Physics:Quantum jump method - Revision history

WikiHarold: Clean Quantum page image and red links

2026-05-23T23:34:43Z

Clean Quantum page image and red links

← Older revision		Revision as of 23:34, 23 May 2026
Line 10:		Line 10:

	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	The '''quantum jump method''', also known as the '''~~[[Monte Carlo method\|~~Monte Carlo]] wave function (MCWF)''' is a technique in ~~[[Physics:Computational physics\|~~computational physics]] used for simulating ~~[[Physics:Open quantum system\|~~open quantum ~~system]]s~~ and [[Physics:Quantum dissipation\|quantum dissipation]]. The quantum jump method was developed by [[Biography:Jean Dalibard\|Dalibard]], Castin and [[Biography:Klaus Mølmer\|Mølmer]] at a similar time to the similar method known as [[Physics:Quantum Trajectory Theory\|Quantum Trajectory Theory]] developed by [[Biography:Howard Carmichael\|Carmichael]]. Other contemporaneous works on wave-function-based ~~[[Monte Carlo method\|~~Monte Carlo]] approaches to open quantum systems include those of Dum, [[Biography:Peter Zoller\|Zoller]] and [[Biography:Helmut Ritsch\|Ritsch]] and Hegerfeldt and Wilser.<ref name="MCD1993" /><ref name="PrimaryPapers">The associated primary sources are, respectively:		The '''quantum jump method''', also known as the '''Monte Carlo wave function (MCWF)''' is a technique in computational physics used for simulating open quantum systems and [[Physics:Quantum dissipation\|quantum dissipation]]. The quantum jump method was developed by [[Biography:Jean Dalibard\|Dalibard]], Castin and [[Biography:Klaus Mølmer\|Mølmer]] at a similar time to the similar method known as [[Physics:Quantum Trajectory Theory\|Quantum Trajectory Theory]] developed by [[Biography:Howard Carmichael\|Carmichael]]. Other contemporaneous works on wave-function-based Monte Carlo approaches to open quantum systems include those of Dum, [[Biography:Peter Zoller\|Zoller]] and [[Biography:Helmut Ritsch\|Ritsch]] and Hegerfeldt and Wilser.<ref name="MCD1993" /><ref name="PrimaryPapers">The associated primary sources are, respectively:

	*{{cite journal\|last=Dalibard\|first=Jean\|author2=Castin, Yvan \|author3=Mølmer, Klaus \|title=Wave-function approach to dissipative processes in quantum optics\|journal=Physical Review Letters\|date=February 1992\|volume=68\|issue=5\|pages=580–583\|doi=10.1103/PhysRevLett.68.580\|pmid=10045937\|bibcode = 1992PhRvL..68..580D \|arxiv=0805.4002}}		*{{cite journal\|last=Dalibard\|first=Jean\|author2=Castin, Yvan \|author3=Mølmer, Klaus \|title=Wave-function approach to dissipative processes in quantum optics\|journal=Physical Review Letters\|date=February 1992\|volume=68\|issue=5\|pages=580–583\|doi=10.1103/PhysRevLett.68.580\|pmid=10045937\|bibcode = 1992PhRvL..68..580D \|arxiv=0805.4002}}
Line 19:		Line 19:

	<div style="width:300px;">		<div style="width:300px;">
	[[File:~~File not found~~.~~png~~\|thumb\|280px\|~~No image available~~.]]		[[File:Master_equation_unravelings.svg\|thumb\|280px\|jump method in the Quantum Collection.]]
	</div>		</div>

Line 25:		Line 25:

	== Method ==		== Method ==
	[[File:Master equation unravelings.svg\|thumb\|An example of the quantum jump method being used to approximate the density matrix of a two-level atom undergoing damped [[Rabi ~~oscillation]]s~~. The random jumps can clearly be seen in the top subplot, and the bottom subplot compares the fully simulated density matrix to the approximation obtained using the quantum jump method.]]		[[File:Master equation unravelings.svg\|thumb\|An example of the quantum jump method being used to approximate the density matrix of a two-level atom undergoing damped Rabi oscillations. The random jumps can clearly be seen in the top subplot, and the bottom subplot compares the fully simulated density matrix to the approximation obtained using the quantum jump method.]]

