EPR Analysis in Superconducting Quantum Circuits
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**EPR / scQubits Tutorial**

 
        EPR means Energy Participation Ratio. It explains what percentage of total electromagnetic
        energy is stored in each circuit component. In QClang documentation, place EPR after HFSS
        and Q3D because EPR converts field simulation information into quantum parameters such as
        qubit frequency, anharmonicity, coupling strength, and Kerr effects. 

Transmon qubit: capacitor plus Josephson junction structure.

            Josephson junction: two superconductors separated by a thin insulating layer.
          

Field-energy visualization used before participation analysis.

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   * - **Why EPR is needed**
     - It predicts qubit behavior before fabrication and reduces trial-and-error design
            iterations.
   * - **Energy distribution**
     - It shows how energy is shared between capacitor, Josephson junction, resonator, and
            other modes.
   * - **HFSS relationship**
     - HFSS calculates fields; EPR converts field information into quantum circuit parameters.
   * - **Parameters obtained**
     - Qubit frequency, anharmonicity, coupling strength, Kerr effects, and mode interactions.
   * - **Industry use**
     - Used in superconducting qubit research, academic labs, circuit QED workflows, and
            scalable chip studies.
   * - **scQubits placement**
     - Use scQubits-style analysis after EM simulation to display Hamiltonian, energy levels,
            coherence, participation, and interactions.