Physical vs Logical Qubits
==========================

The key distinction and overhead cost of quantum error correction.

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   * - **Physical Qubits**
     - Real qubits present in quantum hardware (e.g. transmons, fluxoniums). They store
                    states such as \(\|0\rangle\), \(\|1\rangle\), and \(\|\psi\rangle\) directly, but
                    are highly noisy and error-prone.
   * - **Logical Qubits**
     - Created using multiple physical qubits. QEC protects the encoded state
                    \(\|\psi_L\rangle = \alpha\|0_L\rangle + \beta\|1_L\rangle\), making it
                    error-corrected and reliable.
   * - **Overhead Ratio**
     - \(1\) logical qubit \(=\) \(10^2\) to \(10^3\) physical qubits in many practical
                    surface-code estimates. Many physical qubits work together to behave like a
                    stable logical qubit even when individual physical qubits fail.