Documentation

Technical reference

Formal specifications, proofs, and reference implementations for the Triqee quantum ternary framework.

Status
CompleteIn progressPlanned
§1

Qutrit Formalism

Mathematical foundations of three-level quantum systems, Hilbert space structure, and the Heisenberg-Weyl group over ℤ₃.

State space and basis
Complete
Density matrices and mixed states
Complete
Entanglement and Schmidt rank
Complete
§2

Gate Set Reference

Complete specification of the universal ternary gate set: single-qutrit gates, two-qutrit entangling gates, and decomposition theorems.

Shift and clock operators
Complete
Ternary Fourier transform
Complete
Two-qutrit CSUM and CZ₃
Complete
Universality proof
Complete
§3

Error Correction Codes

Ternary stabilizer formalism, the [[5,1,3]]₃ code, fault-tolerant gate constructions, and threshold theorems for qutrit hardware.

Stabilizer formalism over ℤ₃
Complete
[[5,1,3]]₃ code construction
Complete
Fault-tolerant gates
In progress
Threshold theorem for qutrits
In progress
§4

Compiler Specification

Mixed-radix compilation pipeline: circuit ingestion, ternary rewriting rules, gate synthesis, and coherence-aware scheduling.

Circuit IR and rewriting rules
Complete
Gate synthesis algorithms
In progress
Coherence-aware scheduler
Planned
Backend interface spec
Planned
§5

Algorithm Library

Reference implementations of ternary-native algorithms: arithmetic, phase estimation, variational eigensolver, and search.

Ternary arithmetic circuits
Complete
Qutrit phase estimation
Complete
Ternary VQE ansatz
In progress
Ternary Grover search
Planned

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