def fidelity_error(coef, pxp_config, pxxxp_config):
Hp = gen_Hp(pxp_config, pxxxp_config, coef)
Hm = np.conj(np.transpose(Hp))
H = Hp + Hm
e, u = np.linalg.eigh(H)
z = zm_state(2, 1, pxp, 1)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
t = np.arange(0, 10, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, e, t[n])
# plt.plot(t,f)
# plt.show()
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.1:
cut = n
break
f_max = np.max(f[cut:])
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(4.5, 5.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
# print(f)
if res.x < 1e-5:
return 1000
else:
return -f_max
def fidelity_error(coef, plot=False):
coef = coef[0]
H = H_operations.add(H0, V, np.array([1, coef]))
H = H.sector.matrix()
e, u = np.linalg.eigh(H)
z = zm_state(4, 1, pxp)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
if plot is True:
t = np.arange(0, 20, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, e, t[n])
plt.plot(t, f)
plt.show()
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(4.5, 5.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
if res.x < 1e-5:
return 1000
else:
return -f
def fidelity_error(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
e, u = np.linalg.eigh(H)
z = zm_state(2, 1, pxp, 1)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
t = np.arange(0, 10, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, e, t[n])
# plt.plot(t,f)
# plt.show()
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.1:
cut = n
break
f_max = np.max(f[cut:])
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(4.5, 5.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
# print(f)
if res.x < 1e-5:
return 1000
else:
return -f_max
def pert_opt_fidelity(coef, plot=False):
# H = H_operations.add(H0,V1,np.array([1,coef[0]]))
H = H_operations.add(H0, V1, np.array([1, coef]))
# H = H_operations.add(H,V2,np.array([1,coef[1]]))
# H = H_operations.add(H,V3,np.array([1,coef[2]]))
z = zm_state(3, 1, pxp)
psi = z.prod_basis()
# psi = np.load("./z3,entangled_MPS_coef,15.npy")
H.sector.find_eig()
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors())), psi)
if plot is True:
eig_overlap(z, H).plot()
plt.show()
t = np.arange(0, 20, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, H.sector.eigvalues(), t[n])
plt.plot(t, f)
plt.show()
res = minimize_scalar(
lambda t: fidelity_eval(psi_energy, H.sector.eigvalues(), t),
method="golden",
bracket=(2.5, 5))
# f_max = -fidelity_eval(z_energy,H.sector.eigvalues(),res.x)
f_max = -fidelity_eval(psi_energy, H.sector.eigvalues(), res.x)
print(coef, f_max, res.x)
if np.abs(res.x) < 1e-5:
return 1000
else:
return -f_max
def fidelity_erorr(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1,len(Hp)):
Hp_total = H_operations.add(Hp_total,Hp[n],np.array([1,coef[n-1]]))
Hm = Hp_total.herm_conj()
H = H_operations.add(Hp_total,Hm,np.array([1,1]))
H.sector.find_eig()
z=zm_state(3,1,pxp)
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors())),z.prod_basis())
t=np.arange(0,6,0.001)
