QuTiP

The idea for the QuTip project was conceived in 2010 by PhD student Paul Nation, who was using the 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".{{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}} As a postdoctoral fellow, at the 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.

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.{{cite web |url=https://github.com/qutip

|title= QuTiP - Quantum Toolbox in Python

|publisher= GitHub

|access-date= 11 August 2022}} It has grown in popularity amongst physicists, with over 250.000 downloads in the year 2021.{{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}}

>>> 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]]

>>> 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]]

>>> 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()

{{gallery

|width=400 | height=300

|align=center

|File:Qutip example simulation.png

|results of exemplary simulation: probabilities to measure the states $\backslash psi$ and $\backslash phi$ as functions of time.

}}

{{-}}

Simulating a non-unitary time evolution according to the Lindblad Master Equation is possible with the qutip.mesolve function {{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

}}

• {{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