndergraduate
  113. AA23Quantum chemistry and electronic structure workflowsUndergraduate
  114. AA24Quantum PDE/ODE ideas and differential-equation algorithmsResearch
  115. AA25Quantum finance and stochastic modellingUndergraduate
  116. AA26Quantum methods for scientific optimisation and energy systemsUndergraduate
  117. AA27Query adversary and lower-bound techniquesResearch
  118. AA28Hamiltonian simulation algorithms beyond product formulasResearch
  119. AA29Precision, condition-number and fault-tolerance costsResearch
  120. AA30Dequantisation, quantum-inspired classical algorithms and honest baselinesUndergraduate
  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
  171. T01Quantum teleportationCore
  172. T02Superdense codingCore
  173. T03The Hadamard testUndergraduate
  174. T04The swap testCore
  175. T05Quantum random-access memoryUndergraduate
  176. T06Classical shadowsUndergraduate
  177. T07Regev’s factoring algorithmResearch