f=np.zeros(np.size(t))
for n in range(0,np.size(t,axis=0)):
evolved_state = time_evolve_state(psi_energy,H.sector.eigvalues(),t[n])
f[n] = np.abs(np.vdot(evolved_state,psi_energy))**2
for n in range(0,np.size(f,axis=0)):
if f[n] < 0.1:
cut = n
break
f0 = np.max(f[cut:])
# plt.plot(t,f)
# plt.show()
# res = minimize_scalar(lambda t: -fidelity_eval(psi_energy,H.sector.eigvalues(),t),method="golden",bracket=(2.5,5.5))
# f0 = fidelity_eval(psi_energy,H.sector.eigvalues(),res.x)
return 1-f0
def subspace_variance(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1,len(Hp)):
Hp_total = H_operations.add(Hp_total,Hp[n],np.array([1,coef[n-1]]))
Hm = Hp_total.herm_conj()
H = H_operations.add(Hp_total,Hm,np.array([1,1]))
H.sector.find_eig()
z=zm_state(3,1,pxp)
from Calculations import gen_fsa_basis
fsa_dim = int(2*pxp.N/3)
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(),z.prod_basis(),fsa_dim)
# for n in range(0,np.size(fsa_basis,axis=1)):
# for m in range(0,np.size(fsa_basis,axis=1)):
# temp = np.abs(np.vdot(fsa_basis[:,n],fsa_basis[:,m]))
# if temp > 1e-5:
# print(temp,n,m)
fsa_basis,temp = np.linalg.qr(fsa_basis)
H2 = np.dot(H.sector.matrix(),H.sector.matrix())
H2_fsa = np.dot(np.conj(np.transpose(fsa_basis)),np.dot(H2,fsa_basis))
H_fsa = np.dot(np.conj(np.transpose(fsa_basis)),np.dot(H.sector.matrix(),fsa_basis))
subspace_variance = np.real(np.trace(H2_fsa-np.dot(H_fsa,H_fsa)))
return subspace_variance
def var_error(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
Hz = 1 / 2 * com(Hp_total.sector.matrix(), Hm)
z = zm_state(2, 1, pxp, 1)
fsa_basis = z.prod_basis()
current_state = fsa_basis
for n in range(0, pxp.N):
next_state = np.dot(Hp_total.sector.matrix(), current_state)
next_state = next_state / np.power(np.vdot(next_state, next_state),
0.5)
fsa_basis = np.vstack((fsa_basis, next_state))
current_state = next_state
fsa_basis = np.transpose(fsa_basis)
Hz_var = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(Hz_var, axis=0)):
Hz_var[n] = var(Hz, fsa_basis[:, n])
error = np.max(Hz_var)
print(coef, error)
return error
def spacing_error(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = Hp_total.herm_conj()
Hz = 1 / 2 * com(Hp_total.sector.matrix(), Hm.sector.matrix())
z = zm_state(2, 1, pxp, 1)
from Calculations import gen_fsa_basis
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(), z.prod_basis(), pxp.N)
exp_vals = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(exp_vals, axis=0)):
exp_vals[n] = np.real(exp(Hz, fsa_basis[:, n]))
exp_diff = np.zeros(np.size(exp_vals) - 1)
for n in range(0, np.size(exp_diff, axis=0)):
exp_diff[n] = exp_vals[n + 1] - exp_vals[n]
M = np.zeros((np.size(exp_diff), np.size(exp_diff)))
for n in range(0, np.size(M, axis=0)):
for m in range(0, np.size(M, axis=1)):
M[n, m] = np.abs(exp_diff[n] - exp_diff[m])
error = np.power(np.trace(np.dot(M, np.conj(np.transpose(M)))), 0.5)
return error
def spacing_error(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = np.conj(np.transpose(Hp_total.sector.matrix()))
