def H2(J, g):
I = np.eye(2)
H = Hamiltonian({"ZZ": J, "X": g}).to_matrix()
return 1 / 3 * sum(
[tensor([H, I, I]),
tensor([I, H, I]),
tensor([I, I, H])])
def obj3(p, init_p, U, Rep, C):
# calcultate the states
psi1 = state_from_params(init_p, 3)
psi2 = state_from_params(p, 3)
# claculate the environmet Mr and Ml
U1, U2 = C.paramU(init_p)
U1_, U2_ = C.paramU(p)
Mres = Rep.optimize(r(U1), r(U2), r(U1_.conj().T), r(U2_.conj().T))
Mr = Rep.M(Mres.x[1:])
U_ev = tensor([Mr.conj().T, U, Mr])
return -np.sqrt(2 * np.abs(psi2.conj().T @ U_ev @ psi1)**2)
def obj(p, U1, h_):
LE = LeftEnvironment()
RE = RightEnvironment()
psi1 = bwMPS([np.eye(4), U1], 2).state()
U1_ = U4(p)
_, Ml = LE.exact_environment(r(U1), r(np.eye(4)), r(U1_.conj().T),
r(np.eye(4)))
_, Mr = RE.exact_environment(r(U1), r(np.eye(4)), r(U1_.conj().T),
r(np.eye(4)))
Ut = expm(1j * h_ * 0.01)
Ut_m = tensor([Ml, Ut, Mr])
psi2 = bwMPS([np.eye(4), U1_], 2).state()
return np.abs(psi2.conj().T @ Ut_m @ psi1)**2
def loschmidt():
J, g0, g1 = -1, 1.5, 0.2
I = np.eye(2)
H2_ = H2(J, g0)
H2_ = tensor([I, H2_, I])
gs = ground_state(H2_)
H2_ = H2(J, g1)
te = time_evolve(gs, H2_)
plot_loschmidt(te)
with open("Loschmidt_results.pkl", "wb") as f:
pickle.dump(te, f)
return te
def obj(p, init_p, U, Re, Le, C):
# calcultate the states
psi1 = state_from_params(init_p, 3)
psi2 = state_from_params(p, 3)
# claculate the environmet Mr and Ml
U1, U2 = C.paramU(init_p)
U1_, U2_ = C.paramU(p)
eta_l, Ml = Le.exact_environment(r(U1), r(U2), r(U1_.conj().T),
r(U2_.conj().T))
eta_r, Mr = Re.exact_environment(r(U1), r(U2), r(U1_.conj().T),
r(U2_.conj().T))
U_ev = tensor([eta_l * Ml, U, eta_r * Mr])
return -np.sqrt(2 * np.abs(psi2.conj().T @ U_ev @ psi1))
def evolve_U2():
hh = HH(1)
I = np.eye(4)
h = tensor([I, hh, I])
Ut = expm(1j * h * 0.01)
U1 = np.eye(4)
U2 = np.array([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
def obj(p, U2, Ut):
psi1 = bwMPS([U2, np.eye(4)], 3).state()
U2_ = OO_unitary(p)
psi2 = bwMPS([U2_, np.eye(4)], 3).state()
return np.abs(psi2.conj().T @ Ut @ psi1)**2
STEPS = 500
init_params = np.random.rand(7)
results = []
for i in range(STEPS):
print(i)
res = minimize(obj,
x0=init_params,
args=(U2, Ut),
method="Nelder-Mead",
tol=1e-8,
options={
"maxiter": 20000,
"disp": True,
"adaptive": True
})
init_params = res.x
U2 = OO_unitary(res.x)
results.append(res.x)
return results
def circuit(self, Ml, Mr):
C = tensor([Ml, [np.eye(4)] * (self.l - 1), Mr])
psi = self.state()
return C @ psi