Fault-Tolerant Quantum Computing

Physics: Fault-tolerant QC requires: (1) Clifford gates implemented transversally (can propagate errors without spreading), (2) T gate via magic state distillation (non-Clifford → universal). Eastin-Knill theorem: no transversal universal gate set exists for any code. Bravyi-Kitaev (2005) 15→1 distillation: consume 15 noisy T-states, produce 1 clean T-state with p_out ≈ 35p³. Clifford group generated by H, CNOT, S (phase gate). Solovay-Kitaev: efficient compilation to {H, T, CNOT}. Google 2023: first fault-tolerant logical qubit demonstrating below break-even (logical error < physical error). Magic states are the fuel for quantum computation.