Hp0 = Hp_total.sector.matrix()
Hm0 = np.conj(np.transpose(Hp0))
Hz = 1 / 2 * com(Hp0, Hm0)
#find lowest weight state
e, u = np.linalg.eigh(Hz)
lowest_weight = u[:, 0]
z = zm_state(2, 1, pxp, 1)
fsa_basis = z.prod_basis()
current_state = fsa_basis
fsa_dim = pxp.N
for n in range(0, fsa_dim):
next_state = np.dot(Hp0, current_state)
if np.abs(np.vdot(next_state, next_state)) > 1e-5:
next_state = next_state / np.power(np.vdot(next_state, next_state),
0.5)
fsa_basis = np.vstack((fsa_basis, next_state))
current_state = next_state
else:
break
fsa_basis = np.transpose(fsa_basis)
if np.size(np.shape(fsa_basis)) == 2:
Hz_exp = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(Hz_exp, axis=0)):
Hz_exp[n] = exp(Hz, fsa_basis[:, n])
Hz_diff = np.zeros(np.size(Hz_exp) - 1)
for n in range(0, np.size(Hz_diff, axis=0)):
Hz_diff[n] = np.abs(Hz_exp[n + 1] - Hz_exp[n])
#spacing error
error_matrix = np.zeros((np.size(Hz_diff), np.size(Hz_diff)))
for n in range(0, np.size(Hz_diff, axis=0)):
for m in range(0, np.size(Hz_diff, axis=0)):
error_matrix[n, m] = np.abs(Hz_diff[n] - Hz_diff[m])
error = np.power(
np.trace(np.dot(error_matrix,
np.conj(np.transpose(error_matrix)))), 0.5)
print(coef, error)
return error
else:
return 1000
def fidelity_erorr(coef):
coef = coef[0]
Hp_total = deepcopy(Hp[0])
Hp_total = H_operations.add(Hp_total,Hp[1],np.array([1,coef]))
Hm = Hp_total.herm_conj()
H = H_operations.add(Hp_total,Hm,np.array([1,1]))
H.sector.find_eig()
z=zm_state(2,2,pxp,1)
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors())),z.prod_basis())
res = minimize_scalar(lambda t: -fidelity_eval(psi_energy,H.sector.eigvalues(),t),method="golden",bracket=(4.5,5.5))
f0 = fidelity_eval(psi_energy,H.sector.eigvalues(),res.x)
print(coef,f0)
return 1-f0
def max_variance(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = Hp_total.herm_conj()
Hz = 1 / 2 * com(Hp_total.sector.matrix(), Hm.sector.matrix())
z = zm_state(2, 1, pxp, 1)
from Calculations import gen_fsa_basis
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(), z.prod_basis(), pxp.N)
var_vals = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(var_vals, axis=0)):
var_vals[n] = np.real(var(Hz, fsa_basis[:, n]))
error = np.max(var_vals)
return error
def fidelity_erorr(coef):
coef = coef[0]
Ip_total = H_operations.add(Ip, Ip_pert, np.array([1, coef]))
Im_total = H_operations.add(Im, Im_pert, np.array([1, coef]))
Kp_total = H_operations.add(Kp, Kp_pert, np.array([1, coef]))
Km_total = H_operations.add(Km, Km_pert, np.array([1, coef]))
Lp_total = H_operations.add(Lp, Lp_pert, np.array([1, coef]))
Lm_total = H_operations.add(Lm, Lm_pert, np.array([1, coef]))
H = H_operations.add(Ip_total, Im_total, np.array([1j, -1j]))
H = H_operations.add(H, Kp_total, np.array([1, -1j]))
H = H_operations.add(H, Km_total, np.array([1, 1j]))
H = H_operations.add(H, Lp_total, np.array([1, 1j]))
H = H_operations.add(H, Lm_total, np.array([1, -1j]))
H.sector.find_eig(k)
z = zm_state(2, 1, pxp, 1)
block_refs = pxp_syms.find_block_refs(k)
