def propagator_steadystate(U):
"""Find the steady state for successive applications of the propagator :math:`U`.
Parameters
----------
U : qobj
Operator representing the propagator.
Returns
-------
a : qobj
Instance representing the steady-state vector.
"""
evals, evecs = la.eig(U.full())
ev_min, ev_idx = get_min_and_index(abs(evals - 1.0))
N = int(sqrt(len(evals)))
evecs = evecs.T
rho = Qobj(vec2mat(evecs[ev_idx]))
return rho * (1 / real(rho.tr()))
def propagator_steadystate(U):
"""Find the steady state for successive applications of the propagator :math:`U`.
Parameters
----------
U : qobj
Operator representing the propagator.
Returns
-------
a : qobj
Instance representing the steady-state vector.
"""
evals,evecs = la.eig(U.full())
ev_min, ev_idx = get_min_and_index(abs(evals-1.0))
N = int(sqrt(len(evals)))
evecs = evecs.T
rho = Qobj(vec2mat(evecs[ev_idx]))
return rho * (1 / real(rho.tr()))
def _qfunc_check_state(state: Qobj):
if not isinstance(state, Qobj):
raise TypeError(f"state must be Qobj, but is {state}")
# This is only approximate, but it's enough for our purposes; doing more
# than this would take computational effort we don't _need_ to do.
isdm = (state.isoper and state.dims[0] == state.dims[1] and state.isherm
and abs(state.tr() - 1) < qutip.settings.atol)
if not (state.isket or isdm):
raise ValueError(
f"state must be a ket or density matrix, but is {state}")
if len(state.dims[0]) != 1:
raise ValueError(
"state must not have tensor structure, but has dimensions:"
f" {state.dims}")
return state
print("Sigma Z: ", sz)
wait()
# Arithmetic with quantum objects
H = 1.0 * sz + 0.1 * sy
print("Qubit Hamiltonian (H = sz + 0.1 * sy):\n", H)
print("Eigenenergies/ Eigenvalues of H: ", H.eigenenergies())
wait()
print("sy: ", sy)
print("Hermitian Conjugate/Conjugate Transpose of sy: ",
sy.dag()) # Same as sy
print("Trace of sy: ", sy.tr())
wait()
""" --------------- </States> --------------- """
# Fundamental Basis States (Fock states of oscillator modes)
N = 2 # number of states in the hilbert space
n = 1 # state which will be occupied
print("Basis with {N} states, where state {n} is occupied:\n".format(N=N, n=n),
basis(N, n)) # Same as fock(N,n)
print()
# Similarly,
print("Basis with {N} states, where state {n} is occupied:\n".format(N=4, n=2),
fock(4, 2))
