Analysis of Active Time Hypothesis Validation Through Quantum Circuit Simulation

Dr. Maher Abdelsamie
maherabdelsamie@gmail.com

Enhanced Validation Results Analysis:

Temporal Results: Mean ± SEM: 0.391 ± 0.017 Signal-to-Noise Ratio: 8.317 Linear Correlation (R²): 0.997 Trend Significance (p-value): 8.917e-09 Nonlinear Correlation (R²): 0.999 Dominant Frequency: 0.125

Adaptive Results: Mean ± SEM: 2.555 ± 0.003 Signal-to-Noise Ratio: 308.471 Linear Correlation (R²): 0.006 Trend Significance (p-value): 8.516e-01 Nonlinear Correlation (R²): 0.032 Dominant Frequency: 0.375

Clock Results: Mean ± SEM: 2.953 ± 0.108 Signal-to-Noise Ratio: 9.640 Linear Correlation (R²): 0.013 Trend Significance (p-value): 7.872e-01 Nonlinear Correlation (R²): 0.888 Dominant Frequency: 0.125

Falsification Results: Mean ± SEM: 1.036 ± 0.074 Signal-to-Noise Ratio: 5.265 Linear Correlation (R²): 0.420 Trend Significance (p-value): 1.157e-01 Nonlinear Correlation (R²): 0.722 Dominant Frequency: 0.429

Beyond Quantum Results: Mean ± SEM: 0.160 ± 0.081 Signal-to-Noise Ratio: 0.700 Linear Correlation (R²): 0.702 Trend Significance (p-value): 9.381e-03 Nonlinear Correlation (R²): 0.906 Dominant Frequency: 0.125

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Installation

The simulation is implemented in Python and requires the following libraries:

• numpy
• matplotlib
• qiskit
• scipy
• typing
• datetime
• time
• bluequbit (for interfacing with the quantum computing platform)
• seaborn

To set up the environment, follow these steps:

1. Clone the repository:

   git clone <repository-url>
   cd <repository-name>

2. Install dependencies:

   You can install the required libraries using pip. Run the following command in the root of the repository:

   pip install numpy matplotlib qiskit scipy seaborn bluequbit

3. BlueQubit Authentication: The simulation requires a BlueQubit authentication token to connect to the quantum computing backend. To obtain the token, sign up for an account on BlueQubit’s website and retrieve your API key. Store the token in a secure place, as you’ll need to input it when running the simulation.

4. Running the Simulation: Once the dependencies are installed, you can run the main script using:

   python main.py

This will initiate the simulation, run validation tests, and produce the results and visualizations as specified in the code.

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License

See the LICENSE.md file for details.

Citing This Work

You can cite it using the information provided in the CITATION.cff file available in this repository.