psi = np.zeros(np.size(block_refs))
loc = find_index_bisection(z.ref, block_refs)
psi[loc] = 1
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors(k))), psi)
t = np.arange(0, 20, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
evolved_state = time_evolve_state(psi_energy, H.sector.eigvalues(k),
t[n])
f[n] = np.abs(np.vdot(evolved_state, psi_energy))**2
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.1:
cut = n
break
f0 = np.max(f[cut:])
plt.scatter(H.sector.eigvalues(k), np.log10(np.abs(psi_energy)**2))
plt.title(r"$PCP+\lambda(PPCP+PCPP), N=$" + str(pxp.N))
plt.xlabel(r"$E$")
plt.ylabel(r"$\log(\vert \langle \psi \vert E \rangle \vert^2)$")
plt.show()
plt.plot(t, f)
plt.title(r"$PCP+\lambda(PPCP+PCPP), N=$" + str(pxp.N))
plt.xlabel(r"$t$")
plt.ylabel(r"$\vert \langle \psi(0) \vert \psi(t) \rangle \vert^2$")
plt.show()
return 1 - f0
def var_error(coef, pxp_config, pxxxp_config):
Hp = gen_Hp(pxp_config, pxxxp_config, coef)
Hm = np.conj(np.transpose(Hp))
H = Hp + Hm
Hz = 1 / 2 * com(Hp, Hm)
z = zm_state(2, 1, pxp, 1)
fsa_basis = gen_fsa_basis(Hp, z.prod_basis(), pxp.N)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
Hz_var = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(Hz_var, axis=0)):
Hz_var[n] = var(Hz, fsa_basis[:, n])
# error = np.max(Hz_var)
error = np.sum(Hz_var)
print(coef, error)
return error
def subspace_variance(coef):
coef = coef[0]
Hp_total = deepcopy(Hp[0])
Hp_total = H_operations.add(Hp_total,Hp[1],np.array([1,coef]))
Hm = Hp_total.herm_conj()
H = H_operations.add(Hp_total,Hm,np.array([1,1]))
H.sector.find_eig()
z=zm_state(2,2,pxp,1)
from Calculations import gen_fsa_basis
fsa_dim = 2*pxp.N
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(),z.prod_basis(),fsa_dim)
H2 = np.dot(H.sector.matrix(),H.sector.matrix())
H2_fsa = np.dot(np.conj(np.transpose(fsa_basis)),np.dot(H2,fsa_basis))
H_fsa = np.dot(np.conj(np.transpose(fsa_basis)),np.dot(H.sector.matrix(),fsa_basis))
subspace_variance = np.real(np.trace(H2_fsa-np.dot(H_fsa,H_fsa)))
return subspace_variance
def spacing_error(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
e, u = np.linalg.eigh(H)
z = zm_state(3, 1, pxp)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
overlap = np.log10(np.abs(psi_energy)**2)
scar_indices = get_top_band_indices(e,
overlap,
int(2 * N / 3),
150,
200,
e_diff=0.5)
# plt.scatter(e,overlap)
# for n in range(0,np.size(scar_indices,axis=0)):
# plt.scatter(e[scar_indices[n]],overlap[scar_indices[n]],marker="x",s=100,color="red")
# plt.show()
scar_e = np.zeros(np.size(scar_indices))
for n in range(0, np.size(scar_indices, axis=0)):
scar_e[n] = e[scar_indices[n]]
diffs = np.zeros(np.size(scar_e) - 1)
for n in range(0, np.size(diffs, axis=0)):
diffs[n] = scar_e[n + 1] - scar_e[n]
diff_matrix = np.zeros((np.size(diffs), np.size(diffs)))
for n in range(0, np.size(diff_matrix, axis=0)):
for m in range(0, np.size(diff_matrix, axis=0)):
diff_matrix[n, m] = diffs[n] - diffs[m]
error = np.power(
np.trace(np.dot(diff_matrix, np.conj(np.transpose(diff_matrix)))), 0.5)
