def _single_expect(oper, state):
"""
Private function used by expect
"""
if isinstance(oper, Qobj) and isinstance(state, Qobj):
if isoper(oper):
if state.type == 'oper':
# calculates expectation value via TR(op*rho)
prod = oper.data * state.data
tr = sum(prod.diagonal()) # sum of diagonal elements
if oper.isherm and state.isherm: # if hermitian
return float(np.real(tr))
else: # not hermitian
return tr
elif state.type == 'ket':
# calculates expectation value via <psi|op|psi>
# prod = state.data.conj().T * (oper.data * state.data)
prod = state.data.conj().T.dot(oper.data * state.data)
if oper.isherm:
return float(np.real(prod[0, 0]))
else:
return prod[0, 0]
else:
raise TypeError('Invalid operand types')
# eseries
#
elif isinstance(oper, Qobj) and isinstance(state, eseries):
out = eseries()
if isoper(state.ampl[0]):
out.rates = state.rates
out.ampl = np.array([expect(oper, a) for a in state.ampl])
else:
out.rates = np.array([])
out.ampl = np.array([])
for m in range(len(state.rates)):
op_m = state.ampl[m].data.conj().T * oper.data
for n in range(len(state.rates)):
a = op_m * state.ampl[n].data
if isinstance(a, sp.spmatrix):
a = a.todense()
out.rates = np.append(out.rates,
state.rates[n] - state.rates[m])
out.ampl = np.append(out.ampl, a)
return out
else: # unsupported types
raise TypeError('Arguments must be quantum objects or eseries')
def _single_expect(oper, state):
"""
Private function used by expect
"""
if isinstance(oper, Qobj) and isinstance(state, Qobj):
if isoper(oper):
if state.type == 'oper':
# calculates expectation value via TR(op*rho)
prod = oper.data * state.data
tr = sum(prod.diagonal()) # sum of diagonal elements
if oper.isherm and state.isherm: # if hermitian
return float(np.real(tr))
else: # not hermitian
return tr
elif state.type == 'ket':
# calculates expectation value via <psi|op|psi>
# prod = state.data.conj().T * (oper.data * state.data)
prod = state.data.conj().T.dot(oper.data * state.data)
if oper.isherm:
return float(np.real(prod[0, 0]))
else:
return prod[0, 0]
else:
raise TypeError('Invalid operand types')
# eseries
#
elif isinstance(oper, Qobj) and isinstance(state, eseries):
out = eseries()
if isoper(state.ampl[0]):
out.rates = state.rates
out.ampl = np.array([expect(oper, a) for a in state.ampl])
else:
out.rates = np.array([])
out.ampl = np.array([])
for m in range(len(state.rates)):
op_m = state.ampl[m].data.conj().T * oper.data
for n in range(len(state.rates)):
a = op_m * state.ampl[n].data
if isinstance(a, sp.spmatrix):
a = a.todense()
out.rates = np.append(out.rates, state.rates[n] -
state.rates[m])
out.ampl = np.append(out.ampl, a)
return out
else: # unsupported types
raise TypeError('Arguments must be quantum objects or eseries')
def ode2es(L, rho0):
"""Creates an exponential series that describes the time evolution for the
initial density matrix (or state vector) `rho0`, given the Liouvillian
(or Hamiltonian) `L`.
Parameters
----------
L : qobj
Liouvillian of the system.
rho0 : qobj
Initial state vector or density matrix.
Returns
-------
ode_series : eseries
``eseries`` represention of the system dynamics.
"""
if issuper(L):
# check initial state
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = rho0 * rho0.dag()
w, v = la.eig(L.full())
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = prod(rho0.shape)
r0 = mat2vec(rho0.full())
v0 = la.solve(v,r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(vec2mat(vv[:,i]), dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, w[i])
else:
out = eseries(qo, w[i])
elif isoper(L):
if not isket(rho0):
raise TypeError('Second argument must be a ket if first is a Hamiltonian.')
w, v = la.eig(L.full())
# w[i] = eigenvalue i
# v[:,i] = eigenvector i
rlen = prod(rho0.shape)
r0 = rho0.full()
v0 = la.solve(v,r0)
vv = v * sp.spdiags(v0.T, 0, rlen, rlen)
out = None
for i in range(rlen):
qo = Qobj(matrix(vv[:,i]).T, dims=rho0.dims, shape=rho0.shape)
if out:
out += eseries(qo, -1.0j * w[i])
else:
out = eseries(qo, -1.0j * w[i])
else:
raise TypeError('First argument must be a Hamiltonian or Liouvillian.')
return estidy(out)
# Aesthetic function
def wait():
inp = input("\nProceed? [Y/n]: ")
while inp != 'y' and inp != 'Y':
inp = input("Proceed? [Y/n]: ")
print("\n")
""" --------------- </Exponential Series Objects Examples> --------------- """
print("Exponential Series:\n")
print("sigma-x * exp(i.w.t)")
omega = 1.0 # w
es1 = eseries(sigmax(), 1j * omega)
print(es1)
print("\nsigma-x * cos(w.t)")
omega = 1.0
es2 = eseries(0.5 * sigmax(), 1j * omega) + eseries(0.5 * sigmax(),
-1j * omega)
print(es2)
wait()
""" --------------- </Evaluate the eseries object at various times> --------------- """
# At t = 0
print("sigma-x * cos(w.t) at time t = 0\n", esval(es2, 0.0))
