def ITE_FCI(H_,db,bmax,psi0=None,omega=None):
Hm = Hmat(H_)
N = Hm.shape[0]
nbit = int(np.log2(N))
eps,U = SciLA.eigh(Hm)
m0 = np.argmin(eps)
zeta = np.exp(-db*(eps-eps[m0]))
fout = open('ITE_FCI.out','w')
fout.write("FCI gs energy %.6f \n" % eps[m0])
fout.write("FCI gs wfn \n")
print_state(U[:,m0],nbit,fout)
if(psi0 is None):
i0 = np.argmin(np.diag(Hm))
psi_FCI = np.zeros(N,dtype=complex)
psi_FCI[i0] = 1.0
else:
psi_FCI = psi0.copy()
nbeta = int(bmax/db)+1
fout.write("FCI ITE\n")
data = np.zeros((nbeta,2))
for ib in range(nbeta):
ea,ev = Hmoms(H_,psi_FCI)
#print (ib*db,ea,ev)
psi_FCI = np.dot(np.conj(U.T),psi_FCI)
psi_FCI = zeta*psi_FCI
psi_FCI = np.dot(U,psi_FCI)
psi_FCI /= LA.norm(psi_FCI)
if(omega is None): fide = fidelity(psi_FCI,U[:,m0])
else: fide = LA.norm(psi_FCI[omega])**2
fout.write("%.6f %.6f %.6f %.6f \n" % (ib*db,ea,ev,fide))
#print(ea)
data[ib, 0] = ib*db
data[ib, 1] = ea
if ea < 0.01 and ea > -0.01:
print('wf: ',psi_FCI)
# if ea < 1e-3:
# print("%.6f %.6f %.6f %.6f \n" % (ib*db,ea,ev,fide))
fout.write("FCI ITE gs wfn \n")
#print_state(psi_FCI,nbit,fout)
fout.close()
return data
def QITE(H_, db, bmax, lanczos=False, psi0=None, omega=None, ncheck=1):
Hm = Hmat(H_)
N = Hm.shape[0]
nbit = int(np.log2(N))
eps, U = SciLA.eigh(Hm)
m0 = np.argmin(eps)
zeta = np.exp(-db * (eps - eps[m0]))
fide = 1.0
fout = open('QITE.out', 'w')
fout.write("FCI gs energy %.6f \n" % eps[m0])
fout.write("FCI gs wfn \n")
print_state(U[:, m0], nbit, fout)
psi_QITE = psi0[:]
nbeta = int(bmax / db) + 1
hvect_LANZ = np.zeros(nbeta + 1)
svect_LANZ = np.zeros(nbeta + 1)
xv = None
fout.write("QITE\n")
for ib in range(nbeta):
ea, ev = Hmoms(H_, psi_QITE)
hvect_LANZ[ib] = ea
if (omega is None): fide = fidelity(psi_QITE, U[:, m0])
else: fide = LA.norm(psi_QITE[omega])**2
if (lanczos):
ea_ = Lanczos_QITE(hvect_LANZ[:ib + 1], svect_LANZ[:ib + 1], db)
fout.write("%.6f %.6f %.6f %.6f %.6f \n" %
(ib * db, ea, ev, fide, ea_))
else:
fout.write("%.6f %.6f %.6f %.6f \n" % (ib * db, ea, ev, fide))
fout.flush()
psi_QITE, dnorm, xv = QITE_step(H_, psi_QITE, db, xv, ib % ncheck == 0)
svect_LANZ[ib + 1] = svect_LANZ[ib] + np.log(dnorm)
fout.write("QITE gs wfn \n")
print_state(psi_QITE, nbit, fout)
dump_state(psi_QITE, nbit, 'qite.psi')
dump_lanz_vecs(hvect_LANZ[:nbeta], svect_LANZ[:nbeta], 'qlanz.vecs')
fout.close()
