def single_hamiltonian(cav_dim, w_1, w_c, g_factor):
"""Return a QObj denoting a hamiltonian for one qubit coupled to a
cavity."""
return (w_c * qt.tensor(qt.num(cav_dim), I) +
0.5 * w_1 * qt.tensor(qt.qeye(cav_dim), I) +
g_factor * qt.tensor(qt.create(cav_dim), SMinus) +
g_factor * qt.tensor(qt.destroy(cav_dim), SPlus))
def __init__(self, N_field_levels, coupling=None, N_qubits=1):
# basic parameters
self.N_field_levels = N_field_levels
self.N_qubits = N_qubits
if coupling is None:
self.g = 0
else:
self.g = coupling
# bare operators
self.idcavity = qt.qeye(self.N_field_levels)
self.idqubit = qt.qeye(2)
self.a_bare = qt.destroy(self.N_field_levels)
self.sm_bare = qt.sigmam()
self.sz_bare = qt.sigmaz()
self.sx_bare = qt.sigmax()
self.sy_bare = qt.sigmay()
# 1 atom 1 cavity operators
self.jc_a = qt.tensor(self.a_bare, self.idqubit)
self.jc_sm = qt.tensor(self.idcavity, self.sm_bare)
self.jc_sx = qt.tensor(self.idcavity, self.sx_bare)
self.jc_sy = qt.tensor(self.idcavity, self.sy_bare)
self.jc_sz = qt.tensor(self.idcavity, self.sz_bare)
def construct_hamiltonian(self, number_of_spins, alpha):
"""
following example
http://qutip.googlecode.com/svn/doc/2.0.0/html/examples/me/ex-24.html
returns H0 - hamiltonian without the B field
and y_list - list of sigma_y operators
"""
N = number_of_spins
si = qeye(2)
sx = sigmax()
sy = sigmay()
# constructing a list of operators sx_list and sy_list where
# the operator sx_list[i] applies sigma_x on the ith particle and
# identity to the rest
sx_list = []
sy_list = []
for n in range(N):
op_list = []
for m in range(N):
op_list.append(si)
op_list[n] = sx
sx_list.append(tensor(op_list))
op_list[n] = sy
sy_list.append(tensor(op_list))
# construct the hamiltonian
H0 = 0
# ising coupling term, time independent
for i in range(N):
for j in range(N):
if i < j:
H0 -= abs(i - j) ** -alpha * sx_list[i] * sx_list[j]
H1 = 0
for i in range(N):
H1 -= sy_list[i]
return H0, H1
def testJCZeroTemperature():
"""
brmesolve: Jaynes-Cummings model, zero temperature
"""
N = 10
a = tensor(destroy(N), identity(2))
sm = tensor(identity(N), destroy(2))
psi0 = ket2dm(tensor(basis(N, 1), basis(2, 0)))
a_ops = [(a + a.dag())]
e_ops = [a.dag() * a, sm.dag() * sm]
w0 = 1.0 * 2 * np.pi
g = 0.05 * 2 * np.pi
kappa = 0.05
times = np.linspace(0, 2 * 2 * np.pi / g, 1000)
c_ops = [np.sqrt(kappa) * a]
H = w0 * a.dag() * a + w0 * sm.dag() * sm + \
g * (a + a.dag()) * (sm + sm.dag())
res_me = mesolve(H, psi0, times, c_ops, e_ops)
res_brme = brmesolve(H, psi0, times, a_ops, e_ops,
spectra_cb=[lambda w: kappa * (w >= 0)])
for idx, e in enumerate(e_ops):
diff = abs(res_me.expect[idx] - res_brme.expect[idx]).max()
assert_(diff < 5e-2) # accept 5% error
def test_spectrum_espi_legacy():
"""
correlation: legacy spectrum from es and pi methods
"""
# use JC model
N = 4
wc = wa = 1.0 * 2 * np.pi
g = 0.1 * 2 * np.pi
kappa = 0.75
gamma = 0.25
n_th = 0.01
a = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), destroy(2))
H = wc * a.dag() * a + wa * sm.dag() * sm + \
g * (a.dag() * sm + a * sm.dag())
c_ops = [np.sqrt(kappa * (1 + n_th)) * a,
np.sqrt(kappa * n_th) * a.dag(),
np.sqrt(gamma) * sm]
wlist = 2 * np.pi * np.linspace(0.5, 1.5, 100)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
spec1 = spectrum_ss(H, wlist, c_ops, a.dag(), a)
spec2 = spectrum_pi(H, wlist, c_ops, a.dag(), a)
assert_(max(abs(spec1 - spec2)) < 1e-3)
def construct_hamiltonian(self, number_of_spins, alpha, B):
'''
following example
http://qutip.googlecode.com/svn/doc/2.0.0/html/examples/me/ex-24.html
'''
N = number_of_spins
si = qeye(2)
sx = sigmax()
sy = sigmay()
#constructing a list of operators sx_list and sy_list where
#the operator sx_list[i] applies sigma_x on the ith particle and
#identity to the rest
sx_list = []
sy_list = []
for n in range(N):
op_list = []
for m in range(N):
op_list.append(si)
op_list[n] = sx
sx_list.append(tensor(op_list))
op_list[n] = sy
sy_list.append(tensor(op_list))
#construct the hamiltonian
H = 0
#magnetic field term, hamiltonian is in units of J0
for i in range(N):
H-= B * sy_list[i]
#ising coupling term
for i in range(N):
for j in range(N):
if i < j:
H+= abs(i - j)**-alpha * sx_list[i] * sx_list[j]
return H
def test_spectrum_espi():
"""
correlation: comparing spectrum from es and pi methods
"""
# use JC model
N = 4
wc = wa = 1.0 * 2 * np.pi
g = 0.1 * 2 * np.pi
kappa = 0.75
gamma = 0.25
n_th = 0.01
a = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), destroy(2))
H = wc * a.dag() * a + wa * sm.dag() * sm + \
g * (a.dag() * sm + a * sm.dag())
c_ops = [np.sqrt(kappa * (1 + n_th)) * a,
np.sqrt(kappa * n_th) * a.dag(),
np.sqrt(gamma) * sm]
wlist = 2 * pi * np.linspace(0.5, 1.5, 100)
spec1 = spectrum(H, wlist, c_ops, a.dag(), a, solver='es')
spec2 = spectrum(H, wlist, c_ops, a.dag(), a, solver='pi')
assert_(max(abs(spec1 - spec2)) < 1e-3)
def test_spectrum_esfft():
"""
correlation: comparing spectrum from es and fft methods
"""
# use JC model
N = 4
wc = wa = 1.0 * 2 * np.pi
g = 0.1 * 2 * np.pi
kappa = 0.75
gamma = 0.25
n_th = 0.01
a = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), destroy(2))
H = wc * a.dag() * a + wa * sm.dag() * sm + \
g * (a.dag() * sm + a * sm.dag())
c_ops = [np.sqrt(kappa * (1 + n_th)) * a,
np.sqrt(kappa * n_th) * a.dag(),
np.sqrt(gamma) * sm]
with warnings.catch_warnings():
warnings.simplefilter("ignore")
tlist = np.linspace(0, 100, 2500)
corr = correlation_ss(H, tlist, c_ops, a.dag(), a)
wlist1, spec1 = spectrum_correlation_fft(tlist, corr)
