View source for QuTiP

{{Short description|Simulation software for quantum systems}}
{{Infobox software
| name = QuTiP
| logo = File:Qutip logo.png
| logo alt = Qutip logo
| latest release version = 4.7.0
| latest release date = {{Start date and age|2022|02|08}}
| latest preview version = 5.0.0.dev
| repo = {{URL|https://github.com/qutip/qutip}}
| programming language = [[Python (programming language)|Python]]
| platform = [[Cross-platform]]
| genre = [[Library (computing)|Library]]
| license = [[BSD 3-Clause|BSD 3-clause]]
| website = {{URL|https://qutip.org/}}
}}

'''QuTiP''', short for the '''Quantum Toolbox in Python''', is an [[Open-source software|open-source]] [[computational physics]] software library for [[Quantum simulator|simulating quantum systems]], particularly [[open quantum system]]s.<ref>{{Cite journal|last1=Johansson|first1=J.R.|last2=Nation|first2=P.D.|last3=Nori|first3=Franco|date=April 2013|title=QuTiP 2: A Python framework for the dynamics of open quantum systems|journal=Computer Physics Communications|language=en|volume=184|issue=4|pages=1234–1240|doi=10.1016/j.cpc.2012.11.019|arxiv=1211.6518|bibcode=2013CoPhC.184.1234J |s2cid=15261366 }}</ref><ref name="nationjohansson2">{{Cite journal|last1=Johansson|first1=J.R.|last2=Nation|first2=P.D.|last3=Nori|first3=Franco|date=August 2012|title=QuTiP: An open-source Python framework for the dynamics of open quantum systems|journal=Computer Physics Communications|language=en|volume=183|issue=8|pages=1760–1772|doi=10.1016/j.cpc.2012.02.021|arxiv=1110.0573|bibcode=2012CoPhC.183.1760J |s2cid=15055747 }}</ref>  QuTiP allows simulation of [[Hamiltonian (quantum mechanics)|Hamiltonians]] with arbitrary time-dependence, allowing simulation of situations of interest in [[quantum optics]], [[ion trap]]ping, [[Circuit quantum electrodynamics|superconducting circuits]] and quantum nanomechanical [[resonator]]s.  The library includes extensive [[Scientific visualization|visualization]] facilities for content under simulations.

QuTiP's API provides a [[Python (programming language)|Python]] interface and uses [[Cython]] to allow run-time compilation and extensions via [[C (programming language)|C]] and [[C++]].  QuTiP is built to work well with popular Python packages [[NumPy]], [[SciPy]], [[Matplotlib]] and [[IPython]].

== History ==

The idea for the QuTip project was conceived in 2010 by PhD student Paul Nation, who was using the [[qotoolbox|quantum optics toolbox]] for [[MATLAB]] in his research. According to Paul Nation, he wanted to create a python package similar to qotoolbox because he "was not a big fan of MATLAB" and then decided to "just write it [him]self".<ref name="podcast">{{cite podcast |host=Tobias Macey |title=QuTiP with Paul Nation - Episode 128 |publisher=Podcast.__init__ |date=24 September 2017 |time=6:15 |url=https://www.pythonpodcast.com/qutip-with-paul-nation-episode-128/ |access-date=10 August 2022}}</ref>  As a postdoctoral fellow, at the [[Riken|RIKEN Institute]] in Japan, he met Robert Johansson and the two worked together on the package. 
In contrast to its predecessor qotoolbox, which relies on the proprietary MATLAB environment, it was published in 2012 under an open source license.<ref name="nationjohansson2" />

The Version created by Nation and Johansson already contained the most important features of the package, but QuTips scope and features are constantly being extended by a large community of contributors.<ref>{{cite web |url=https://github.com/qutip
|title= QuTiP - Quantum Toolbox in Python
|publisher= GitHub
|access-date= 11 August 2022}}</ref> It has grown in popularity amongst physicists, with over 250.000 downloads in the year 2021.<ref>{{cite web |url=https://github.com/qutip/governance/blob/main/annual-reports/report-2021.md
|title= QuTiP 2021 Annual Report
|author = The QuTip Admin Team
|publisher= GitHub
|access-date= 11 August 2022}}</ref>

