Introduction
============

Basic hardware noise sources and the role of fault tolerance.

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   * - **Noise**
     - Unwanted interactions that scramble qubit states, caused by environment, control
                    imperfections, and crosstalk.
   * - **Decoherence**
     - The process by which quantum information leaks into the surrounding environment
                    over time, destroying superposition.
   * - **Gate Errors**
     - Imperfect operations that cause incorrect transformations, arising from
                    calibration drift, pulse shape errors, and leakage.
   * - **Measurement Errors**
     - Readout mistakes that misreport a qubit’s state, stemming from
                    insufficient dispersive shift, thermal photons, or amplifier noise.

 
                Fault tolerance combines quantum error correction, redundancy, and error detection
                techniques to maintain reliable computation even in the presence of hardware
                imperfections.