def makeLambda_mk(U_k, m, rho_f):
n = len(U_k)
# Product of U_k_n ... U_k_m+1
U = U_k[n - 1]
for j in range(n-2, m-1, -1):
U = np.dot(U, U_k[j])
return np.dot(np.dot(U.conj().T, rho_f), U)
def fidSingleTxFull(rho_0, rho_f, T, N, Us):
U_k_ts = [np.array(U_k(T), np.complex128) for U_k in Us]
mats = [
np.dot(np.dot(rho_f.conj().T, U_k_t), np.dot(rho_0,
U_k_t.conj().T))
for U_k_t in U_k_ts
]
terms = [np.trace(mat) for mat in mats]
return (1. / N) * sum(terms)
def G(t_):
if profiling:
start = time.time()
hp = H_p(a, eta_k, t_)
teatime = time.time()
th_time[0] += teatime - start
res = np.dot(cvec, hp)
g_time[0] += time.time() - teatime
return res
return np.dot(cvec, H_t2(a(t_), eta_k(t_)))
def BCH(A, B, order=4):
start = time.time()
c1 = np.dot(k1,comm(A, B))
c2 = np.dot(k2,comm(A, c1))
c3 = np.dot(k3,comm(B, c1))
res = A + B + c1 + c2 + c3
if order > 3:
c4 = np.dot(k4,comm(B, c2))
res += c4
if order > 4:
c5 = np.dot(k5,(bch5(A, B) + bch5(B, A)))
res += c5
if profiling:
bch_time[0] += time.time() - start
return res
def makeTerm(k):
# U_k = Us_mk[k]
# Us_nm_k = U_k[m:(n-1)]
# # Us_nm_k.reverse()
# Us_m1_k = U_k[0:(m-1)]
# # Us_m1_k.reverse()
#
# U_nm_k = reduce(np.dot, reversed(Us_nm_k),identity)
# U_nm_kH = U_nm_k.conj().T
# U_m1_k = reduce(np.dot, reversed(Us_m1_k),identity)
# U_m1_kH = U_m1_k.conj().T
#
# lambda_mk = reduce(np.dot, [U_nm_kH, rho_f, U_nm_k])
# lambda_H = lambda_mk.conj().T
# rho_mk = reduce(np.dot, [U_m1_k, rho_0, U_m1_kH])
U_k = Us_mk[k]
lambda_mk = makeLambda_mk(U_k, m, rho_f)
lambda_H = lambda_mk.conj().T
rho_mk = makeRho_mk(U_k, m, rho_0)
term = np.trace(np.dot(lambda_H, comm(sigmaX, rho_mk)))
return term
def fidSingleTxDirect(rho_f, rho, T):
return np.trace(np.dot(rho_f.conj().T, rho(T)))
def comm(A, B):
return np.dot(A, B) - np.dot(B, A)
def R(U_k):
U = np.array(U_k(t))
return np.dot(np.dot(U, rho_0), U.conj().T)
def makeRho_mk(U_k, m, rho_0):
# Product of U_k_m ... U_k_1
U = U_k[m - 1]
for j in range(m-2, -1, -1):
U = np.dot(U, U_k[j])
return np.dot(np.dot(U, rho_0), U.conj().T)