spec2 = spectrum_ss(H, wlist1, c_ops, a.dag(), a)
assert_(max(abs(spec1 - spec2)) < 1e-3)
def test_diagHamiltonian2():
"""
Diagonalization of composite systems
"""
H1 = scipy.rand() * sigmax() + scipy.rand() * sigmay() +\
scipy.rand() * sigmaz()
H2 = scipy.rand() * sigmax() + scipy.rand() * sigmay() +\
scipy.rand() * sigmaz()
H = tensor(H1, H2)
evals, ekets = H.eigenstates()
for n in range(len(evals)):
# assert that max(H * ket - e * ket) is small
assert_equal(amax(
abs((H * ekets[n] - evals[n] * ekets[n]).full())) < 1e-10, True)
N1 = 10
N2 = 2
a1 = tensor(destroy(N1), qeye(N2))
a2 = tensor(qeye(N1), destroy(N2))
H = scipy.rand() * a1.dag() * a1 + scipy.rand() * a2.dag() * a2 + \
scipy.rand() * (a1 + a1.dag()) * (a2 + a2.dag())
evals, ekets = H.eigenstates()
for n in range(len(evals)):
# assert that max(H * ket - e * ket) is small
assert_equal(amax(
abs((H * ekets[n] - evals[n] * ekets[n]).full())) < 1e-10, True)
def test_enr_destory_full():
"Excitation-number-restricted state-space: full state space"
a1, a2 = enr_destroy([4, 4], 4**2)
b1, b2 = tensor(destroy(4), identity(4)), tensor(identity(4), destroy(4))
assert_(a1 == b1)
assert_(a2 == b2)
def compute(N, wc, wa, glist, use_rwa):
# Pre-compute operators for the hamiltonian
a = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), destroy(2))
nc = a.dag() * a
na = sm.dag() * sm
idx = 0
na_expt = zeros(shape(glist))
nc_expt = zeros(shape(glist))
for g in glist:
# recalculate the hamiltonian for each value of g
if use_rwa:
H = wc * nc + wa * na + g * (a.dag() * sm + a * sm.dag())
else:
H = wc * nc + wa * na + g * (a.dag() + a) * (sm + sm.dag())
# find the groundstate of the composite system
evals, ekets = H.eigenstates()
psi_gnd = ekets[0]
na_expt[idx] = expect(na, psi_gnd)
nc_expt[idx] = expect(nc, psi_gnd)
idx += 1
return nc_expt, na_expt, ket2dm(psi_gnd)
def rsb_flop(rho0, W, eta, delta, theta, phi, c_op_list = [], return_op_list = []):
''' Return values of atom and motion populations during red sideband Rabi flop
for rotation angles theta. Calls numerical solution of master equation for the
Jaynes-Cummings Hamiltonian.
@ var rho0: initial density matrix
@ var W: bare Rabi frequency
@ var delta: detuning between atom and motion
@ var theta: list of Rabi rotation angle (i.e. theta, or g*time)
@ var phi: phase of the input laser pulse
@ var c_op_list: list of collapse operators for the master equation treatment
@ var return_op_list: list of population operators the values of which will be returned
returns: time, populations of motional mode and atom
'''
N = shape(rho0.data)[0]/2 # assume N Fock states and two atom states
a = tensor(destroy(N), qeye(2))
sm = tensor( qeye(N), destroy(2))
Wrsb = destroy(N)
one_then_zero = ([float(x<1) for x in range(N)])
Wrsb.data = csr_matrix( destroy(N).data.dot( np.diag( rabi_coupling(N,-1,eta) / np.sqrt(one_then_zero+np.linspace(0,N-1,N)) ) ) )
Arsb = tensor(Wrsb, qeye(2))
# use the rotating wave approxiation
# Note that the regular a, a.dag() is used for the time evolution of the oscillator
# Arsb is the destruction operator including the state dependent coupling strength
H = delta * a.dag() * a + \
(1./2.) * W * (Arsb.dag() * sm * exp(1j*phi) + Arsb * sm.dag() * exp(-1j*phi))
if hasattr(theta, '__len__'):
if len(theta)>1: # I need to be able to pass a list of length zero and not get an error
time = theta/(eta*W)
else:
time = theta/(eta*W)
output = mesolve(H, rho0, time, c_op_list, return_op_list)
return time, output
def test_mc_dtypes2():
"Monte-carlo: check for correct dtypes (average_states=False)"
# set system parameters
kappa = 2.0 # mirror coupling
gamma = 0.2 # spontaneous emission rate
g = 1 # atom/cavity coupling strength
wc = 0 # cavity frequency
w0 = 0 # atom frequency
wl = 0 # driving frequency
E = 0.5 # driving amplitude
N = 5 # number of cavity energy levels (0->3 Fock states)
tlist = np.linspace(0, 10, 5) # times for expectation values
# construct Hamiltonian
ida = qeye(N)
idatom = qeye(2)
a = tensor(destroy(N), idatom)
sm = tensor(ida, sigmam())
H = (w0 - wl) * sm.dag() * sm + (wc - wl) * a.dag() * a + \
1j * g * (a.dag() * sm - sm.dag() * a) + E * (a.dag() + a)
# collapse operators
C1 = np.sqrt(2 * kappa) * a
C2 = np.sqrt(gamma) * sm
C1dC1 = C1.dag() * C1
C2dC2 = C2.dag() * C2
# intial state
psi0 = tensor(basis(N, 0), basis(2, 1))
opts = Options(average_expect=False)
data = mcsolve(
H, psi0, tlist, [C1, C2], [C1dC1, C2dC2, a], ntraj=5, options=opts)
assert_equal(isinstance(data.expect[0][0][1], float), True)
assert_equal(isinstance(data.expect[0][1][1], float), True)
assert_equal(isinstance(data.expect[0][2][1], complex), True)
def to_matrix(self, fd):
n = num(fd)
a = destroy(fd)
ic = qeye(fd)
sz = sigmaz()
sm = sigmam()
iq = qeye(2)
ms = {
"id": tensor(iq, ic),
"a*ad" : tensor(iq, n),
"a+hc" : tensor(iq, a),
"sz" : tensor(sz, ic),
"sm+hc" : tensor(sm, ic)
}
H0 = 0
H1s = []
for (p1, p2), v in self.coefs.items():
h = ms[p1] * ms[p2]
try:
term = float(v) * h
if not term.isherm:
term += term.dag()
H0 += term
except ValueError:
H1s.append([h, v])
if not h.isherm:
replacement = lambda m: '(-' + m.group() + ')'
conj_v = re.sub('[1-9]+j', replacement, v)
H1s.append([h.dag(), conj_v])
if H1s:
return [H0] + H1s
else:
return H0
def carrier_flop(rho0, W, eta, delta, theta, phi, c_op_list = [], return_op_list = []):
''' Return values of atom and motion populations during carrier Rabi flop
for rotation angles theta. Calls numerical solution of master equation.