	[[File:MC-ensemble average.gif\|thumb\|Animation of the Monte Carlo prediction (blue) for the population of a coherently-driven, damped two-level system as more trajectories are added to the ensemble average, compared to the master equation prediction (red).]]		[[File:MC-ensemble average.gif\|thumb\|Animation of the Monte Carlo prediction (blue) for the population of a coherently-driven, damped two-level system as more trajectories are added to the ensemble average, compared to the master equation prediction (red).]]

	The quantum jump method is an approach which is much like the master-equation treatment except that it operates on the wave function rather than using a ~~[[Density matrix\|~~density matrix]] approach. The main component of this method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each time step, a quantum jump (discontinuous change) may take place with some probability. The calculated system state as a function of time is known as a ~~[[Quantum stochastic calculus#Quantum trajectories\|~~quantum trajectory]], and the desired ~~[[Density matrix\|~~density matrix]] as a function of time may be calculated by averaging over many simulated trajectories. For a Hilbert space of dimension N, the number of wave function components is equal to N while the number of density matrix components is equal to N<sup>2</sup>. Consequently, for certain problems the quantum jump method offers a performance advantage over direct master-equation approaches.<ref name=MCD1993>{{Cite journal \| last1 = Mølmer \| first1 = K. \| last2 = Castin \| first2 = Y. \| last3 = Dalibard \| first3 = J. \| doi = 10.1364/JOSAB.10.000524 \| title = Monte Carlo wave-function method in quantum optics \| journal = Journal of the Optical Society of America B \| volume = 10 \| issue = 3 \| pages = 524 \| year = 1993 \|bibcode = 1993JOSAB..10..524M }}</ref>		The quantum jump method is an approach which is much like the master-equation treatment except that it operates on the wave function rather than using a density matrix approach. The main component of this method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each time step, a quantum jump (discontinuous change) may take place with some probability. The calculated system state as a function of time is known as a quantum trajectory, and the desired density matrix as a function of time may be calculated by averaging over many simulated trajectories. For a Hilbert space of dimension N, the number of wave function components is equal to N while the number of density matrix components is equal to N<sup>2</sup>. Consequently, for certain problems the quantum jump method offers a performance advantage over direct master-equation approaches.<ref name=MCD1993>{{Cite journal \| last1 = Mølmer \| first1 = K. \| last2 = Castin \| first2 = Y. \| last3 = Dalibard \| first3 = J. \| doi = 10.1364/JOSAB.10.000524 \| title = Monte Carlo wave-function method in quantum optics \| journal = Journal of the Optical Society of America B \| volume = 10 \| issue = 3 \| pages = 524 \| year = 1993 \|bibcode = 1993JOSAB..10..524M }}</ref>

	<!-- Sections to be written: Algorithm; Equivalence to master equation treatment (maybe); Applications -->		<!-- Sections to be written: Algorithm; Equivalence to master equation treatment (maybe); Applications -->
Line 40:		Line 40:

	== External links ==		== External links ==
	* [http://qutip.org/docs/latest/guide/dynamics/dynamics-monte.html mcsolve] {{Webarchive\|url=https://web.archive.org/web/20230930194128/https://qutip.org/docs/latest/guide/dynamics/dynamics-monte.html \|date=2023-09-30 }} Quantum jump (~~[[Monte Carlo method\|~~Monte Carlo]]) solver from ~~[[Software:QuTiP\|~~QuTiP]] for [[Python ~~(programming language)\|Python]]~~.		* [http://qutip.org/docs/latest/guide/dynamics/dynamics-monte.html mcsolve] {{Webarchive\|url=https://web.archive.org/web/20230930194128/https://qutip.org/docs/latest/guide/dynamics/dynamics-monte.html \|date=2023-09-30 }} Quantum jump (Monte Carlo) solver from QuTiP for Python.
	* [https://qojulia.org QuantumOptics.jl] the quantum optics toolbox in ~~[[Julia (programming language)\|~~Julia]].		* [https://qojulia.org QuantumOptics.jl] the quantum optics toolbox in Julia.
	* [https://qo.phy.auckland.ac.nz/toolbox/ Quantum Optics Toolbox] for ~~[[Software:MATLAB\|~~Matlab]]		* [https://qo.phy.auckland.ac.nz/toolbox/ Quantum Optics Toolbox] for Matlab

	[[Category:Quantum mechanics]]		[[Category:Quantum mechanics]]
	[[Category:Computational physics]]		[[Category:Computational physics]]
	[[Category:Monte Carlo methods]]		[[Category:Monte Carlo methods]]



