Draft:Open-system formulations in quantum computing.: Difference between revisions

Revision as of 01:23, 29 August 2025

Revision as of 01:33, 29 August 2025

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<math>U(t)=\mathcal{T}\exp\!\left[-\frac{i}{\hbar}\int_0^t H(t')\,dt'\right]</math>

where \(\mathcal{{math|{T}\)}} is the [[Time-ordering|time-ordering operator]], \(\hbar\){{math|H}} is the [[Reduced Planck constant|reduced Planck constant]], and \({{math|U(t)\)}} is the [[Timetime evolution operator|time evolution]].

Real devices are never perfectly isolated; interactions with [[particle physics|particles]], [[Phonon|phonons]], [[Photon|photons]], and [[Control engineering|control electronics]] affect [[qubit]]. Open-system methods capture these effects via [[Quantum channel|quantum channels]] or environment-dependent modifications to the generator of the time evolution.<ref name="BreuerPetruccione" /><ref name="RivasHuelga" />