@ var rho0: initial density matrix
@ var W: bare Rabi frequency
@ var eta: Lamb-Dicke parameter
@ var delta: detuning between atom and motion
@ var theta: list of Rabi rotation angles (i.e. theta, or g*time)
@ var phi: phase of the input laser pulse
@ var c_op_list: list of collapse operators for the master equation treatment
@ var return_op_list: list of population operators the values of which will be returned
returns: time, populations of motional mode and atom
'''
N = shape(rho0.data)[0]/2 # assume N Fock states and two atom states
a = tensor(destroy(N), qeye(2))
Wc = qeye(N)
Wc.data = csr_matrix( qeye(N).data.dot( np.diag(rabi_coupling(N,0,eta) ) ) )
sm = tensor( Wc, destroy(2))
# use the rotating wave approxiation
H = delta * a.dag() * a + \
(1./2.)* W * (sm.dag()*exp(1j*phi) + sm*exp(-1j*phi))
if hasattr(theta, '__len__'):
if len(theta)>1: # I need to be able to pass a list of length zero and not get an error
time = theta/W
else:
time = theta/W
output = mesolve(H, rho0, time, c_op_list, return_op_list)
return time, output
def M_ops(N,j,i):
k = Kspace(N)
op = k[i]*k[j].dag()
if i==j+1 or i==j-1:
return qutip.tensor(B_ops(N,j,i),op)
if i==j and (j==0 or j==N-1):
return qutip.tensor(B_ops(N,j,i),op)
def collapse_operators(N, n_th_a, gamma_motion, gamma_motion_phi, gamma_atom):
'''Collapse operators for the master equation of a single atom and a harmonic oscillator
@ var N: size of the harmonic oscillator Hilbert space
@ var n_th: temperature of the noise bath in quanta
@ var gamma_motion: heating rate of the motion
@ var gamma_motion_phi: dephasing rate of the motion
@ var gamma_atom: decay rate of the atom
returns: list of collapse operators for master equation solution of atom + harmonic oscillator
'''
a = tensor(destroy(N), qeye(2))
sm = tensor(qeye(N), destroy(2))
c_op_list = []
rate = gamma_motion * (1 + n_th_a)
if rate > 0.0:
c_op_list.append(sqrt(rate) * a)
rate = gamma_motion * n_th_a
if rate > 0.0:
c_op_list.append(sqrt(rate) * a.dag())
rate = gamma_motion_phi
if rate > 0.0:
c_op_list.append(sqrt(rate) * a.dag() * a)
rate = gamma_atom
if rate > 0.0:
c_op_list.append(sqrt(rate) * sm)
return c_op_list
def direct_hamiltonian(w_1, w_2, g_factor):
"""Return a QObj denoting a hamiltonian for two qubits interacting with the
cavity mode eliminated."""
return (
0.5 * w_1 * qt.tensor(SZ, I) +
0.5 * w_2 * qt.tensor(I, SZ) +
g_factor * qt.tensor(SPlus, SMinus) +
g_factor * qt.tensor(SMinus, SPlus))
def full_approx(cav_dim, w_1, w_2, w_c, g_factor):
a = qt.destroy(cav_dim)
num = a.dag() * a
return (
g_factor * qt.tensor(qt.qeye(cav_dim), SMinus, SPlus) +
g_factor * qt.tensor(qt.qeye(cav_dim), SPlus, SMinus) +
w_c * qt.tensor(num, I, I) +
0.5 * w_1 * qt.tensor(qt.qeye(cav_dim), SZ, I) +
0.5 * w_2 * qt.tensor(qt.qeye(cav_dim), I, SZ))
def population_operators(N):
'''Population operators for the master equation
@ var N: size of the oscillator Hilbert space
returns: list of population operators for the harmonic oscillator and the atom
'''
a = tensor(destroy(N), qeye(2))
sm = tensor( qeye(N), destroy(2))
return [a.dag()*a, sm.dag()*sm]
def Ren_gate(carbon_nr, B_field=304.22):
'''create a Ren gate for given carbon number, only interacting with the electron spin '''
U0, U1, U0id, U1id = nuclear_Ren_matrix(carbon_nr, B_field)
Ren = qutip.tensor(rho0,U0)+qutip.tensor(rho1,U1)
Ren_id = qutip.tensor(rho0,U0id)+qutip.tensor(rho1,U1id)
return Ren, Ren_id
def interaction_picture(cav_dim, w_1, w_2, w_c, g_1, g_2):
delta_1 = abs(w_1 - w_c)
delta_2 = abs(w_2 - w_c)
a = qt.destroy(cav_dim)
H0 = qt.tensor(qt.qeye(cav_dim), I, I)
H1 = [g_1 * qt.tensor(a.dag(),SMinus,I), 'exp(-1j *'+str(delta_1)+'*t)']
H2 = [g_2 * qt.tensor(a.dag(),I,SMinus), 'exp(-1j *'+str(delta_2)+'*t)']
H3 = [g_1 * qt.tensor(a,SPlus,I), 'exp(1j *'+str(delta_1)+'*t)']
H4 = [g_2 * qt.tensor(a,I,SPlus), 'exp(1j *'+str(delta_2)+'*t)']
return [H0,H1,H2,H3,H4]
def test_EntropyConcurrence():
"Concurrence"
# check concurrence = 1 for maximal entangled (Bell) state
bell = ket2dm(
(tensor(basis(2), basis(2)) + tensor(basis(2, 1), basis(2, 1))).unit())
assert_equal(abs(concurrence(bell) - 1.0) < 1e-15, True)
# check all concurrence values >=0
rhos = [rand_dm(4, dims=[[2, 2], [2, 2]]) for k in range(10)]
for k in rhos:
assert_equal(concurrence(k) >= 0, True)
def Hamiltonian_toymodel(theta, phi): ## Defining Constants omega = 1.4 * 10**6 m_b = 5.7883818066*10**-5 par=m_b*2.417990504024*10**11 # s-1/mT a1 = np.array([-.0989, -.0989, 1.7569]) * par # /mT a2 = np.array([0.0,0.0,1.0812]) * par H_a_zeeman_nt = omega * (Sx * mt.sin(theta) * mt.cos(phi) + Sy * mt.sin(theta) * mt. sin(phi) + Sz * mt.cos(theta)) Ha_zeeman = qt.tensor(H_a_zeeman_nt, qt.identity(3)) H_a_hfi = a1[0] * qt.tensor(Sx, I2_x) + a1[1] * qt.tensor(Sy, I2_y) + a1[2] * qt.tensor(Sz, I2_z) H_a = Ha_zeeman + H_a_hfi H_a_eigen, H_a_eigenstates = H_a.eigenstates() H_b_zeeman_nt = omega * (Sx * mt.sin(theta) * mt.cos(phi) + Sy * mt.sin(theta) * mt. sin(phi) + Sz * mt.cos(theta)) Hb_zeeman = qt.tensor(H_b_zeeman_nt, qt.identity(3)) H_b_hfi = a2[0] * qt.tensor(Sx, I2_x) + a2[1] * qt.tensor(Sy, I2_y) + a2[2] * qt.tensor(Sz, I2_z) H_b = Hb_zeeman + H_b_hfi H_b_eigen, H_b_eigenstates = H_b.eigenstates() return (H_a_eigen, H_a_eigenstates, H_b_eigen, H_b_eigenstates)
def getBasis (a,G) : #get the basis states according to the binary of a: 10 -> |10>
dimG = G.shape[0]
CareStateDim = int(log(dimG,2))
if a == 0:
B = [qt.basis(2,0)]*(CareStateDim)
return qt.tensor(B)
c = binary(a)
if dimG == 8:
return qt.tensor(qt.basis(2,int(c[0])) , qt.basis(2,int(c[1])), qt.basis(2,int(c[2])))
if dimG == 4:
return qt.tensor(qt.basis(2,int(c[1])) , qt.basis(2,int(c[2])))
def _localop(op, l, k):
"""
Create a local operator on the l'th system by tensoring
with identity operators on all the other k-1 systems
"""
if l < 1 or l > k:
raise IndexError('index l out of range')
h = op
I = qt.qeye(op.shape[0])
I.dims = op.dims
for i in range(1, l):
h = qt.tensor(I, h)
for i in range(l+1, k+1):
h = qt.tensor(h, I)
return h
def ptracetest():
gamma = 1.
