Quasi Quantum Computing — Q²C v2

Author: grisun0 · ORCID: 0009-0002-7622-3916 DOI: 10.5281/zenodo.18795538 License: AGPL v3

A functional quasi-quantum computing simulator on classical hardware using physics models as a backend, now extended with Matrix Product State (MPS) tensor networks for scalable simulation.

What is Q²C?

Q²C simulates quantum systems on classical hardware through two complementary modes selectable at runtime:

| Mode | Backend | Precision | Max Qubits | When to use | |------|---------|-----------|-----------|-------------| | Direct (exact) | Full statevector | Machine ε (~1e-15) | ~14 | Need exact amplitudes | | MPS (scalable) | Tensor network | Tunable (chi) | 33+ | Need more qubits |

Both modes share the same gate library, algorithms, and physics backends. The user chooses via precision_mode in quantum_framework_config.toml or at the interactive menu prompt.

Architecture

quantum_framework_main.py        ← CLI entry point
quantum_framework_menu.py        ← Interactive menu (11 sections)
    │
    ├── quantum_framework_core.py     ← MPS tensor network engine
    │     ├── MPSState / MPSCore      ← O(n·χ²) memory representation
    │     ├── QuantumCircuit          ← Gate builder (H, X, Y, Z, CNOT, CZ, SWAP, Rx/Ry/Rz, ...)
    │     └── MPSQuantumComputer      ← Bell, GHZ, W-state, Grover, QFT
    │
    ├── quantum_framework_physics.py  ← Neural physics backends
    │     ├── HamiltonianBackboneNet  ← Spectral FFT Hamiltonian network
    │     ├── SchrodingerSpectralNet  ← Wavefunction evolution network
    │     └── DiracSpectralNet        ← Relativistic 8-channel spinor network
    │
    ├── quantum_framework_molecular*.py  ← VQE molecular simulations
    │     ├── UCCSD ansatz (Jordan-Wigner)
    │     └── Molecules: H2, LiH, H2O
    │
    ├── quantum_computer.py           ← Legacy statevector simulator (exact)
    │     └── Backends: Hamiltonian, Schrodinger, Dirac (float32)
    │
    ├── higgs_four_lepton_analysis.py ← Higgs → ZZ* → 4l on CMS Open Data
    ├── quantum_visualizer.py         ← Probability / Bloch / phase visualizer
    ├── quantum_dash.py               ← Brutalist matplotlib + Plotly visualizer
    ├── quantum_3dview.py             ← 3D holographic Plotly dashboard + audio
    ├── app.py                        ← H2 polarizability VQE (Stark effect)
    │
    ├── relativistic_hydrogen.py      ← Dirac equation, fine structure, Zitterbewegung
    ├── entangled_hydrogen.py         ← Entangled hydrogen orbital simulations
    ├── topological_hilbert_compression2.py  ← Topological Hilbert space analysis
    ├── advanced_experiments.py       ← Grover, QFT, phase estimation, Simon
    └── test_quantum_framework.py     ← 34 pytest tests (100% pass rate)

Key Results

Quantum Algorithms (both modes)

| Algorithm | Result | |-----------|--------| | Bell state entropy | 1.000000 bits (exact) | | GHZ state (n=3) | 50/50 distribution | | Grover 3-qubit search | 94.53% marked-state probability | | QFT norm preservation | sum(P) = 1 to machine precision | | Phase coherence (HZH=X, XX=I, etc.) | 22/22 tests pass |

Molecular Chemistry

| Molecule | HF Energy (Ha) | VQE Energy (Ha) | FCI Ref (Ha) | Corr. recovered | |----------|---------------|----------------|-------------|----------------| | H2 | −1.1168 | −1.1373060358 | −1.1373060358 | 100% | | LiH | −7.87 | — | −7.88 | — | | H2O | −74.963 | — | −75.012 | — |

Polarizability (H2, Stark effect)

α = 2.750 a₀³ — exact match with STO-3G diagonalization
|E(+F) − E(−F)| at machine precision (10⁻¹⁵) across all field values

QED Effects

Anomalous magnetic moment (g−2)/2 to 5th order: 0.3% error vs experiment
Lamb shift: 57.31 MHz (perturbative; experimental: 1057.84 MHz)

MPS Scaling (new in v2)

| Qubits | MPS Memory | Full statevector | Compression | |--------|-----------|-----------------|-------------| | 10 | 21 KB | 16 KB | — (chi=32 saturated) | | 20 | 182 KB | 16 MB | ~90× | | 33 | ~350 KB | 128 GB | ~370,000× |

Quick Start

Interactive Menu

python3 quantum_framework_main.py

Run all experiments (non-interactive)

python3 quantum_framework_main.py --run-all

Run tests

pytest test_quantum_framework.py -v

CLI options

python3 quantum_framework_main.py --help
python3 quantum_framework_main.py --benchmark --max-qubits 20
python3 quantum_framework_main.py --info

