A deviation from the correct result in a computation, often caused by noise or imprecise control.In computation and measurement, error is any deviation from the true or expected result. It is an unavoidable companion of every physical measurement and numerical simulation, arising from sources as varied as thermal noise in electronic circuits, quantum fluctuations, rounding in algorithms, or imperfect control of experimental parameters. The study of error is not merely about eliminating it — in many modern techniques, understanding the structure of error allows scientists to correct for it or even exploit it.
The formal study of errors dates back to the 18th century, with Carl Friedrich Gauss developing the method of least squares to handle measurement errors in astronomical observations.
Errors are typically classified as systematic (consistent bias from calibration or setup) or random (fluctuating, unpredictable deviations). In quantum sensing, for example, noise can limit sensitivity, but techniques like dynamical decoupling or error mitigation in quantum computing use repeated measurements and clever pulse sequences to cancel out certain error contributions. In machine learning, errors guide training via loss functions, and understanding bias-variance tradeoffs helps models generalize.
Error analysis is fundamental in experimental physics, engineering, and data science — from calibrating sensors to training neural networks and correcting quantum computations.
Some quantum sensors use deliberately introduced disorder to reduce the influence of certain types of noise, turning error into a resource.
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