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test_basis_transformation.py
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test_basis_transformation.py
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# This file is part of QuTiP: Quantum Toolbox in Python.
#
# Copyright (c) 2011 and later, Paul D. Nation and Robert J. Johansson.
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
# of its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
import sys
from qutip import *
from numpy.testing import assert_equal, assert_, run_module_suite
import scipy
def test_Transformation1():
"Transform 2-level to eigenbasis and back"
H1 = scipy.rand() * sigmax() + scipy.rand() * sigmay() + \
scipy.rand() * sigmaz()
evals, ekets = H1.eigenstates()
Heb = H1.transform(ekets) # eigenbasis (should be diagonal)
H2 = Heb.transform(ekets, True) # back to original basis
assert_equal((H1 - H2).norm() < 1e-6, True)
def test_Transformation2():
"Transform 10-level real-values to eigenbasis and back"
N = 10
H1 = Qobj((0.5 - scipy.rand(N, N)))
H1 = H1 + H1.dag()
evals, ekets = H1.eigenstates()
Heb = H1.transform(ekets) # eigenbasis (should be diagonal)
H2 = Heb.transform(ekets, True) # back to original basis
assert_equal((H1 - H2).norm() < 1e-6, True)
def test_Transformation3():
"Transform 10-level to eigenbasis and back"
N = 10
H1 = Qobj((0.5 - scipy.rand(N, N)) + 1j * (0.5 - scipy.rand(N, N)))
H1 = H1 + H1.dag()
evals, ekets = H1.eigenstates()
Heb = H1.transform(ekets) # eigenbasis (should be diagonal)
H2 = Heb.transform(ekets, True) # back to original basis
assert_equal((H1 - H2).norm() < 1e-6, True)
def test_Transformation4():
"Transform 10-level imag to eigenbasis and back"
N = 10
H1 = Qobj(1j * (0.5 - scipy.rand(N, N)))
H1 = H1 + H1.dag()
evals, ekets = H1.eigenstates()
Heb = H1.transform(ekets) # eigenbasis (should be diagonal)
H2 = Heb.transform(ekets, True) # back to original basis
assert_equal((H1 - H2).norm() < 1e-6, True)
def test_Transformation5():
"Consistency between transformations of kets and density matrices"
N = 4
psi0 = rand_ket(N)
# generate a random basis
evals, rand_basis = rand_dm(N, density=1).eigenstates()
rho1 = ket2dm(psi0).transform(rand_basis, True)
rho2 = ket2dm(psi0.transform(rand_basis, True))
assert_((rho1 - rho2).norm() < 1e-6)
def test_Transformation5():
"Check diagonalization via eigenbasis transformation"
cx, cy, cz = np.random.rand(), np.random.rand(), np.random.rand()
H = cx * sigmax() + cy * sigmay() + cz * sigmaz()
evals, evecs = H.eigenstates()
Heb = H.transform(evecs).tidyup() # Heb should be diagonal
assert_(abs(Heb.full() - np.diag(Heb.full().diagonal())).max() < 1e-6)
if __name__ == "__main__":
run_module_suite()