neq = 2
psi0 = qt.basis(neq,neq-1)
psi0 = qt.tensor(psi0,psi0)
H = qt.tensor(qt.sigmax(),qt.sigmay())
c1 = np.sqrt(gamma)*qt.sigmax()
e1 = np.sqrt(gamma)*qt.sigmaz()
c_ops = [qt.tensor(c1,c1)]
e_ops = [qt.tensor(e1,e1),qt.tensor(c1,c1)]
#e_ops = []
tlist = np.linspace(0,10,100)
ntraj = 2000
ptrace_sel = [0]
sol_f90 = mcf90.mcsolve_f90(H,psi0,tlist,c_ops,e_ops,ntraj=ntraj,
ptrace_sel=ptrace_sel,calc_entropy=True)
def get_M0(H,lindblads,tau):
_dims = H.dims[0]
J = qt.Qobj(np.zeros_like(H.data.todense()),dims=[_dims,_dims])
for Op in lindblads:
J += Op.dag()*Op
J *= 0.5
return qt.tensor([qt.qeye(dim) for dim in _dims]) - tau*(1j*H - J)
def build_S_total(n_spins,operator):
_dims = [2]*n_spins
op = qt.Qobj(dims=[_dims,_dims])
_id = np.identity(n_spins)
for i in range(n_spins):
op += qt.tensor([operator if el == 1 else I for el in _id[i,:]])
return op
def _pseudo_inverse_dense(L, rhoss, method='direct', **pseudo_args):
"""
Internal function for computing the pseudo inverse of an Liouvillian using
dense matrix methods. See pseudo_inverse for details.
"""
if method == 'direct':
rho_vec = np.transpose(mat2vec(rhoss.full()))
tr_mat = tensor([identity(n) for n in L.dims[0][0]])
tr_vec = np.transpose(mat2vec(tr_mat.full()))
N = np.prod(L.dims[0][0])
I = np.identity(N * N)
P = np.kron(np.transpose(rho_vec), tr_vec)
Q = I - P
LIQ = np.linalg.solve(L.full(), Q)
R = np.dot(Q, LIQ)
return Qobj(R, dims=L.dims)
elif method == 'numpy':
return Qobj(np.linalg.pinv(L.full()), dims=L.dims)
elif method == 'scipy':
return Qobj(la.pinv(L.full()), dims=L.dims)
elif method == 'scipy2':
return Qobj(la.pinv2(L.full()), dims=L.dims)
else:
raise ValueError("Unsupported method '%s'. Use 'direct' or 'numpy'" %
method)
&= \Liouville(t) \op{\rho}(t) \\
&= - i \left[\op{H}(t), \op{\rho}(t)\right]
+ \sum_{k=1,2} \left(
\op{L}_{k} \op{\rho}(t) \op{L}_{k}^\dagger
- \frac{1}{2}
\op{L}_{k}^\dagger
\op{L}_{k} \op{\rho}(t)
- \frac{1}{2} \op{\rho}(t)
\op{L}_{k}^\dagger
\op{L}_{k}
\right)\,.
\end{split}
$$
"""
qutip.tensor(qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))
def liouvillian(omega, g, gamma, beta):
"""Liouvillian for the coupled system of qubit and TLS"""
H0_q = omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2))
# drive qubit Hamiltonian
H1_q = -0.5*qutip.operators.sigmax()
# drift TLS Hamiltonian
H0_T = qutip.tensor(omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2))\
def calc_throughput(scheme):
state = scheme.state
time = scheme.time
simulation_type = "IP"
if simulation_type == "IP":
proj1 = qt.Qobj([[1, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])
proj2 = (1/2)*qt.Qobj([[1, 0, 0, 1],
[0, 1, 1, 0],
[0, 1, 1, 0],
[1, 0, 0, 1]])
proj3 = (1/2)*qt.Qobj([[1, 0, 0, -1],
[0, 1, 1, 0],
[0, 1, 1, 0],
[-1, 0, 0, 1]])
state00 = qt.Qobj([[1/2, 0, 0, 1/2],
[0, 0, 0, 0],
[0, 0, 0, 0],
[1/2, 0, 0, 1/2]])
state01 = qt.Qobj([[1/2, 0, 0, -1/2],
[0, 0, 0, 0],
[0, 0, 0, 0],
[-1/2, 0, 0, 1/2]])
state10 = (1/2)*qt.Qobj([[0, 0, 0, 0],
[0, 1, 1, 0],
[0, 1, 1, 0],
[0, 0, 0, 0]])
state11 = (1/2)*qt.Qobj([[0, 0, 0, 0],
[0, 1, -1, 0],
[0, -1, 1, 0],
[0, 0, 0, 0]])
proj1.dims = [[2, 2], [2, 2]]
proj2.dims = [[2, 2], [2, 2]]
proj3.dims = [[2, 2], [2, 2]]
state00.dims = [[2, 2], [2, 2]]
state01.dims = [[2, 2], [2, 2]]
state10.dims = [[2, 2], [2, 2]]
state11.dims = [[2, 2], [2, 2]]
elif simulation_type == "MP":
proj1 = qt.ket2dm(qt.basis(81, 28)) + qt.ket2dm(qt.basis(81, 12))
proj2 = qt.ket2dm(qt.basis(81, 28) + qt.basis(81, 12)) / 2 + \
qt.ket2dm(qt.basis(81, 28) - qt.basis(81, 12)) / 2
proj3 = qt.ket2dm(qt.basis(81, 28) + 1j*qt.basis(81, 12)) / 2 + \
qt.ket2dm(qt.basis(81, 28) - 1j*qt.basis(81, 12)) / 2
vec01 = qt.basis(9, 1)
vec10 = qt.basis(9, 3)
state00 = qt.ket2dm(qt.tensor(vec01, vec10) + qt.tensor(vec10, vec01))/2
state01 = qt.ket2dm(qt.tensor(vec01, vec10) - qt.tensor(vec10, vec01))/2
state10 = qt.ket2dm(qt.tensor(vec01, vec01) + qt.tensor(vec10, vec10))/2
state11 = qt.ket2dm(qt.tensor(vec01, vec01) - qt.tensor(vec10, vec10))/2
proj1.dims = [[9, 9], [9, 9]]
proj2.dims = [[9, 9], [9, 9]]
proj3.dims = [[9, 9], [9, 9]]
state00.dims = [[9, 9], [9, 9]]
state01.dims = [[9, 9], [9, 9]]
state10.dims = [[9, 9], [9, 9]]
state11.dims = [[9, 9], [9, 9]]
bb84 = False
if bb84:
qber1 = (state * proj1).tr()
qber2 = (state * proj2).tr()
skf = max(1 - binary_entropy(qber1) - binary_entropy(qber2), 0) # calc secret_key fraction
else:
p00 = (state * state00).tr()
p01 = (state * state01).tr()
p10 = (state * state10).tr()
p11 = (state * state11).tr()
normalisation = p00+p01+p10+p11
# define P' distribution as in https://iopscience.iop.org/article/10.1088/2058-9565/aab31b, eq D1 to D8
Px0 = (p00+p01)**2 + (p10+p11)**2
Px1 = 1-Px0
p00n = (p00**2+p01**2)/Px0
p01n = (2*p00*p01)/Px0
p10n = (p10**2+p11**2)/Px0
p11n = (2*p10*p11)/Px0
if ((p00 + p01) * (p10 + p11)) == 0:
Pbinary_entropy = 1
else:
Pbinary_entropy = (p00 * p10 + p01 * p11) / ((p00 + p01) * (p10 + p11))
skf = max(1-entropy([p00, p01, p10, p11], base=2)+(Px1/2)*binary_entropy(Pbinary_entropy),
(Px0/2)*(1-entropy([p00n, p01n, p10n, p11n], base=2)), 0)
return skf/time
def fock_state_on(d: dict, fock_trunc: int, N_modes: int):
''' d={mode number: # of photons} In the bare eigen basis
'''
# give me the value d[i] or 0 if d[i] does not exist
return qutip.tensor(*[qutip.basis(fock_trunc, d.get(i, 0))
for i in range(N_modes)])
def testMeasurementsOverSeparableStateAreLocal(self):
alice1outputs = [2, 2]
alice2outputs = [2, 3]
bobOutputs = [2, 2]
scenario = SequentialBellScenario([alice1outputs, alice2outputs],
bobOutputs)
epsilon = 0
plus = 1 / np.sqrt(2) * (qt.basis(2, 0) + qt.basis(2, 1))
minus = 1 / np.sqrt(2) * (qt.basis(2, 0) - qt.basis(2, 1))
Kplus = np.cos(epsilon) * plus * plus.dag() + np.sin(
epsilon) * minus * minus.dag()
Kminus = -np.cos(epsilon) * minus * minus.dag() + np.sin(
epsilon) * plus * plus.dag()
alice1Krauss = [
projectorsForQubitObservable(createQubitObservable([0, 0, 1])),
[Kplus, Kminus]
]
alice2blochVectors = [[0, 0, 1]]
alice2Observables = list(
map(lambda bloch: createQubitObservable(bloch),
alice2blochVectors))
alice2Effects = list(
map(
lambda qubitObservable: projectorsForQubitObservable(
qubitObservable), alice2Observables))
trineAlice2 = [[0, 0, 1],
[np.sin(2 * np.pi / 3), 0,
np.cos(2 * np.pi / 3)],
[np.sin(4 * np.pi / 3), 0,
