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

Revision as of 10:05, 29 August 2025

Revision as of 13:42, 29 August 2025

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<math>\frac{d\rho}{dt}=-\frac{i}{\hbar}[H,\rho]+\sum_k\left(L_k\rho L_k^\dagger-\tfrac{1}{2}\{L_k^\dagger L_k,\rho\}\right)</math>

where <math>L_k</math> represent specific [[Quantum noise|noise processes]] such as [[Quantum decoherence#Dephasing|dephasing]]. The commutator is <math>[A,B]=AB-BA</math> and the anticommutator is <math>\{A,B\}=AB+BA</math>.<ref name="Lindblad">{{cite journal |last=Lindblad |first=Göran |title=On the generators of quantum dynamical semigroups |journal=Communications in Mathematical Physics |year=1976 |volume=48 |issue=2 |pages=119–130 |doi=10.1007/BF01608499 |bibcode=1976CMaPh..48..119L }}</ref><ref name="GKS">{{cite journal |last1=Gorini |first1=Vittorio |last2=Kossakowski |first2=Andrzej |last3=Sudarshan |first3=E. C. G. |title=Completely positive dynamical semigroups of N-level systems |journal=Journal of Mathematical Physics |year=1976 |volume=17 |issue=5 |pages=821–825 |doi=10.1063/1.522979 |bibcode=1976JMP....17..821G }}</ref>

* '''Redfield equation (non-Markovian noise)''': For environments with memory effects, the [[Redfield equation]] is used:

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<ref name="RivasHuelga">{{cite book |last1=Rivas |first1=Ángel |last2=Huelga |first2=Susana F. |title=Open Quantum Systems: An Introduction |series=Springer Briefs in Physics |publisher=Springer |year=2012 |doi=10.1007/978-3-642-23354-8 |arxiv=1104.5242 |isbn=978-3-642-23353-1 }}</ref>

<ref name="GneitingNori">{{cite journal |last1=Gneiting |first1=Clemens |last2=Nori |first2=Franco |title=Quantum evolution in open systems: Master equations and dynamical maps |journal=Journal of Statistical Physics |year=2017 |volume=168 |issue=6 |pages=1223–1240 |doi=10.1007/s10955-017-1901-0}}</ref>

<ref name="Lindblad">{{cite journal |last=Lindblad |first=Göran |title=On the generators of quantum dynamical semigroups |journal=Communications in Mathematical Physics |year=1976 |volume=48 |issue=2 |pages=119–130 |doi=10.1007/BF01608499 |bibcode=1976CMaPh..48..119L }}</ref>

<ref name="GKS">{{cite journal |last1=Gorini |first1=Vittorio |last2=Kossakowski |first2=Andrzej |last3=Sudarshan |first3=E. C. G. |title=Completely positive dynamical semigroups of N-level systems |journal=Journal of Mathematical Physics |year=1976 |volume=17 |issue=5 |pages=821–825 |doi=10.1063/1.522979 |bibcode=1976JMP....17..821G }}</ref>

</references>

== Further reading ==

* {{cite journal |last1=Breuer |first1=H.-P. |last2=Laine |first2=E.-M. |last3=Piilo |first3=J. |last4=Vacchini |first4=B. |title=Colloquium: Non-Markovian dynamics in open quantum systems |journal=Reviews of Modern Physics |year=2016 |volume=88 |issue=2 |page=021002 |doi=10.1103/RevModPhys.88.021002 |arxiv=1505.01385 |bibcode=2016RvMP...88b1002B |hdl=2434/387123 }}

{{Tech-stub}}