	{{Sourceattribution\|Quantum jump method}}		{{Sourceattribution\|Quantum jump method}}

Harold: Add missing image fallback to Quantum header

2026-05-17T22:33:18Z

Add missing image fallback to Quantum header

← Older revision		Revision as of 22:33, 17 May 2026
Line 19:		Line 19:

	<div style="width:300px;">		<div style="width:300px;">
	~~<!--~~ No ~~lead~~ image available ~~in existing page~~. ~~-->~~		[[File:File not found.png\|thumb\|280px\|No image available.]]
	</div>		</div>

Harold: Restore Quantum article header template

2026-05-17T21:52:43Z

Restore Quantum article header template

@@ Line 1: / Line 1: @@
- {{Short description|Computational simulation method for open quantum systems}}
+{{Short description|Computational simulation method for open quantum systems}}
 The '''quantum jump method''', also known as the '''[[Monte Carlo method|Monte Carlo]] wave function (MCWF)''' is a technique in [[Physics:Computational physics|computational physics]] used for simulating [[Physics:Open quantum system|open quantum system]]s and [[Physics:Quantum dissipation|quantum dissipation]]. The quantum jump method was developed by [[Biography:Jean Dalibard|Dalibard]], Castin and [[Biography:Klaus Mølmer|Mølmer]] at a similar time to the similar method known as [[Physics:Quantum Trajectory Theory|Quantum Trajectory Theory]] developed by [[Biography:Howard Carmichael|Carmichael]]. Other contemporaneous works on wave-function-based [[Monte Carlo method|Monte Carlo]] approaches to open quantum systems include those of Dum, [[Biography:Peter Zoller|Zoller]] and [[Biography:Helmut Ritsch|Ritsch]] and Hegerfeldt and Wilser.<ref name="MCD1993" /><ref name="PrimaryPapers">The associated primary sources are, respectively:
@@ Line 6: / Line 16: @@
 *{{cite journal|last=Dum|first=R.|author2=Zoller, P. |author3=Ritsch, H. |title=Monte Carlo simulation of the atomic master equation for spontaneous emission|journal=Physical Review A|year=1992|volume=45|issue=7|pages=4879–4887|doi=10.1103/PhysRevA.45.4879|pmid=9907570|bibcode = 1992PhRvA..45.4879D }}
 *{{cite book |last1=Hegerfeldt |first1=G. C. |last2=Wilser |first2=T. S. |year=1992 |title=Classical and Quantum Systems |series= Proceedings of the Second International Wigner Symposium |publisher=World Scientific|url=http://www.theorie.physik.uni-goettingen.de/~hegerf/collaps_gesamt.pdf|pages=104–105|chapter=Ensemble or Individual System, Collapse or no Collapse: A Description of a Single Radiating Atom|editor1=H.D. Doebner|editor2=W. Scherer|editor3=F. Schroeck, Jr.}}</ref>
 == Method ==

imported>WikiHarold: update

2026-02-12T01:59:13Z

update

← Older revision	Revision as of 01:59, 12 February 2026
(No difference)

imported>WikiHarold: update

2026-02-12T01:59:13Z

update

New page

{{Short description|Computational simulation method for open quantum systems}}
The '''quantum jump method''', also known as the '''[[Monte Carlo method|Monte Carlo]] wave function (MCWF)''' is a technique in [[Physics:Computational physics|computational physics]] used for simulating [[Physics:Open quantum system|open quantum system]]s and [[Physics:Quantum dissipation|quantum dissipation]]. The quantum jump method was developed by [[Biography:Jean Dalibard|Dalibard]], Castin and [[Biography:Klaus Mølmer|Mølmer]] at a similar time to the similar method known as [[Physics:Quantum Trajectory Theory|Quantum Trajectory Theory]] developed by [[Biography:Howard Carmichael|Carmichael]]. Other contemporaneous works on wave-function-based [[Monte Carlo method|Monte Carlo]] approaches to open quantum systems include those of Dum, [[Biography:Peter Zoller|Zoller]] and [[Biography:Helmut Ritsch|Ritsch]] and Hegerfeldt and Wilser.<ref name="MCD1993" /><ref name="PrimaryPapers">The associated primary sources are, respectively:

*{{cite journal|last=Dalibard|first=Jean|author2=Castin, Yvan |author3=Mølmer, Klaus |title=Wave-function approach to dissipative processes in quantum optics|journal=Physical Review Letters|date=February 1992|volume=68|issue=5|pages=580–583|doi=10.1103/PhysRevLett.68.580|pmid=10045937|bibcode = 1992PhRvL..68..580D |arxiv=0805.4002}}
*{{cite book |last=Carmichael |first=Howard |title=An Open Systems Approach to Quantum Optics |year=1993 |publisher=Springer-Verlag |isbn=978-0-387-56634-4}}
*{{cite journal|last=Dum|first=R.|author2=Zoller, P. |author3=Ritsch, H. |title=Monte Carlo simulation of the atomic master equation for spontaneous emission|journal=Physical Review A|year=1992|volume=45|issue=7|pages=4879–4887|doi=10.1103/PhysRevA.45.4879|pmid=9907570|bibcode = 1992PhRvA..45.4879D }}
*{{cite book |last1=Hegerfeldt |first1=G. C. |last2=Wilser |first2=T. S. |year=1992 |title=Classical and Quantum Systems |series= Proceedings of the Second International Wigner Symposium |publisher=World Scientific|url=http://www.theorie.physik.uni-goettingen.de/~hegerf/collaps_gesamt.pdf|pages=104–105|chapter=Ensemble or Individual System, Collapse or no Collapse: A Description of a Single Radiating Atom|editor1=H.D. Doebner|editor2=W. Scherer|editor3=F. Schroeck, Jr.}}</ref>

== Method ==
[[File:Master equation unravelings.svg|thumb|An example of the quantum jump method being used to approximate the density matrix of a two-level atom undergoing damped [[Rabi oscillation]]s. The random jumps can clearly be seen in the top subplot, and the bottom subplot compares the fully simulated density matrix to the approximation obtained using the quantum jump method.]]

[[File:MC-ensemble average.gif|thumb|Animation of the Monte Carlo prediction (blue) for the population of a coherently-driven, damped two-level system as more trajectories are added to the ensemble average, compared to the master equation prediction (red).]]

The quantum jump method is an approach which is much like the master-equation treatment except that it operates on the wave function rather than using a [[Density matrix|density matrix]] approach. The main component of this method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each time step, a quantum jump (discontinuous change) may take place with some probability. The calculated system state as a function of time is known as a [[Quantum stochastic calculus#Quantum trajectories|quantum trajectory]], and the desired [[Density matrix|density matrix]] as a function of time may be calculated by averaging over many simulated trajectories. For a Hilbert space of dimension N, the number of wave function components is equal to N while the number of density matrix components is equal to N<sup>2</sup>. Consequently, for certain problems the quantum jump method offers a performance advantage over direct master-equation approaches.<ref name=MCD1993>{{Cite journal | last1 = Mølmer | first1 = K. | last2 = Castin | first2 = Y. | last3 = Dalibard | first3 = J. | doi = 10.1364/JOSAB.10.000524 | title = Monte Carlo wave-function method in quantum optics | journal = Journal of the Optical Society of America B | volume = 10 | issue = 3 | pages = 524 | year = 1993 |bibcode = 1993JOSAB..10..524M }}</ref>



== References ==
{{Reflist}}

== Further reading ==
* {{cite journal|last=Plenio|first=M. B.|author2=Knight, P. L. |title=The quantum-jump approach to dissipative dynamics in quantum optics|journal=Reviews of Modern Physics|date=1 January 1998|volume=70|issue=1|pages=101–144|doi=10.1103/RevModPhys.70.101|bibcode=1998RvMP...70..101P|arxiv = quant-ph/9702007 |s2cid=14721909 }}

== External links ==
* [http://qutip.org/docs/latest/guide/dynamics/dynamics-monte.html mcsolve] {{Webarchive|url=https://web.archive.org/web/20230930194128/https://qutip.org/docs/latest/guide/dynamics/dynamics-monte.html |date=2023-09-30 }} Quantum jump ([[Monte Carlo method|Monte Carlo]]) solver from [[Software:QuTiP|QuTiP]] for [[Python (programming language)|Python]].
* [https://qojulia.org QuantumOptics.jl] the quantum optics toolbox in [[Julia (programming language)|Julia]].
* [https://qo.phy.auckland.ac.nz/toolbox/ Quantum Optics Toolbox] for [[Software:MATLAB|Matlab]]

[[Category:Quantum mechanics]]
[[Category:Computational physics]]
[[Category:Monte Carlo methods]]

{{Sourceattribution|Quantum jump method}}