print(coef, error)
print(scar_e)
# print(coef)
# if (np.abs(coef).any())>0.5:
# return 1000
# else:
return error
def opt_fidelity(coef, plot=False):
H = H0.sector.matrix() + coef[0] * V1 + coef[1] * V2 + coef[2] * V3
# H = H0.sector.matrix()+coef[0]*V3
e, u = np.linalg.eigh(H)
psi = zm_state(3, 1, pxp)
psi_energy = np.conj(u[pxp.keys[psi.ref], :])
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(2.5, 3.5))
f_max = fidelity_eval(psi_energy, e, res.x)
print(coef, -f_max, res.x)
if plot is True:
t = np.arange(0, 20, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, e, t[n])
# plt.plot(t,f,label="$H_0+\lambda_i V_i$")
# plt.show()
# if np.abs(res.x) < 1e-5:
# f_max = 0
return f
def fidelity_erorr(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = Hp_total.herm_conj()
Hz = 1 / 2 * com(Hp_total.sector.matrix(), Hm.sector.matrix())
e, u = np.linalg.eigh(Hz)
psi = u[:, 0]
psi = zm_state(4, 1, pxp).prod_basis()
H = H_operations.add(Hp_total, Hm, np.array([1, 1]))
H.sector.find_eig()
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors())), psi)
t = np.arange(0, 6, 0.001)
# t=np.arange(0,20,0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
evolved_state = time_evolve_state(psi_energy, H.sector.eigvalues(),
t[n])
f[n] = np.abs(np.vdot(evolved_state, psi_energy))**2
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.1:
cut = n
break
f0 = np.max(f[cut:])
print(coef, f0)
np.save("pxxxp,1stOrder,coef," + str(pxp.N), coef)
# plt.plot(t,f)
# plt.show()
# res = minimize_scalar(lambda t: -fidelity_eval(psi_energy,H.sector.eigvalues(),t),method="golden",bracket=(2.5,5.5))
# f0 = fidelity_eval(psi_energy,H.sector.eigvalues(),res.x)
if (np.abs(coef) > 0.5).any():
return 1000
else:
return 1 - f0
def krylov_su2_coupling_error(coef):
coef = coef[0]
H = H_operations.add(H0,V,np.array([1,coef]))
z=zm_state(2,1,pxp)
krylov_basis = gen_krylov_basis(H.sector.matrix(),pxp.N,z.prod_basis(),pxp,orth="qr")
H_krylov = np.dot(np.conj(np.transpose(krylov_basis)),np.dot(H.sector.matrix(),krylov_basis))
couplings = np.diag(H_krylov,1)
s = pxp.N/4
m = np.arange(-s,s)
su2_couplings_half = np.power(s*(s+1)-m*(m+1),0.5)
s = pxp.N/2
m = np.arange(-s,s)
su2_couplings_full = np.power(s*(s+1)-m*(m+1),0.5)
coupling_diff_full = couplings - su2_couplings_full
error = np.power(np.abs(np.vdot(coupling_diff_full,coupling_diff_full)),0.5)
# error = np.abs(couplings[3] - su2_couplings_half[3])
print(coef,error)
return error
def cost(alpha):
H=Hamiltonian(pxp_half,"x")
H.site_ops[1] = np.array([[0,alpha[0]],[alpha[0],0]])
H.model = np.array([[1]])
H.model_coef=np.array((1))
H.gen()
H.sector.find_eig()
z_rydberg = zm_state(2,1,pxp_half)
f_neel_ham = fidelity(z_rydberg,H).eval(t,z_rydberg)
# plt.plot(t,f_neel_ham)
# plt.show()
cut_index = 5
for n in range(0,np.size(f_neel_ham,axis=0)):
if f_neel_ham[n]<0.1:
cut_index = n
break
max_index = np.argmax(f_neel_ham[cut_index:])
t0_ham = t[max_index]
print(cost,t0_ham)
return np.abs(t0_ham-t0_floquet)
