test_basis_transformation.py

# This file is part of QuTiP: Quantum Toolbox in Python.
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import numpy as np
from numpy.testing import assert_equal, assert_, run_module_suite
import scipy

from qutip import sigmax, sigmay, sigmaz, Qobj, rand_ket, rand_dm, ket2dm


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_Transformation6():
    "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()