QHCA: SymPy/QuTiP Simulation Examples
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This package contains three small experiments for the "Quantum Holographic Consciousness Architecture (QHCA)".

Files
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- qhca_sympy_qutip_examples.py  : Main script with three experiments

Experiments
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(A) Temporal Recursive Superposition (SymPy)
    - Models a time-recursive superposition |psi_t> mixing past and future states.
    - Produces a plot: figs/experiment_A_overlap.png

(B) Entanglement Gradient on a 1D Chain (QuTiP)
    - 6-qubit chain, spatially varying ZZ coupling; computes single-site entropies and a gradient proxy.
    - Produces two plots: figs/experiment_B_entropy.png and figs/experiment_B_gradient.png

(C) Entropy-Tuned Decoherence & CHSH (QuTiP)
    - Starts from a Bell state; applies local dephasing; computes CHSH S to show violation decay vs noise.
    - Produces a plot: figs/experiment_C_CHSH.png

Usage
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1) Install dependencies in a local environment:
   pip install numpy sympy qutip matplotlib

2) Run:
   python qhca_sympy_qutip_examples.py

3) See figures under ./figs

Notes
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- The QuTiP parts (B) and (C) assume QuTiP >= 4.7 (or 5.x). Adjust imports if needed.
- You can adapt the chain size N, couplings J0, and time t to explore different regimes.
- For (C), the threshold S/sqrt(2) ~ 0.707 corresponds to |E| > 1/sqrt(2); the classical bound is S=2.
