Key Takeaways
=============

Core insights on the transition from physical to logical quantum processing.

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   * - **Qubits are noisy**
     - Every physical qubit suffers from noise, decoherence, and gate/readout errors.
                    QEC is a fundamental requirement for scaling.
   * - **Logical encoding**
     - Logical qubits are built from many noisy physical qubits, often 
                    :math:`\\sim 10^2\\text{--}10^3`, to create stable, error-corrected units.
   * - **Surface Code dominance**
     - The Surface Code is the current leader due to its high threshold 
                    :math:`p_{\\mathrm{th}} \\approx 1\\%` and compatibility with 2D planar
                    layouts.
   * - **Threshold dependency**
     - If :math:`p < p_{\\mathrm{th}}`, scaling up the code distance \(d\) improves
                    reliability and drives \(P_L\) down. Above threshold, increasing \(d\) cannot
                    rescue the computation.
   * - **Advanced alternatives**
     - GKP, XZZX, and quantum LDPC codes are prime candidates to reduce the physical
                    qubit overhead for future processors.