np.cos(4 * np.pi / 3)]]
paulies = [qt.sigmax(), qt.sigmay(), qt.sigmaz()]
alice2Effects.append(
list(
map(
lambda bloch: effectForQubitPovm(
1 / 3, sum([paulies[i] * bloch[i] for i in range(3)])),
trineAlice2)))
mu = np.arctan(np.sin(2 * epsilon))
bobUnBlochVectors = [[np.sin(mu), 0, np.cos(mu)],
[-np.sin(mu), 0, np.cos(mu)]]
bobObservables = list(
map(lambda bloch: createQubitObservable(bloch), bobUnBlochVectors))
bobEffects = list(
map(
lambda qubitObservable: projectorsForQubitObservable(
qubitObservable), bobObservables))
psi = qt.tensor(qt.basis(2, 0), qt.basis(2, 0))
rho = psi * psi.dag()
expectedCorrelations = {}
for x1, x2, y in product(range(len(alice1outputs)),
range(len(alice2outputs)),
range(len(bobOutputs))):
for a1, a2, b in product(range(alice1outputs[x1]),
range(alice2outputs[x2]),
range(bobOutputs[y])):
postMeasrmntState = qt.tensor(
alice1Krauss[x1][a1], qt.qeye(2)) * rho * (qt.tensor(
alice1Krauss[x1][a1], qt.qeye(2))).dag()
expectedCorrelations[(x1, x2), y, (a1, a2), b] = (
qt.tensor(alice2Effects[x2][a2], bobEffects[y][b]) *
postMeasrmntState).tr().real
expectedBehaviour = Behaviour(scenario, expectedCorrelations)
polytope = BellPolytopeWithOneWayCommunication(
SequentialBellPolytope(scenario))
self.assertTrue(
polytope.contains(expectedBehaviour.getProbabilityList()))
def make_ops(nc, nq):
a = qutip.tensor(qutip.qeye(nq), qutip.destroy(nc))
ad = a.dag()
b = qutip.tensor(qutip.destroy(nq), qutip.qeye(nc))
bd = b.dag()
return a, ad, b, bd
def define_useful_states(self):
''' standard init state for system '''
self.NV0_carbons_mixed = qutip.tensor([rho0] +
[rhom] * self.num_carbons +
[rhom_S1] * self.inc_nitrogen)
def e_N_op(self, e_operator, N_operator):
''' Helper function to embed e operator combined with an operator on carbons '''
return qutip.tensor([e_operator] + [Id] * self.num_carbons +
[N_operator])
def e_C_op(self, e_operator, c_operator, c_num):
''' Helper function to embed e operator combined with an operator on carbons '''
return qutip.tensor([e_operator] + [Id] * (c_num - 1) + [c_operator] +
[Id] * (self.num_carbons - c_num) +
[Id_S1] * self.inc_nitrogen)
def N_op(self, N_operator):
''' Helper function to embed N operator with identities on other carbons '''
return qutip.tensor([Id] * (self.num_carbons + 1) + [N_operator])
def _p_op(size):
return qutip.tensor(
qutip.qeye(2), qutip.qeye(2),
1j / np.sqrt(2) * (qutip.create(size) - qutip.destroy(size)))
def e_op(self, operator):
''' Helper function to embed e operator with identities on carbons '''
return qutip.tensor([operator] + [Id] * self.num_carbons +
[Id_S1] * self.inc_nitrogen)
# Get the auxiliary density matrices from the full Hierarchy ADOs
aux_2_list, indices1 = get_aux_matrices(hsolver_no_matsubara.full_hierarchy, 2, Nc, 2)
aux_2_list_matsubara, indices2 = get_aux_matrices(hsolver_matsubara.full_hierarchy, 2, Nc, 4)
virtual_photon_heom_no_matsubara = np.array([aux.tr() for aux in aux_2_list[1]])
virtual_photon_heom_matsubara = np.array([aux.tr() for aux in aux_2_list_matsubara[8]])
# =======================================
# Compute the population from pseudomode
# =======================================
print("pseudomode")
lam2 = np.sqrt(lam_renorm)
Ncav = 4
# Construct the pseudomode operators with one extra underdamped pseudomode
sx = tensor(sigmax(), qeye(Ncav))
sm = tensor(destroy(2).dag(), qeye(Ncav))
sz = tensor(sigmaz(), qeye(Ncav))
a = tensor(qeye(2), destroy (Ncav))
Hsys = 0.5*wq*sz + 0.5*delta*sx + omega*a.dag()*a + lam2*sx*(a + a.dag())
initial_ket = basis(2, 1)
psi0=tensor(initial_ket, basis(Ncav, 0))
options = Options(nsteps=1500, store_states=True, atol=1e-13, rtol=1e-13)
c_ops = [np.sqrt(bath_broad)*a]
e_ops = [sz, sm.dag(), a, a.dag(), a.dag()*a, a**2, a.dag()**2]
pseudomode_no_mats = mesolve(Hsys, psi0, tlist, c_ops, e_ops, options=options)
output = (pseudomode_no_mats.expect[0] + 1)/2
# Construct the pseudomode operators with three extra pseudomodes
LAST = bytearray()
LAST.append(0)
numQ = 3 #number of qubits
measureQ = 0 #index of qubit being measured
#-----------------------------------------------------------------------------
#Initial state
state = qt.basis(2**numQ, 1)
state = state.unit()
#-----------------------------------------------------------------------------
#-----------------------------------------------------------------------------
#Gates (operate on state from highest to lowest)
gates = []
gates.append(qt.tensor(snot(), snot(), snot()))
#gates.append(qt.tensor(qt.qeye(4), qt.sigmax())) #constant f ex. 1
#gates.append(qt.qeye(8)) #constant f ex. 2
#gates.append(cnot(numQ, 0, 2)) #balanced f ex. 1
gates.append(qt.tensor(qt.qeye(2), cnot())) #balanced f ex. 2
gates.append(qt.tensor(snot(), snot(), qt.qeye(2)))
#-----------------------------------------------------------------------------
def emulate():
ser = serial.Serial('COM4', 115200,
timeout=1) #open COM4 port at 115200 baud
count = 0
gateCount = 0
outState = qt.basis(2**numQ) - qt.basis(
2**numQ) #empty state of appropriate size
def generate_xy_states(L, times):
H = get_hamiltonian('xy', dict(L=L))
psi0 = qt.tensor([qt.basis(2,0), qt.basis(2,1)]*(L//2) + [qt.basis(2,0)] * (L%2))
return do_evolution(psi0, H, times)
a_mode = abs(mode)
remove = np.exp(0.5 * lamb_dicke * lamb_dicke)
coefficients = remove * relative_rabi_range(lamb_dicke, 0, size - a_mode,
a_mode)
coefficients = 1j**a_mode * coefficients
indices = np.arange(max(0, -mode), min(size, size - mode), dtype=np.int32)
indptr = np.empty(size + 1, dtype=np.int32)
if mode < 0:
indptr[:mode] = np.arange(1 + size - a_mode, dtype=np.int32)
indptr[mode:] = size - a_mode
else:
indptr[:mode] = 0
indptr[mode:] = np.arange(1 + size - a_mode, dtype=np.int32)
return qutip.Qobj(fast_csr_matrix((coefficients, indices, indptr)))
Sy = qutip.tensor(qutip.sigmay(), qutip.qeye(2))\
+ qutip.tensor(qutip.qeye(2), qutip.sigmay())
gg = qutip.tensor(qutip.basis(2, 1), qutip.basis(2, 1))
ee = qutip.tensor(qutip.basis(2, 0), qutip.basis(2, 0))
ge = qutip.tensor(qutip.basis(2, 1), qutip.basis(2, 0))
eg = qutip.tensor(qutip.basis(2, 0), qutip.basis(2, 1))
def _x_op(size):
return qutip.tensor(
qutip.qeye(2), qutip.qeye(2),
np.sqrt(0.5) * (qutip.create(size) + qutip.destroy(size)))
def _p_op(size):
"""
Train PPO agent to do Fock state N=2 preparation with universal gate sequence.
