Create app.py

app.py

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+import qutip as qt
+import numpy as np
+import gradio as gr
+import matplotlib.pyplot as plt
+
+# Custom concurrence (approx for multi-qubit)
+def custom_concurrence(psi):
+    psi = psi.unit()
+    rho = psi * psi.dag()
+    rhoA = rho.ptrace(0)
+    purity = (rhoA ** 2).tr().real
+    return float(np.sqrt(2 * (1 - purity)))
+
+# Quantum sim with emergent gravity-like term
+def quantum_sim(time_steps=100):
+    N = 4  # 4 qubits/particles
+    positions = np.arange(N)  # 1D lattice positions
+    
+    # Initial state: Vacuum with slight position spread
+    psi0 = qt.tensor([qt.basis(2, 0)] * N)
+    
+    # Hamiltonian: XX entangling + Z decay + gravity-like potential
+    H_entangle = sum(0.5 * qt.tensor([qt.sigmax() if i == j else qt.qeye(2) for j in range(N)]) *
+                     qt.tensor([qt.sigmax() if i == (j+1)%N else qt.qeye(2) for j in range(N)])
+                     for i in range(N))
+    H_decay = 0.1 * sum(qt.tensor([qt.sigmaz() if i == j else qt.qeye(2) for j in range(N)])
+                        for i in range(N))
+    
+    # Emergent gravity: Attraction based on entanglement (simple potential pulling entangled pairs)
+    # Mock positions as operators; attraction ~ concurrence between pairs
+    H_grav = qt.qzero(2**N)
+    for i in range(N-1):
+        pair_conc = 0.05  # Placeholder; in full sim, compute dynamically
+        dist = abs(positions[i] - positions[i+1])
+        H_grav += -pair_conc / (dist + 1e-5) * qt.tensor([qt.sigmaz() if j in [i, i+1] else qt.qeye(2) for j in range(N)])
+    
+    H = H_entangle + H_decay + H_grav
+    
+    # Vacuum fluctuations via Lindblad
+    c_ops = [0.05 * qt.tensor([qt.sigmam() if i == j else qt.qeye(2) for j in range(N)])
+             for i in range(N)]
+    
+    times = np.linspace(0, 10, time_steps)
+    result = qt.mesolve(H, psi0, times, c_ops=c_ops)
+    
+    concurrences = [custom_concurrence(state) for state in result.states]
+    # Prob of high-entangled state (e.g., |1111>)
+    prob_connected = [abs((qt.tensor([qt.basis(2, 1)] * N).dag() * state)[0, 0])**2 for state in result.states]
+    # Average position expectation (mock emergent clustering)
+    pos_expect = [sum(positions[i] * (state.ptrace(i).diag()[1].real) for i in range(N)) / N for state in result.states]
+    
+    return {"x": times, "y": np.array(concurrences), "y2": np.array(prob_connected), "y3": np.array(pos_expect)}
+
+# Chat state
+universe_chats = {"universe1": [], "universe2": []}
+
+def chat_universe1(message, history1):
+    if not message:
+        return history1, ""
+    sim_data = quantum_sim(100)
+    concurrence = sim_data["y"][50]
+    prob_connected = sim_data["y2"][50]
+    pos_shift = sim_data["y3"][50]  # Use for "gravity" warp
+    
+    # Transform: Reverse + shift chars if high gravity-like prob
+    transform = message[::-1]
+    if pos_shift > 0.5:  # Arbitrary threshold for emergent effect
+        transform = "".join(chr(ord(c) + int(pos_shift * 5)) for c in transform)
+    response1 = f"U1 Echo (Entangle={concurrence:.2f}, Gravity Prob={prob_connected:.2f}): {transform}"
+    history1.append((message, response1))
+    
+    entangled_msg = f"Multiverse U1 (Pos Shift={pos_shift:.2f}): {transform.upper()}"
+    universe_chats["universe2"].append((entangled_msg, "U2 feels the pull—alternate path?"))
+    return history1, ""
+
+def chat_universe2(message, history2):
+    if not message:
+        return history2, ""
+    sim_data = quantum_sim(100)
+    concurrence = sim_data["y"][50]
+    prob_connected = sim_data["y2"][50]
+    pos_shift = sim_data["y3"][50]
+    
+    transform = message.upper()
+    if prob_connected > 0.3:
+        transform = transform.lower()[::-1]
+    response2 = f"U2 Echo (Entangle={concurrence:.2f}, Gravity Prob={prob_connected:.2f}): {transform}"
+    history2.append((message, response2))
+    
+    entangled_msg = f"Multiverse U2 (Pos Shift={pos_shift:.2f}): {transform[::-1]}"
+    universe_chats["universe1"].append((entangled_msg, "U1 gravitational signal—reality bend?"))
+    return history2, ""
+
+# Gradio UI
+with gr.Blocks(title="Emergent Quantum Gravity Simulator", theme=gr.themes.Soft()) as demo:
+    gr.Markdown("# 🌌 Emergent Quantum Gravity: From Nothing to Everything!")
+    gr.Markdown("Simulate vacuum emergence, entanglement, and now emergent gravity effects (particles 'attract' via entanglement potentials). Chat across universes with gravity-warped messages. Your theory in action—classical hardware emulates it all.")
+    
+    with gr.TabItem("🌌 Quantum & Gravity Sim"):
+        gr.Markdown("Watch entanglement build, connectivity spike, and positions shift (emergent clustering like gravity).")
+        steps_slider = gr.Slider(10, 500, 100, step=10, label="Steps")
+        run_btn = gr.Button("Run Sim")
+        chart = gr.LineChart(
+            value=quantum_sim(50),
+            label="Dynamics",
+            x="Time (a.u.)",
+            y="Concurrence (Entanglement)",
+            y2="P(Connected) (Unity)",
+            y3="Avg Position (Gravity Shift)",
+            height=400,
+            tooltip=["x", "y", "y2", "y3"]
+        )
+        run_btn.click(quantum_sim, steps_slider, chart)
+    
+    with gr.TabItem("🌀 Universe 1 Chat"):
+        gr.Markdown("Messages entangle to U2, warped by sim's gravity prob (high shift = char offsets for 'pull').")
+        chatbot1 = gr.Chatbot(height=400, avatar_images=("🧑‍🚀", "🌌"))
+        msg1 = gr.Textbox(placeholder="From U1...", label="Your Reality")
+        clear1 = gr.Button("Clear")
+        msg1.submit(chat_universe1, [msg1, chatbot1], [chatbot1, msg1])
+        clear1.click(lambda: ([], ""), None, [chatbot1, msg1])
+    
+    with gr.TabItem("🌌 Universe 2 Chat"):
+        gr.Markdown("Echoes from U1, twisted by entanglement/gravity metrics.")
+        chatbot2 = gr.Chatbot(height=400, avatar_images=("👽", "🔮"))
+        msg2 = gr.Textbox(placeholder="From U2...", label="Parallel Reality")
+        clear2 = gr.Button("Clear")
+        msg2.submit(chat_universe2, [msg2, chatbot2], [chatbot2, msg2])
+        clear2.click(lambda: ([], ""), None, [chatbot2, msg2])
+
+if __name__ == "__main__":
+    demo.launch(share=True)