Menu Sections

| # | Section | Contents | |---|---------|----------| | 1 | Quantum Circuits | Custom circuits, Bell, GHZ, W-state, gate demos | | 2 | Entanglement | Entropy scaling, cut-position analysis, heatmaps | | 3 | Molecular Simulations | VQE H2/LiH/H2O, energy landscape, polarizability | | 4 | Orbital Visualization | Hydrogen orbitals, 3D scatter, probability distributions | | 5 | Relativistic Physics | Dirac equation, fine structure, Zitterbewegung | | 6 | QED Effects | Lamb shift, anomalous magnetic moment, vacuum polarization | | 7 | Advanced Algorithms | Grover, QFT, phase estimation, Simon, teleportation | | 8 | Benchmarks | MPS scaling, memory efficiency, timing | | 9 | Configuration | Atoms, molecules, parameters | | 10 | Particle Physics | Higgs → 4 lepton on CMS Open Data + quantum backends | | 11 | Quantum Visualization | Brutalist matplotlib/Plotly, 3D holographic dashboard |

Configuration

Edit quantum_framework_config.toml:

[simulation]
precision_mode = false     # true = exact statevector, false = MPS
max_qubits = 33            # max qubits for MPS mode
max_qubits_direct = 14     # max qubits for direct mode

[mps]
bond_dimension = 16        # χ — higher = more precise, more memory
max_bond_dimension = 64    # maximum χ
svd_threshold = 1.0e-10    # truncation threshold
adaptive_bond = true

Neural Network Checkpoints

Three pre-trained physics networks are included:

| File | Network | Size | Purpose | |------|---------|------|---------| | weights/latest.pth | HamiltonianBackboneNet | 18.9 MB | Spectral Hamiltonian operator | | weights/schrodinger_crystal_final.pth | SchrodingerSpectralNet | 18.9 MB | Wavefunction time evolution | | weights/dirac_phase5_latest.pth | DiracSpectralNet | 18.9 MB | Relativistic spinor dynamics |

All networks use FFT-based spectral convolution layers (SpectralLayer) operating in Fourier space.

Dependencies

pip install -r requirements.txt

| Package | Required | Purpose | |---------|----------|---------| | torch | ✅ | MPS tensors, neural backends | | numpy | ✅ | Numerical computation | | scipy | ✅ | VQE optimizer (L-BFGS-B) | | matplotlib | ✅ | Visualization | | tomllib/tomli | ✅ | TOML config (Python 3.11+ built-in) | | plotly | ⚡ Optional | 3D holographic visualization | | openfermion | ⚡ Optional | Molecular Hamiltonians | | pyscf | ⚡ Optional | Ab initio molecular integrals | | pytest | 🔧 Dev | Test suite |

Particle Physics Module

The higgs_four_lepton_analysis.py module downloads real CMS Open Data from CERN and processes H → ZZ* → 4ℓ events through the quantum neural backends:

python3 higgs_four_lepton_analysis.py

This will:

Download 6 CSV files from the CERN Open Data Portal (~100 MB)
Reconstruct 4-lepton invariant mass spectra
Identify Higgs candidates in the 120–130 GeV window
Evolve each lepton's wavefunction through DiracBackend, HamiltonianBackend, SchrodingerBackend
Generate a Plotly 3D detector visualization with quantum-modulated tracks

Differences from v1 (GitHub original)

| Feature | v1 | v2 (this) | |---------|-----|-----------| | State representation | Full statevector (2^n, 2, G, G) | MPS O(n·χ²) + exact mode | | Numerical precision | float32 | float64 | | Max qubits | 8 | 33+ (MPS) / 14 (exact) | | Architecture | Monolithic files | Modular (7 framework modules) | | Tests | None | 34 pytest tests (100% pass) | | Particle physics | ❌ | Higgs 4-lepton + CMS data | | 3D visualization | ❌ | Holographic Plotly dashboard | | Polarizability VQE | Separate script | Integrated in menu | | Grover (framework) | via advanced_experiments | run_grover_search() in core | | Configuration | Basic TOML | Extended TOML (9 sections) |

Limitations

MPS oracle for multi-controlled gates is circuit-approximate; run_grover_search() uses statevector for correctness
GPU execution untested (CPU only)
Higgs analysis requires internet connection for CMS data download
PySCF/OpenFermion required for full molecular VQE (graceful fallback otherwise)
Polarizability (app.py) tested only for H2 STO-3G

Citation

@software{grisuno_qc2026,
  author  = {grisun0},
  title   = {Q²C: Quasi Quantum Computing Simulator v2},
  year    = {2026},
  doi     = {10.5281/zenodo.18795538},
  url     = {https://github.com/grisuno/QC},
  orcid   = {0009-0002-7622-3916}
}

QC

Install / Use

README