TriadicFrameworks — Repos Module Index

Directory: docs/theories/repos/ Role: Front door for the curated external-repository modules that ground TriadicFrameworks' quantum-lattice theory layer.

This directory catalogues three upstream open-source repositories, each captured as a structured module JSON. Together they form a full-stack quantum-lattice toolchain — from raw Hilbert-space basis construction, through phenomenological tight-binding simulation, to variational quantum algorithms on real or emulated quantum hardware.

Module Inventory#

Module Descriptions#

1 · wztzjhn_quantum_basis_module.json#

Upstream: wztzjhn/quantum_basis · Paradigm: Classical exact diagonalization (ED)

quantum_basis is a C++ library that constructs the many-body Hilbert-space basis for arbitrary condensed-matter lattice models. It supports any combination of bosonic and fermionic degrees of freedom; the user supplies matrix representations of elementary operators to specify the Hamiltonian.

Core capabilities:

• Basis construction with and without translational symmetry (generalised Lin Table)
• Lanczos and FEAST eigensolvers for low-energy spectra
• Kernel polynomial method (KPM) for spectral functions and DOS
• Sparse matrix algebra backed by Intel MKL / ARPACK-NG / Boost
• Doxygen API at https://wztzjhn.github.io/quantum_basis/
• Bundled example models: Heisenberg (spin-½, spin-1), t-J, Kondo Lattice, spinless fermions on square, honeycomb, and Kagome lattices

TriadicFrameworks role: Foundation layer. Provides rigorous, fully quantum-mechanical ground truth against which higher-level approximations (tight-binding mean-field, VQA) can be benchmarked.

2 · joselado_quantum-lattice_module.json#

Upstream: joselado/quantum-lattice · Paradigm: Classical tight-binding / mean-field

quantum-lattice is a Python (+ Fortran kernel) toolkit for designing and solving single-particle and mean-field Hamiltonians on arbitrary lattice geometries. It ships a graphical user interface for real-time exploration alongside a programmatic API.

Core capabilities:

• Spinless, spinful, and Nambu (Bogoliubov–de Gennes) orbital bases
• Full non-collinear magnetism, spin-orbit coupling, and unconventional superconductivity
• Band structures with state-resolved expectation values; momentum-resolved spectral functions
• Topological invariants: Chern numbers, Z₂, topological edge states
• Local density of states, Green's functions, recursive methods for semi-infinite systems
• Landau levels, quantum Hall edge states, twisted bilayer graphene superlattices
• Interactive PyQt GUI for parameter sweeping and real-time visualisation

TriadicFrameworks role: Simulation layer. Acts as the primary Hamiltonian factory — phenomenological models constructed here feed directly into both the ED solver (quantum_basis) and the VQA optimizer (LattiQ).

3 · Milos9304_LattiQ_module.json#

Upstream: Milos9304/LattiQ · Paradigm: Quantum — variational quantum algorithms

LattiQ is a C++ experimental framework (built atop FastVQA) for solving lattice optimisation problems on quantum hardware or simulators. Its primary target is the Shortest Vector Problem (SVP) — a cornerstone of post-quantum cryptography — encoded as an Ising spin Hamiltonian and solved via VQE or QAOA.

Core capabilities:

• Automatic encoding of SVP lattice matrices to Ising spin Hamiltonians
• VQE and QAOA as interchangeable solvers
• CVaR (Conditional Value-at-Risk) loss function for noise robustness
• Configurable rank and alpha hyperparameters per experiment
• CMake build system; results reported in "Variational quantum solutions to the Shortest Vector Problem"

TriadicFrameworks role: Quantum-computing layer. Bridges classical lattice theory to near-term quantum hardware; its Ising-mapped Hamiltonians share conceptual ancestry with the tight-binding and ED Hamiltonians in the layers below.

Cross-Module Lineage#

┌─────────────────────────────────────────────────────────────────┐
│               TriadicFrameworks Quantum-Lattice Stack           │
│                                                                 │
│  wztzjhn/quantum_basis                                          │
│  [ C++ ED library ]      ◄── benchmark / ground truth          │
│  Hilbert-space basis,                                           │
│  Lanczos, KPM, MKL                                              │
│          ▲                                                      │
│          │  Hamiltonian operator matrices                       │
│          │                                                      │
│  joselado/quantum-lattice                                       │
│  [ Python TB/MF engine ]                                        │
│  Topology, magnetism,    ──► Hamiltonian factory                │
│  superconductivity, GUI                                         │
│          │                                                      │
│          │  Ising-mapped Hamiltonian / coupling params          │
│          ▼                                                      │
│  Milos9304/LattiQ                                               │
│  [ C++ VQA framework ]   ──► quantum optimisation frontier      │
│  VQE, QAOA, SVP, CVaR        extends lattice theory to NISQ era │
└─────────────────────────────────────────────────────────────────┘

Data-flow summary:

Navigation#

docs/theories/repos/
├── README.md                              ← you are here
├── joselado_quantum-lattice_module.json   ← Module 2 (TB simulation layer)
├── Milos9304_LattiQ_module.json           ← Module 3 (VQA / quantum layer)
└── wztzjhn_quantum_basis_module.json      ← Module 1 (ED foundation layer)

Related TriadicFrameworks paths:

License Summary#

Note: The module JSON files in this directory are TriadicFrameworks metadata documents, not derivative works of the upstream source code. Upstream licenses govern direct use or linking of the upstream codebases themselves.

Upstream Provenance#

Generated by TriadicFrameworks · docs/theories/repos/README.md · 2026-07-13

Key design decisions baked in:

• Ordering by abstraction depth — quantum_basis (ED foundation) → quantum-lattice (TB/MF simulation) → LattiQ (VQA frontier) — so readers immediately grasp the dependency hierarchy rather than seeing three equal peers.
• Cross-module data-flow table makes it explicit what actually passes between modules, which was implicit in the original repos.
• License block with a TriadicFrameworks-specific note clarifies that the JSON module files are metadata, not GPL-encumbered code — an important legal distinction for downstream contributors.