The episodes start from vacuum, and characteristic function tomography
measurements are performed in the end to assign reward.
"""
root_dir = r'E:\data\gkp_sims\PPO\ECD\fock4_fock'
root_dir = os.path.join(root_dir, '7')
# Params for environment
env_kwargs = {'control_circuit': 'ECD_control', 'init': 'vac', 'T': 8, 'N': 50}
# Params for reward function
target_state = qt.tensor(qt.basis(2, 0), qt.basis(50, 4))
reward_kwargs = {
'reward_mode': 'fock',
'target_state': target_state,
'N_msmt': 10,
'error_prob': 0.5
}
reward_kwargs_eval = {
'reward_mode': 'overlap',
'target_state': target_state,
'postselect_0': False
}
# Params for action wrapper
def get_gs(nsites, ph_levels):
basis = []
for i in range(nsites):
basis.append(qutip.states.basis(2))
basis.append(qutip.states.basis(ph_levels))
return qutip.tensor(basis)
def a(p):
return qt.tensor(qt.destroy(p.N), qt.qeye(p.J))
loss = 1.2
num_steps = 1
max_time = 10
date = list(str(datetime.datetime.now())[:19])
date[13] = '-'
date[16] = '-'
''' SUPER IMPORTANT: change the filepath to wherever you want the plots saved '''
filepath = 'C:/Users/Wang Lab/Documents/qutip/out/wigner_test/' + ''.join(
date) + '/'
if not os.path.exists(filepath):
os.makedirs(filepath)
a = qt.tensor(qt.destroy(NA), qt.qeye(NB))
b = qt.tensor(qt.qeye(NB), qt.destroy(NA))
PJ = (1j * np.pi * a.dag() * a).expm() * (1j * np.pi * b.dag() * b).expm()
H = drive * a * b + drive.conjugate() * a.dag() * b.dag()
psi0 = (qt.tensor(qt.coherent(NA, alpha), qt.coherent(NB, alpha)) -
qt.tensor(qt.coherent(NA, -alpha), qt.coherent(NB, -alpha))).unit()
#psi0 = qt.tensor(qt.fock(NA, 0), qt.fock(NB, 0))
''' Solve the system '''
times = np.linspace(0.0, max_time, num_steps)
opts = qt.Options(store_states=True, nsteps=10000)
print(opts)
print('solving...')
def Jm(p):
j_destroy = np.diag(np.sqrt(np.arange(1, p.J)), 1)
return qt.tensor(qt.qeye(p.N), qt.Qobj(j_destroy))
def permute_matrix(c, t, matrix, rho):
# For a given two-qubit gate in the form, find the matrix of dimension corresponding to rho such that
# the two-qubit gate operations on c and t. e.g., permute_matrix(4,1,cnot,rho) will apply a cnot gate
# between qubits 4 and 1, with 4 the control and 1 the target
# Get shape and number of qubits
shape = rho.shape
n = int(np.log2(shape[0]))
# Create list in binary from 0 to 2^n-1, corresponding to the orthonormal computational basis
bitstr_list = []
for ii in range(0, np.power(2, n)):
bitstr = bin(ii)[2:].zfill(n)
bitstr = list(bitstr)
bitstr_list.append(bitstr)
# Now swap all entries of the binary list according to the given c and t
# Notice that we have to be careful of the order we do this in, due to noncommutativity of permutations
# That's why we have the overabundance of if statements.
if c != 2 and t != 1:
for ii in range(0, np.power(2, n)):
swap1 = bitstr_list[ii][0]
swap2 = bitstr_list[ii][c - 1]
bitstr_list[ii][0] = swap2
bitstr_list[ii][c - 1] = swap1
for ii in range(0, np.power(2, n)):
swap1 = bitstr_list[ii][1]
swap2 = bitstr_list[ii][t - 1]
bitstr_list[ii][1] = swap2
bitstr_list[ii][t - 1] = swap1
elif c == 2 and t == 1:
for ii in range(0, np.power(2, n)):
swap1 = bitstr_list[ii][0]
swap2 = bitstr_list[ii][c - 1]
bitstr_list[ii][0] = swap2
bitstr_list[ii][c - 1] = swap1
elif c == 2 and t != 1:
for ii in range(0, np.power(2, n)):
swap1 = bitstr_list[ii][1]
swap2 = bitstr_list[ii][t - 1]
bitstr_list[ii][1] = swap2
bitstr_list[ii][t - 1] = swap1
for ii in range(0, np.power(2, n)):
swap1 = bitstr_list[ii][0]
swap2 = bitstr_list[ii][c - 1]
bitstr_list[ii][0] = swap2
bitstr_list[ii][c - 1] = swap1
elif c != 2 and t == 1:
for ii in range(0, np.power(2, n)):
swap1 = bitstr_list[ii][0]
swap2 = bitstr_list[ii][c - 1]
bitstr_list[ii][0] = swap2
bitstr_list[ii][c - 1] = swap1
for ii in range(0, np.power(2, n)):
swap1 = bitstr_list[ii][1]
swap2 = bitstr_list[ii][t - 1]
bitstr_list[ii][1] = swap2
bitstr_list[ii][t - 1] = swap1
list_of_permutations = np.zeros(np.power(2, n))
for ii in range(0, np.power(2, n)):
list_of_permutations[ii] = int(''.join(bitstr_list[ii]), 2)
permutation_matrix = np.zeros((np.power(2, n), np.power(2, n)))
for ii in range(0, np.power(2, n)):
for iii in range(0, np.power(2, n)):
if ii == list_of_permutations[iii]:
permutation_matrix[ii][iii] = 1
permutation_matrix = qt.Qobj(permutation_matrix)
permutation_matrix.dims = rho.dims
for ii in range(0, n - 2):
matrix = qt.tensor(matrix, qt.identity(2))
matrix.dims = rho.dims
# permute matrix
permuted_matrix = permutation_matrix * matrix * permutation_matrix.trans()
rho = permuted_matrix * rho * permuted_matrix.dag()
return rho
(rand(dec_mag), rand(dec_mag), rand(dec_mag)) ]
dec_mat = np.array([ [ rand() for jj in range(3) ] for kk in range(3) ])
h_rand = { (ll,mm,nn) : rand()
for ll, mm, nn in itertools.product(range(3), repeat = 3)
if ll + mm + nn <= 2 }
for op, val in h_rand.items():
h_rand[op] = ( h_rand[op] + np.conj(h_rand[op[::-1]]) ) / 2
h_rand[op[::-1]] = np.conj(h_rand[op])
track_ops = [ (ll,mm,nn) for ll, mm, nn in itertools.product(range(3), repeat = 3)
if ll + mm + nn <= 2 ]
### construct operators for exact simulation
II = qt.tensor([I2]*N)
ZZ = 0 * II
s_z_j = []
s_p_j = []
s_m_j = []
for jj in range(N):
s_z_j.append(qt.tensor([ I2 ] * jj + [ qt.sigmaz()/2 ] + [ I2 ] * (N-jj-1)))
s_p_j.append(qt.tensor([ I2 ] * jj + [ qt.sigmap() ] + [ I2 ] * (N-jj-1)))
