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ψQuantum Computing 2026

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I · Foundations

01Information, probability, and computation 02Complex amplitudes and quantum states 03Measurement and changes of basis 04Gates, observables, and the Bloch sphere 05Registers, circuits, and entanglement 06Density matrices and subsystems 07Bell correlations, teleportation, and dense coding 08Noise channels, measurement data, and mitigation

II · Algorithms

09Oracle algorithms: Deutsch, Deutsch–Jozsa, and Bernstein–Vazirani 10Simon's algorithm and hidden XOR structure 11Grover search and amplitude amplification 12Fourier transforms and phase estimation 13Period finding and Shor's factoring algorithm 14Hamiltonian simulation and modern algorithmic tools 15Variational algorithms and their limits

III · Reliable systems

16Classical simulation and the cost of representation 17Stabilizers and quantum error correction 18Surface codes and decoding 19Fault-tolerant computation and modern codes 20Resource estimation: from circuits to machines

IV · Platforms and practice

21Physical qubits, control, and hardware benchmarks 22Quantum networks, BB84, and post-quantum cryptography 23Programming reproducible quantum experiments 24Reading the experimental frontier in 2026 25Integrated laboratories and a path to research

Appendices

AMathematical toolkit BGlossary and laboratory directory ↗Academic references

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Research cutoff · 5 September 2026One manuscript · Two editions · 26 laboratoriesAbout this work Files and reproducibility