def fidelity_error(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
e, u = np.linalg.eigh(H)
z = zm_state(3, 1, pxp)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(2.5, 3.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
# print(f)
if res.x < 1e-5:
return 1000
if (np.abs(coef) > 0.5).any():
return 1000
return -f
def spacing_error(coef, pxp_config, pxxxp_config):
Hp = gen_Hp(pxp_config, pxp_config, coef)
Hm = np.conj(np.transpose(Hp))
Hz = 1 / 2 * com(Hp, Hm)
#find lowest weight state
e, u = np.linalg.eigh(Hz)
lowest_weight = u[:, 0]
z = zm_state(2, 1, pxp, 1)
fsa_basis = gen_fsa_basis(Hp, z.prod_basis(), pxp.N)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
if np.size(np.shape(fsa_basis)) == 2:
Hz_exp = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(Hz_exp, axis=0)):
Hz_exp[n] = exp(Hz, fsa_basis[:, n])
Hz_diff = np.zeros(np.size(Hz_exp) - 1)
for n in range(0, np.size(Hz_diff, axis=0)):
Hz_diff[n] = np.abs(Hz_exp[n + 1] - Hz_exp[n])
#spacing error
error_matrix = np.zeros((np.size(Hz_diff), np.size(Hz_diff)))
for n in range(0, np.size(error_matrix, axis=0)):
for m in range(0, np.size(error_matrix, axis=0)):
error_matrix[n, m] = np.abs(Hz_diff[n] - Hz_diff[m])
error = np.power(
np.trace(np.dot(error_matrix,
np.conj(np.transpose(error_matrix)))), 0.5)
print(coef, error)
return error
else:
return 1000
def exp(Q, psi):
return np.vdot(psi, np.dot(Q, psi))
def var(Q, psi):
Q2 = np.dot(Q, Q)
return exp(Q2, psi) - exp(Q, psi)**2
N = 12
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=4), PT(pxp)])
H = Hamiltonian(pxp, pxp_syms)
H.site_ops[1] = np.array([[0, 1], [1, 0]])
H.model = np.array([[0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0]])
H.model_coef = np.array([1, -1, -1])
H.uc_size = np.array([1, 4, 4])
H.uc_pos = np.array([0, 3, 1])
H.gen()
H.sector.find_eig()
z = zm_state(4, 1, pxp)
eig_overlap(z, H).plot()
plt.show()
fidelity(z, H).plot(np.arange(0, 20, 0.01), z)
plt.show()
# plt.scatter(pxp.keys[z.ref],ref_non_zero_sectors[pxp.keys[z.ref]],marker="s",s=50,label="z2")
# z=zm_state(3,1,pxp)
# plt.scatter(pxp.keys[z.ref],ref_non_zero_sectors[pxp.keys[z.ref]],marker="s",s=50,label="z3")
# z=zm_state(3,1,pxp,1)
# plt.scatter(pxp.keys[z.ref],ref_non_zero_sectors[pxp.keys[z.ref]],marker="s",s=50,label="z3")
# z=zm_state(3,1,pxp,2)
# plt.scatter(pxp.keys[z.ref],ref_non_zero_sectors[pxp.keys[z.ref]],marker="s",s=50,label="z3")
# plt.legend()
# plt.plot(ref_non_zero_sectors)
# plt.xlabel("State label")
# plt.ylabel("No. of non zero Hamming sectors")
# plt.title("Non zero Hamming sectors from computational basis states, PXP, N="+str(pxp.N))
# plt.show()
# z=ref_state(0,pxp)
z = zm_state(2, 1, pxp)
hamming_sectors = find_hamming_sectors(z.bits)
# H = Hamiltonian(pxp,pxp_syms)
# H.site_ops[1] = np.array([[0,1],[1,0]])
# H.model = np.array([[0,1,0],[0,0,1,0],[0,1,0,0]])
# # H.model = np.array([[0,1,0],[0,1,1,1,0]])
# coef = 1/8
# H.model_coef = np.array((1,coef,coef))
# H.model_coef = np.array((1,coef))
H = spin_Hamiltonian(pxp, "x", pxp_syms)
