def bds_circuit_(alpha, beta, gamma):
# ref: arXiv:1912.06105
ket0 = st.cb(2, 0)
ket1 = st.cb(2, 1)
proj0 = mf.proj(2, ket0)
proj1 = mf.proj(2, ket1)
psi = ket0
for j in range(1, 4):
psi = np.kron(psi, ket0)
gate = np.kron(gates.O2(alpha / 2), gates.id(8))
psi = np.dot(gate, psi)
cn = gates.cnot(4, 0, 1)
psi = np.dot(cn, psi)
gate = np.kron(gates.O2(beta / 2), gates.O2(gamma / 2))
gate = np.kron(gate, gates.id(4))
psi = np.dot(gate, psi)
cn = gates.cnot(4, 0, 2)
psi = np.dot(cn, psi)
cn = gates.cnot(4, 1, 3)
psi = np.dot(cn, psi)
gate = np.kron(gates.id(8), gates.hadamard())
psi = np.dot(gate, psi)
cn = gates.cnot(4, 3, 2)
psi = np.dot(cn, psi)
return psi
def dbs_rpv_test():
from states import bell
ns = 5 * 10**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
for j in range(0, ns):
rpv = rpvg.rpv_zhsl(4)
rhor = rpv[0] * mf.proj(4, bell(0, 0)) + rpv[1] * mf.proj(
4, bell(0, 1))
rhor += (rpv[2] * mf.proj(4, bell(1, 0)) +
rpv[3] * mf.proj(4, bell(1, 1)))
cm = gm.corr_mat(2, 2, rhor)
cxx[j] = cm[0][0]
cyy[j] = cm[1][1]
czz[j] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=0.5)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()
def dbs_circuit_test_():
ns = 5 * 10**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
p = np.zeros((2, 2))
a = np.zeros(4)
for j in range(0, ns):
rpv = rpvg.rpv_zhsl(4)
a = np.reshape(rpv, (2, 2))
alpha, beta, gamma = bds_circuit_angles(a)
psi = bds_circuit_(alpha, beta, gamma)
rhor = ptr.pTraceL(4, 4, mf.proj(16, psi))
cm = gm.corr_mat(2, 2, rhor)
cxx[j] = cm[0][0]
cyy[j] = cm[1][1]
czz[j] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=0.75)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()
def dbs_circuit_test():
ns = 5 * 10**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
for j in range(0, ns):
rpv = rpvg.rpv_zhsl(4)
theta = 2.0 * math.acos(math.sqrt(rpv[0] + rpv[1]))
alpha = 2.0 * math.acos(math.sqrt(rpv[0] + rpv[2]))
psi = bds_circuit(theta, alpha)
rhor = ptr.pTraceL(4, 4, mf.proj(16, psi))
cm = gm.corr_mat(2, 2, rhor)
cxx[j] = cm[0][0]
cyy[j] = cm[1][1]
czz[j] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=1)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()
def bds_circuit(theta, alpha):
ket0 = st.cb(2, 0)
ket1 = st.cb(2, 1)
proj0 = mf.proj(2, ket0)
proj1 = mf.proj(2, ket1)
psi = ket0
for j in range(1, 4):
psi = np.kron(psi, ket0)
gate = np.kron(gates.O2(theta / 2), gates.O2(alpha / 2))
gate = np.kron(gate, gates.id(4))
psi = np.dot(gate, psi)
cn = gates.cnot(4, 0, 2)
psi = np.dot(cn, psi)
cn = gates.cnot(4, 1, 3)
psi = np.dot(cn, psi)
gate = np.kron(gates.id(8), gates.hadamard())
psi = np.dot(gate, psi)
cn = gates.cnot(4, 3, 2)
psi = np.dot(cn, psi)
return psi
def cnot(n, c, t):
'''returns the control-NOT for n qubits, control c & target t'''
list1 = []
list2 = []
for j in range(0, n):
if j == c:
list1.append(mf.proj(2, st.cb(2, 0)))
list2.append(mf.proj(2, st.cb(2, 1)))
elif j == t:
list1.append(pauli(0))
list2.append(pauli(1))
else:
list1.append(pauli(0))
list2.append(pauli(0))
kp1 = np.kron(list1[0], list1[1])
kp2 = np.kron(list2[0], list2[1])
for j in range(2, n):
kp1 = np.kron(kp1, list1[j])
kp2 = np.kron(kp2, list2[j])
cn = kp1 + kp2
return cn
def dbs_circuit_test_angles_():
ns = 20**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
m = -1
da = math.pi / 20
alpha = -math.pi / 2 - da
for j in range(0, 20):
alpha += da
beta = -da
for k in range(0, 20):
beta += da
gamma = -da
for l in range(0, 20):
gamma += da
psi = bds_circuit_(alpha, beta, gamma)
rhor = ptr.pTraceL(4, 4, mf.proj(16, psi))
cm = gm.corr_mat(2, 2, rhor)
m += 1
cxx[m] = cm[0][0]
cyy[m] = cm[1][1]
czz[m] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=0.75)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()
def Werner(w):
return ((1 - w) / 4) * np.eye(4) + w * proj(4, Bell(1, 1))