Quantum Logic Gates: Principles, Physical Implementations and Recent Progress

This note explains how quantum logic gates work, which gate sets are universal, and why non-Clifford (T) gates dominate the cost of fault-tolerant computation. Comparing public results across six platforms with evidence up to 7 October 2026: in the peer-reviewed literature, single-qubit error on a single ion reaches 1.5×10⁻⁷ and best single-pair two-qubit errors lie in the 10⁻³–10⁻⁴ range, while about 8.4×10⁻⁵ on a two-ion prototype remains a preprint; system-wide averages can be about an order of magnitude worse than best single-pair values (for example, 7.9×10⁻⁴ on the 98-qubit Helios, and 0.33% CZ error with all gates running simultaneously on Willow's error-correction chip according to Google's specification). Because reporting conventions differ, cross-platform comparisons are indicative only. The note then reviews the move from physical to logical gates — lattice surgery, logical non-Clifford gates and magic-state preparation — most of which remain at small code distance, some with postselection, and many still in preprints. It is a structured evidence synthesis and technical guide based on public literature and reports no new experiments or measurements.