H.gen()
def get_state_connections(state_ref, h_sector, H_matrix):
Lm_pert.uc_pos = np.array([0, 1, 1, 0]) # Ip.gen() # Im.gen() # Kp.gen() # Km.gen() # Lp.gen() # Lm.gen() # Ip_pert.gen() # Im_pert.gen() # Kp_pert.gen() # Km_pert.gen() # Lp_pert.gen() # Lm_pert.gen() z = zm_state(2, 1, pxp) # k=pxp_syms.find_k_ref(z.ref) k = [0, 0] Ip.gen(k) Im.gen(k) Kp.gen(k) Km.gen(k) Lp.gen(k) Lm.gen(k) Ip_pert.gen(k) Im_pert.gen(k) Kp_pert.gen(k) Km_pert.gen(k) Lp_pert.gen(k) Lm_pert.gen(k)
z = ref_state(pxp.basis_refs[index], pxp)
index = pxp.keys[z.ref]
rho = np.zeros((pxp.dim, pxp.dim))
rho[index, index] = 1
#integrate linblad with runge kutta
rho
delta_t = 0.1
t_max = 10
t = np.arange(0, t_max + delta_t, delta_t)
rho_t = dict()
rho_t[0] = rho
coef = 0.1
f = np.zeros(np.size(t))
f[0] = 1
z_anti = zm_state(2, 1, pxp, 1)
rho_anti = np.zeros((pxp.dim, pxp.dim))
index = pxp.keys[z_anti.ref]
rho_anti[index, index] = 1
for n in range(1, np.size(t, axis=0)):
k1 = delta_t * linblad(rho_t[n - 1], H.sector.matrix(), P, coef)
k2 = delta_t * (linblad(rho_t[n - 1] + k1 / 2, H.sector.matrix(), P,
coef))
k3 = delta_t * (linblad(rho_t[n - 1] + k2 / 2, H.sector.matrix(), P,
coef))
k4 = delta_t * (linblad(rho_t[n - 1] + k3, H.sector.matrix(), P, coef))
rho_t[n] = rho_t[n - 1] + 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4)
f[n] = np.real(
np.trace(np.dot(np.conj(np.transpose(rho_t[n])), rho_t[0])))
plt.plot(t, f)
roots = find_root_refs(np.array([2,0]),np.array([2,2]))
temp_basis = find_subcube_basis(roots[0],2,"Right")
for m in range(1,np.size(roots,axis=0)):
temp_basis = temp_basis + find_subcube_basis(roots[m],2,"Right")
for m in range(0,np.size(temp_basis,axis=1)):
temp_basis[:,m] = temp_basis[:,m] / np.power(np.vdot(basis[:,m],basis[:,m]),0.5)
basis = np.hstack((basis,temp_basis))
neel_subcube_system = unlocking_System([0,1],"open",2,int(pxp.N/2))
neel_subcube_system.gen_basis()
z=ref_state(np.max(neel_subcube_system.basis_refs),neel_subcube_system)
neel_hamming = find_hamming_sectors(z.bits,neel_subcube_system)
#hypercube from Neel/AntiNeel
z0=zm_state(2,1,pxp)
z1=zm_state(2,1,pxp,1)
cube_dim = int(pxp.N/2)
cube_basisL = np.zeros(pxp.dim)
cube_basisR = np.zeros(pxp.dim)
for n in range(0,len(neel_hamming)):
# for n in range(0,2):
refs = neel_hamming[n]
temp_stateL = np.zeros(pxp.dim)
temp_stateR = np.zeros(pxp.dim)
one_locL = np.arange(0,pxp.N-1,2)
one_locR = np.arange(1,pxp.N,2)
for m in range(0,np.size(refs,axis=0)):
state_bits = neel_subcube_system.basis[neel_subcube_system.keys[refs[m]]]
temp_bitsL = np.zeros(pxp.N)
temp_bitsR = np.zeros(pxp.N)
Hm = np.conj(np.transpose(Hp))
def com(a, b):
return np.dot(a, b) - np.dot(b, a)
Hz = 1 / 2 * com(Hp, Hm)
# plt.matshow(np.abs(Hz))
# plt.show()
# print((np.abs(Hz-np.conj(np.transpose(Hz)))<1e-5).all())
H = spin_Hamiltonian(pxp, "x", pxp_syms)
H.gen()
z = zm_state(3, 1, pxp, 2)
k = pxp_syms.find_k_ref(z.ref)
U = dict()
for n in range(0, np.size(k, axis=0)):
U[n] = pxp_syms.basis_transformation(k[n])