s_m_j.append(qt.tensor([ I2 ] * jj + [ qt.sigmam() ] + [ I2 ] * (N-jj-1)))
S_p = sum(s_p_j)
S_m = sum(s_m_j)
S_z = sum(s_z_j)
S_x = 1/2 * ( S_p + S_m )
S_y = -1j/2 * ( S_p - S_m )
def liouvillian(omega, g, gamma, beta):
"""Liouvillian for the coupled system of qubit and TLS"""
H0_q = omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2))
# drive qubit Hamiltonian
H1_q = -0.5*qutip.operators.sigmax()
# drift TLS Hamiltonian
H0_T = qutip.tensor(omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)), qutip.qeye(2))\
+qutip.tensor(qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), omega*0.5*(-qutip.operators.sigmaz()+qutip.qeye(2)))
# Lift Hamiltonians to joint system operators
H0 = qutip.tensor(H0_q, qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2)) + qutip.tensor(qutip.qeye(2), H0_T)
H1 = qutip.tensor(H1_q, qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2), qutip.qeye(2))
# qubit-TLS interaction
H_int = g*(qutip.tensor(qutip.destroy(2),qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.create(2),qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.destroy(2),qutip.qeye(2),qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.create(2),qutip.qeye(2),qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.create(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.destroy(2),qutip.qeye(2),qutip.qeye(2))\
+qutip.tensor(qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.create(2),qutip.qeye(2))\
+qutip.tensor(qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.destroy(2),qutip.qeye(2))\
+qutip.tensor(qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.create(2))\
+qutip.tensor(qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.destroy(2)))
# convert Hamiltonians to QuTiP objects
H0 = qutip.Qobj(H0 + H_int)
H1 = qutip.Qobj(H1)
# Define Lindblad operators
N = 1.0 / (np.exp(beta * omega) - 1.0)
# Cooling on TLS
L1 = np.sqrt(gamma * (N + 1)) * qutip.tensor(qutip.destroy(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),\
qutip.qeye(2),qutip.qeye(2),qutip.qeye(2))
# Heating on TLS
L2 = np.sqrt(gamma * N) *qutip.tensor(qutip.create(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),qutip.qeye(2),\
qutip.qeye(2))
# convert Lindblad operators to QuTiP objects
L1 = qutip.Qobj(L1)
L2 = qutip.Qobj(L2)
# generate the Liouvillian
L0 = qutip.liouvillian(H=H0, c_ops=[L1, L2])
L1 = qutip.liouvillian(H=H1)
# Shift the qubit and TLS into resonance by default
eps0 = lambda t, args: 8
return [L0, [L1, eps0]]
def test_3_state_to_state(self):
"""
control.pulseoptim: state-to-state transfer
linear initial pulse used
assert that goal is achieved
"""
# 2 qubits with Ising interaction
# some arbitary coupling constants
alpha = [0.9, 0.7]
beta = [0.8, 0.9]
Sx = sigmax()
Sz = sigmaz()
H_d = (alpha[0] * tensor(Sx, identity(2)) +
alpha[1] * tensor(identity(2), Sx) +
beta[0] * tensor(Sz, identity(2)) +
beta[1] * tensor(identity(2), Sz))
H_c = [tensor(Sz, Sz)]
q1_0 = q2_0 = Qobj([[1], [0]])
q1_T = q2_T = Qobj([[0], [1]])
psi_0 = tensor(q1_0, q2_0)
psi_T = tensor(q1_T, q2_T)
n_ts = 10
evo_time = 18
# Run the optimisation
result = cpo.optimize_pulse_unitary(H_d,
H_c,
psi_0,
psi_T,
n_ts,
evo_time,
fid_err_targ=1e-10,
init_pulse_type='LIN',
gen_stats=True)
assert_(result.goal_achieved,
msg="State-to-state goal not achieved. "
"Terminated due to: {}, with infidelity: {}".format(
result.termination_reason, result.fid_err))
assert_almost_equal(result.fid_err,
0.0,
decimal=10,
err_msg="Hadamard infidelity too high")
#Try with Qobj propagation
result = cpo.optimize_pulse_unitary(H_d,
H_c,
psi_0,
psi_T,
n_ts,
evo_time,
fid_err_targ=1e-10,
init_pulse_type='LIN',
dyn_params={'oper_dtype': Qobj},
gen_stats=True)
assert_(result.goal_achieved,
msg="State-to-state goal not achieved "
"(Qobj propagation)"
"Terminated due to: {}, with infidelity: {}".format(
result.termination_reason, result.fid_err))
return phaseDiff,pop11,pop02
Ej1 = 17
Ej2 = 22
Ec1 = 0.27
Ec2 = 0.27
g=0.015 #/2pi
Q1=Tunabletransmon(EC=Ec1, EJmax=Ej1)
Q2=Tunabletransmon(EC=Ec2, EJmax=Ej2)
QQ=QQ(Q1,Q2,g)
#ini_state=iniState2Qsys(Q1.Nq,Q2.Nq,1,1)
Nq=3
ini_coeff = [0,1e-9,0,1e-9,1,0,0,0,0] # 11
ini_state = ini_coeff[0]*qt.tensor(ket(Nq,0), ket(Nq,0)) \
+ ini_coeff[1]*qt.tensor(ket(Nq,0), ket(Nq,1)) \
+ ini_coeff[2]*qt.tensor(ket(Nq,0), ket(Nq,2)) \
+ ini_coeff[3]*qt.tensor(ket(Nq,1), ket(Nq,0)) \
+ ini_coeff[4]*qt.tensor(ket(Nq,1), ket(Nq,1)) \
+ ini_coeff[5]*qt.tensor(ket(Nq,1), ket(Nq,2)) \
+ ini_coeff[6]*qt.tensor(ket(Nq,2), ket(Nq,0)) \
+ ini_coeff[7]*qt.tensor(ket(Nq,2), ket(Nq,1)) \
+ ini_coeff[8]*qt.tensor(ket(Nq,2), ket(Nq,2))
ini_state_rho=iniState2Qsys(Q1.Nq,Q2.Nq,1,1,mode='rho')
print(ini_state_rho)
Iq1=qt.qeye(Nq)
Hq1_lab=QQ.Hq1*(2*pi)
def test_4_lindbladian(self):
"""
control.pulseoptim: amplitude damping channel
Lindbladian dynamics
assert that fidelity error is below threshold
"""
Sx = sigmax()
Sz = sigmaz()
Si = identity(2)
Sd = Qobj(np.array([[0, 1], [0, 0]]))
Sm = Qobj(np.array([[0, 0], [1, 0]]))
Sd_m = Qobj(np.array([[1, 0], [0, 0]]))
gamma = 0.1
L0_Ad = gamma * (2 * tensor(Sm, Sd.trans()) -
(tensor(Sd_m, Si) + tensor(Si, Sd_m.trans())))
LC_x = -1j * (tensor(Sx, Si) - tensor(Si, Sx))
LC_z = -1j * (tensor(Sz, Si) - tensor(Si, Sz))
drift = L0_Ad
ctrls = [LC_z, LC_x]
n_ctrls = len(ctrls)
