Fix/physics engine correction

README.md

@@ -3,33 +3,43 @@
 ## Overview
 This document details the integration of Walter Russell's metaphysical principles into the quantum simulation framework, specifically focusing on the Cosmic Duality Operator (ĉ) and Rhythmic Balanced Interchange Operator (V_RB(t)).
 
-## Mathematical Framework
+## Corrected Mathematical Framework
 
-### Cosmic Duality Operator
-The Cosmic Duality Operator is implemented as:
+The mathematical framework has been corrected to be dimensionally consistent and physically sound.
+
+### Enhanced Hamiltonian
+The core of the simulation is the `enhanced_hamiltonian`, which is now defined as:
 
 ```math
-ĉ = exp(i χ Ĥ)
+Ĥ_{enh}(t) = Ĉ Ĥ₀ Ĉ† + Ĥ_{RB}(t)
 ```
 
-where:
-- χ is the coupling strength parameter
-- Ĥ is the system Hamiltonian
-
-### Rhythmic Balanced Interchange Operator
-The RBI operator is defined as:
+This formula describes a quantum system with a base Hamiltonian `Ĥ₀` that is "dressed" by a unitary transformation `Ĉ` and driven by a time-dependent term `Ĥ_{RB}(t)`.
 
+### Cosmic Duality Operator (Ĉ)
+This operator performs a unitary transformation (a rotation) on the Hamiltonian. It is defined as:
 ```math
-V_RB(t) = α ℏω sin(ωt)
+Ĉ = exp(i χ Ĥ₀)
 ```
+- `Ĥ₀` is the base system Hamiltonian.
+- `χ` is a tunable parameter. In this implementation, `χ` is treated as dimensionless, assuming the input Hamiltonian `Ĥ₀` has been scaled appropriately.
 
-where:
-- α is the coupling strength
-- ω is the oscillation frequency
-- t is time
+### Rhythmic Balanced Interchange (RBI) Term (Ĥ_RB)
+This term represents a time-dependent external field driving the system. It is now correctly implemented as an operator-valued term, not a scalar. For a two-level system, it is defined as:
+```math
+Ĥ_{RB}(t) = α ħω sin(ωt) σ̂_x
+```
+- `α` is a dimensionless coupling strength.
+- `ħω` provides the energy scale for the driving field. In the code, we adopt the common convention of setting `ħ=1`.
+- `σ̂_x` is the Pauli-X matrix, `[[0, 1], [1, 0]]`, which is the operator that couples to the field.
 
 ## Implementation Details
 
+### QHR Model (LSTM Predictor)
+The repository includes a `QHRModel` that uses an LSTM network to predict quantum state evolution.
+
+**Important Note:** As highlighted in a physical audit of this repository, the QHR model in its current form has significant limitations. It does not enforce physical constraints like unitarity or probability conservation by construction. To be a reliable tool, it would require a specialized training pipeline with loss functions that penalize non-physical predictions. This work has not yet been done.
+
 ### Key Components
 
 1. **walter_russell_principles()**
@@ -64,14 +74,46 @@ plot_energy_levels(H0, H_enhanced)
 
 ## Testing
 
-The implementation includes comprehensive tests:
-- Unitary properties of Cosmic Duality Operator
-- Periodicity of RBI Operator
-- Hermiticity of enhanced Hamiltonian
-- QHR model functionality
+The test suite is being updated to verify the physical correctness of the simulation. The following tests are being implemented:
+- **Unitarity of Ĉ:** Verifies that `Ĉ†Ĉ = Î`.
+- **Spectrum Invariance:** Verifies that the eigenvalues of `Ĥ₀` and `ĈĤ₀Ĉ†` are identical.
+- **Probability Conservation:** Verifies that the norm of an evolving state vector remains 1.
+
+Further tests related to energy conservation and the accuracy of the QHR model are pending.
 
 ## References
 
 1. Russell, W. (1926). *The Universal One*. University of Science and Philosophy.
 2. Nielsen, M. A., & Chuang, I. L. (2010). *Quantum Computation and Quantum Information*. Cambridge University Press.
 3. Haroche, S., & Raimond, J.-M. (2006). *Exploring the Quantum: Atoms, Cavities, and Photons*. Oxford University Press.
+
+---
+
+## Cosmic Duality Simulation (Quantum Field Theory Model)
+
+Based on user feedback, a new simulation has been added to model the core Russellian concepts of "Generation" (creation) and "Radiation" (annihilation) as a "Two-Way Motion". This is achieved using the formalism of quantum field theory (QFT).
+
+### The Physical Model
+
+This simulation models a quantum field that can create and destroy particles (or quanta of energy). The dynamics are governed by the following Hamiltonian:
+
+```math
+H = ε(a†a) + g(a† + a)
+```
+
+- **`ε(a†a)`**: This is the energy term. `ε` is the energy of a single particle, and the number operator `N = a†a` counts how many particles exist.
+- **`g(a† + a)`**: This is the interaction term that drives the "two-way motion". The creation operator `a†` adds a particle to the system, while the annihilation operator `a` removes one. The parameter `g` controls the rate of this creation/destruction process.
+
+### Running the Simulation
+
+A new script has been added to run and visualize this simulation.
+
+To run it, execute the following command from the root of the repository:
+```bash
+python src/run_qft_simulation.py
+```
+
+This will:
+1. Initialize the system in a vacuum state (zero particles).
+2. Evolve the system in time according to the Hamiltonian above.
+3. Generate a plot named `qft_simulation_particle_number.png` which shows the expected number of particles in the system as a function of time, directly visualizing the continuous process of creation and annihilation.

environment.yml

@@ -1,21 +1,17 @@
-name: quantum-simulation
+name: qiskit-env
 channels:
   - conda-forge
-  - defaults
 dependencies:
   - python=3.10
   - pip
-  - numpy
-  - pyqt=5
-  - pyqtgraph
-  - pyopengl
   - pytest
-  - pytest-qt
-  - flake8
+  # Core scientific packages
+  - numpy
   - scipy
+  - h5py
   - matplotlib
-  - pyyaml
-  - pip:
-    - pyopencl
-    - qutip
-    - pennylane
+  # Qiskit ecosystem for quantum chemistry
+  - qiskit-nature
+  - qiskit-aer
+  - qiskit-algorithms
+  - pyscf