== Examples ==

=== Creating quantum objects ===

<syntaxhighlight lang="pycon">
>>> import qutip 
>>> import numpy as np
>>> psi = qutip.Qobj([[0.6], [0.8]]) # create quantum state from a list
>>> psi
Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket
Qobj data =
[[0.6]
 [0.8]]
>>> phi=qutip.Qobj(np.array([0.8, -0.6])) # create quantum state from a numpy-array
>>> phi
Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket
Qobj data =
[[ 0.8]
 [-0.6]]
>>> e0=qutip.basis(2, 0) # create a basis vector
>>> e0
Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket
Qobj data =
[[1.]
 [0.]]
>>> A=qutip.Qobj(np.array([[1,2j], [-2j,1]])) # create quantum operator from numpy array
>>> A
Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True
Qobj data =
[[1.+0.j 0.+2.j]
 [0.-2.j 1.+0.j]]
>>> qutip.sigmay() # some common quantum objects, like pauli matrices, are predefined in the qutip package
Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True
Qobj data =
[[0.+0.j 0.-1.j]
 [0.+1.j 0.+0.j]]
</syntaxhighlight>

=== Basic operations ===
<syntaxhighlight lang="pycon">
>>> A*qutip.sigmax()+qutip.sigmay() # we can add and multiply quantum objects of compatible shape and dimension
Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False
Qobj data =
[[0.+2.j 1.-1.j]
 [1.+1.j 0.-2.j]]
>>> psi.dag() # hermitian conjugate
Quantum object: dims = [[1], [2]], shape = (1, 2), type = bra
Qobj data =
[[0.6 0.8]]
>>> psi.proj() # projector onto a quantum state
Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True
Qobj data =
[[0.36 0.48]
 [0.48 0.64]]
>>> A.tr() # trace of operator
2.0
>>> A.eigenstates() # diagonalize an operator
(array([-1.,  3.]), array([Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket
       Qobj data =
       [[-0.70710678+0.j        ]
        [ 0.        -0.70710678j]]                                  ,
       Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket
       Qobj data =
       [[-0.70710678+0.j        ]
        [ 0.        +0.70710678j]]                                  ],
      dtype=object))
>>> (1j * A).expm() # matrix exponential of an operator
Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = False
Qobj data =
[[-0.2248451-0.35017549j -0.4912955-0.7651474j ]
 [ 0.4912955+0.7651474j  -0.2248451-0.35017549j]]
>>> qutip.tensor(qutip.sigmaz(), qutip.sigmay()) # tensor product
Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = True
Qobj data =
[[0.+0.j 0.-1.j 0.+0.j 0.+0.j]
 [0.+1.j 0.+0.j 0.+0.j 0.+0.j]
 [0.+0.j 0.+0.j 0.+0.j 0.+1.j]
 [0.+0.j 0.+0.j 0.-1.j 0.+0.j]]
</syntaxhighlight>

=== Time evolution ===

<syntaxhighlight lang="pycon">
>>> Hamiltonian = qutip.sigmay()
>>> times = np.linspace(0, 2, 10)
>>> result = qutip.sesolve(Hamiltonian, psi, times, [psi.proj(), phi.proj()]) # unitary time evolution of a system according to schroedinger equation
>>> expectpsi, expectphi = result.expect # expectation values of projectors onto psi and phi 
>>> plt.figure(dpi=200)
>>> plt.plot(times, expectpsi)
>>> plt.plot(times, expectphi)
>>> plt.legend([r"$\psi$",r"$\phi$"])
>>> plt.show()
</syntaxhighlight>

{{gallery
|width=400 | height=300
|align=center
|File:Qutip example simulation.png
|results of exemplary simulation: probabilities to measure the states <math>\psi</math> and <math>\phi</math> as functions of time.
}}
{{-}}

Simulating a non-unitary time evolution according to the Lindblad Master Equation is possible with the <code>qutip.mesolve</code> function <ref>{{Cite web
| url = https://qutip.org/docs/latest/guide/dynamics/dynamics-master.html
| title = Lindblad Master Equation Solver
| author = ((QuTiP developers and contributors))
| access-date = 2022-07-24
}}</ref>

== References ==
<references />

== External links ==
* {{Official website|https://qutip.org/}}
* {{GitHub|qutip/qutip}}

[[Category:Articles with example Python (programming language) code]]
[[Category:Computational physics]]
[[Category:Free software programmed in Python]]
[[Category:Simulation software]]
[[Category:Software using the BSD license]]
[[Category:Quantum Monte Carlo]]