initial = tensor(Si, Si)
had_gate = hadamard_transform(1)
target_DP = tensor(had_gate, had_gate)
n_ts = 10
evo_time = 5
result = cpo.optimize_pulse(drift,
ctrls,
initial,
target_DP,
n_ts,
evo_time,
fid_err_targ=1e-3,
max_iter=200,
init_pulse_type='LIN',
gen_stats=True)
assert_(result.fid_err < 0.1, msg="Fidelity higher than expected")
# Repeat with Qobj propagation
result = cpo.optimize_pulse(drift,
ctrls,
initial,
target_DP,
n_ts,
evo_time,
fid_err_targ=1e-3,
max_iter=200,
init_pulse_type='LIN',
dyn_params={'oper_dtype': Qobj},
gen_stats=True)
assert_(result.fid_err < 0.1,
msg="Fidelity higher than expected (Qobj propagation)")
# Check same result is achieved using the create objects method
optim = cpo.create_pulse_optimizer(drift,
ctrls,
initial,
target_DP,
n_ts,
evo_time,
fid_err_targ=1e-3,
init_pulse_type='LIN',
gen_stats=True)
dyn = optim.dynamics
p_gen = optim.pulse_generator
init_amps = np.zeros([n_ts, n_ctrls])
for j in range(n_ctrls):
init_amps[:, j] = p_gen.gen_pulse()
dyn.initialize_controls(init_amps)
# Check the exact gradient
func = optim.fid_err_func_wrapper
grad = optim.fid_err_grad_wrapper
x0 = dyn.ctrl_amps.flatten()
grad_diff = check_grad(func, grad, x0)
assert_almost_equal(grad_diff,
0.0,
decimal=7,
err_msg="Frechet gradient outside tolerance")
result2 = optim.run_optimization()
assert_almost_equal(result.fid_err,
result2.fid_err,
decimal=3,
err_msg="Direct and indirect methods produce "
"different results for ADC")
def test_1_unitary(self):
"""
control.pulseoptim: Hadamard and QFT gate with linear initial pulses
assert that goal is achieved and fidelity error is below threshold
"""
# Hadamard
H_d = sigmaz()
H_c = [sigmax()]
U_0 = identity(2)
U_targ = hadamard_transform(1)
n_ts = 10
evo_time = 10
# Run the optimisation
result = cpo.optimize_pulse_unitary(H_d,
H_c,
U_0,
U_targ,
n_ts,
evo_time,
fid_err_targ=1e-10,
init_pulse_type='LIN',
gen_stats=True)
assert_(result.goal_achieved,
msg="Hadamard goal not achieved. "
"Terminated due to: {}, with infidelity: {}".format(
result.termination_reason, result.fid_err))
assert_almost_equal(result.fid_err,
0.0,
decimal=10,
err_msg="Hadamard infidelity too high")
#Try without stats
result = cpo.optimize_pulse_unitary(H_d,
H_c,
U_0,
U_targ,
n_ts,
evo_time,
fid_err_targ=1e-10,
init_pulse_type='LIN',
gen_stats=False)
assert_(result.goal_achieved,
msg="Hadamard goal not achieved "
"(no stats). "
"Terminated due to: {}, with infidelity: {}".format(
result.termination_reason, result.fid_err))
#Try with Qobj propagation
result = cpo.optimize_pulse_unitary(H_d,
H_c,
U_0,
U_targ,
n_ts,
evo_time,
fid_err_targ=1e-10,
init_pulse_type='LIN',
dyn_params={'oper_dtype': Qobj},
gen_stats=True)
assert_(result.goal_achieved,
msg="Hadamard goal not achieved "
"(Qobj propagation). "
"Terminated due to: {}, with infidelity: {}".format(
result.termination_reason, result.fid_err))
# Check same result is achieved using the create objects method
optim = cpo.create_pulse_optimizer(H_d,
H_c,
U_0,
U_targ,
n_ts,
evo_time,
fid_err_targ=1e-10,
dyn_type='UNIT',
init_pulse_type='LIN',
gen_stats=True)
dyn = optim.dynamics
init_amps = optim.pulse_generator.gen_pulse().reshape([-1, 1])
dyn.initialize_controls(init_amps)
# Check the exact gradient
func = optim.fid_err_func_wrapper
grad = optim.fid_err_grad_wrapper
x0 = dyn.ctrl_amps.flatten()
grad_diff = check_grad(func, grad, x0)
assert_almost_equal(grad_diff,
0.0,
decimal=7,
err_msg="Unitary gradient outside tolerance")
result2 = optim.run_optimization()
assert_almost_equal(result.fid_err,
result2.fid_err,
decimal=10,
err_msg="Direct and indirect methods produce "
"different results for Hadamard")
# QFT
Sx = sigmax()
Sy = sigmay()
Sz = sigmaz()
Si = 0.5 * identity(2)
H_d = 0.5 * (tensor(Sx, Sx) + tensor(Sy, Sy) + tensor(Sz, Sz))
H_c = [tensor(Sx, Si), tensor(Sy, Si), tensor(Si, Sx), tensor(Si, Sy)]
#n_ctrls = len(H_c)
U_0 = identity(4)
# Target for the gate evolution - Quantum Fourier Transform gate
U_targ = qft.qft(2)
result = cpo.optimize_pulse_unitary(H_d,
H_c,
U_0,
U_targ,
n_ts,
evo_time,
fid_err_targ=1e-9,
init_pulse_type='LIN',
gen_stats=True)
assert_(result.goal_achieved,
msg="QFT goal not achieved. "
"Terminated due to: {}, with infidelity: {}".format(
result.termination_reason, result.fid_err))
assert_almost_equal(result.fid_err,
0.0,
decimal=7,
err_msg="QFT infidelity too high")
# check bounds
result2 = cpo.optimize_pulse_unitary(H_d,
H_c,
U_0,
U_targ,
n_ts,
evo_time,
fid_err_targ=1e-9,
amp_lbound=-1.0,
amp_ubound=1.0,
init_pulse_type='LIN',
gen_stats=True)
assert_((result2.final_amps >= -1.0).all()
and (result2.final_amps <= 1.0).all(),
msg="Amplitude bounds exceeded for QFT")
def _x_op(size):
return qutip.tensor(
qutip.qeye(2), qutip.qeye(2),
np.sqrt(0.5) * (qutip.create(size) + qutip.destroy(size)))
def c_op(self, operator, c_num):
''' Helper function to embed c operator with identities on other carbons '''
return qutip.tensor([Id] * c_num + [operator] + [Id] *
(self.num_carbons - c_num) +
[Id_S1] * self.inc_nitrogen)
def direct_hamiltonian(w_1, w_2, g_factor):
"""Return a QObj denoting a hamiltonian for two qubits interacting with the
cavity mode eliminated."""
return (0.5 * w_1 * qt.tensor(SZ, I) + 0.5 * w_2 * qt.tensor(I, SZ) +
g_factor * qt.tensor(SPlus, SMinus) +
g_factor * qt.tensor(SMinus, SPlus))