fsa_basis = z.prod_basis()
fsa_basis2 = z.prod_basis()
krylov_basis = z.prod_basis()
current_state = fsa_basis
current_state2 = fsa_basis
current_stateK = fsa_basis
fsa_dim = int(2 * N / 3)
for n in range(0, fsa_dim):
next_state = np.dot(Hp, current_state)
next_state2 = np.dot(Hp2, current_state2)
H.model = np.array([[2,1,2],[2,1,3],[3,1,2]])
V=30e-1
H.model_coef = np.array([V,1,1])
# H.model = np.array([[0,1]])
# H.model_coef = np.array([1])
k=[0]
H.gen(k)
H.sector.find_eig(k)
block_refs = pxp_syms.find_block_refs(k)
block_keys = dict()
for n in range(0,np.size(block_refs,axis=0)):
block_keys[block_refs[n]] = n
neel=zm_state(2,1,pxp,1)
pol = ref_state(0,pxp)
all_ones = bin_state(np.append([0],np.ones(pxp.N-1)),pxp)
neel_trans = np.zeros(np.size(block_refs))
pol_trans = np.zeros(np.size(block_refs))
all_ones_trans = np.zeros(np.size(block_refs))
neel_trans[block_keys[neel.ref]] = 1
pol_trans[block_keys[pol.ref]] = 1
all_ones_trans[block_keys[all_ones.ref]] = 1
neel_trans_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors(k))),neel_trans)
pol_trans_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors(k))),pol_trans)
all_ones_trans_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors(k))),all_ones_trans)
from Construction_functions import bin_to_int_base_m, int_to_bin_base_m, cycle_bits_state
from Search_functions import find_index_bisection
from State_Classes import zm_state, sym_state, prod_state, bin_state, ref_state
from rw_functions import save_obj, load_obj
from Calculations import level_stats, fidelity, eig_overlap, entropy, site_precession, site_projection, time_evolve_state
import math
N = 18
D = 2
d = 2
#convert MPS -> wf array
pxp = unlocking_System([0], "periodic", d, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=3)])
z = zm_state(3, 1, pxp)
k = pxp_syms.find_k_ref(z.ref)
U = dict()
for n in range(0, np.size(k, axis=0)):
U[int(k[n])] = pxp_syms.basis_transformation(k[n])
wf = np.load("./z3,entangled_MPS_coef," + str(pxp.N) + ".npy")
#project wf to symmetry basis
wf_sym = dict()
for n in range(0, np.size(k, axis=0)):
wf_sym[int(k[n])] = np.dot(np.conj(np.transpose(U[int(k[n])])), wf)
# dynamics + fidelity
V1_ops = dict()
V1_ops[0] = Hamiltonian(pxp, pxp_syms)
## for Palatino and other serif fonts use:
#rc('font',**{'family':'serif','serif':['Palatino']})
rc('text', usetex=True)
# matplotlib.rcParams['figure.dpi'] = 400
N=20
pxp = unlocking_System([0],"periodic",2,N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp,[translational(pxp)])
H = Hamiltonian(pxp,pxp_syms)
H.site_ops[1] = np.array([[0,1],[1,0]])
H.model = np.array([[0,1,1,1,0]])
H.model_coef = np.array([1])
z=zm_state(4,1,pxp)
z1=zm_state(4,1,pxp,1)
z2=zm_state(4,1,pxp,2)
z3=zm_state(4,1,pxp,3)
k=pxp_syms.find_k_ref(z.ref)
for n in range(0,np.size(k,axis=0)):
H.gen(k[n])
H.sector.find_eig(k[n])
eig_overlap(z,H,k[n]).plot()
plt.show()
t=np.arange(0,20,0.01)
f0 = fidelity(z,H,"use sym").eval(t,z)
f1 = fidelity(z,H,"use sym").eval(t,z1)
f2 = fidelity(z,H,"use sym").eval(t,z2)