R = 1.50 db = 0.01 bmax = 8.00 vrtex = [x for x in range(nspin)] if(nspin==4): np.random.seed(1953) else: np.random.seed(14657) links = [] for i in range(nspin): for j in range(i+1,nspin): x = np.random.randint(2,size=1)[0] if(x==1): links.append((i,j)) #if(nspin==4): links=[(0,1),(0,2),(0,3),(1,3),(2,3)] # IBM graph gamma = (vrtex,links) H = MaxCut(gamma,R) print_Hamiltonian(H) Hm = np.diag(Hmat(H)) E0 = np.min(Hm) omega = np.where(np.abs(Hm-E0)<1e-6)[0] theta0 = np.random.random()*2.0*np.pi theta1,e1 = hom_mf_solution(theta0,nspin,H) psi_1 = hom_mf_state(theta1,nspin) print "HOM mf-energy ",e1 ITE_FCI(H,db,bmax,psi0=psi_1,omega=omega) QITE(H,db,bmax,lanczos=False,psi0=psi_1,omega=omega,ncheck=10)
from scipy.linalg import eigh
nspin = 3
R = 0.5
db = 0.5
bmax = 2.00
#H = Heisenberg_LR(nspin,R)
J = 1/np.sqrt(2)
#H = TransverseIsing(nspin, R, J, J)
#H = Ising(nspin, R, pi/2)
H = single_qubit_field(pi/4)
#print('Hamiltonian\n',H)
print_Hamiltonian(H)
Hm = Hmat(H)
evl, evc = eigh(Hm)
print(evl)
# print()
# print(np.real(Hm))
# AFM initial guess
psi_0 = np.zeros(2**nspin,dtype=complex)
#psi_0 = np.array([ 0, 0,0,1],dtype=complex)
#print(psi_0)
xvec = [0,1]*ceil((nspin/2))
xind = Bas2Int(xvec,2)
#psi_0[xind] = 1.0
psi_0[0] = 1.0
def QITE(H_, db, bmax, lanczos=False, psi0=None, omega=None, ncheck=1):
Hm = Hmat(H_)
N = Hm.shape[0]
nbit = int(np.log2(N))
eps, U = SciLA.eigh(Hm)
m0 = np.argmin(eps)
epsm0 = eps[m0]
Um0 = U[:, m0]
zeta = np.exp(-db * (eps - eps[m0]))
fide = 1.0
fout = open('QITE.out', 'w')
fout.write("FCI gs energy %.6f \n" % epsm0)
fout.write("FCI gs wfn \n")
print_state(Um0, nbit, fout)
psi_QITE = psi0[:]
nbeta = int(bmax / db) + 1
hvect_LANZ = np.zeros(nbeta + 1)
svect_LANZ = np.zeros(nbeta + 1)
xv = None
hpauli = {}
fout.write("QITE\n")
data = np.zeros((nbeta, 2))
for ib in range(nbeta):
print('B: ', ib * db)
ea, ev = Hmoms(H_, psi_QITE)
print('Energy: ', ea)
hvect_LANZ[ib] = ea
if (omega is None):
fide = fidelity(psi_QITE, Um0)
else:
fide = LA.norm(psi_QITE[omega])**2
if (lanczos):
ea_ = Lanczos_QITE(hvect_LANZ[:ib + 1], svect_LANZ[:ib + 1], db)
fout.write("%.6f %.6f %.6f %.6f %.6f \n" %
(ib * db, ea, ev, fide, ea_))
else:
fout.write("%.6f %.6f %.6f %.6f \n" % (ib * db, ea, ev, fide))
#print("%.6f %.6f %.6f %.6f \n" % (ib*db,ea,ev,fide))
fout.flush()
b = ib * db
data[ib, 0] = b
data[ib, 1] = ea
if (ncheck > 0):
check = (ib % ncheck == 0)
else:
check = False
psi_QITE, dnorm, xv, Xop = QITE_step(H_, psi_QITE, db, xv, check)
hpauli[b] = Xop
# Feedback portion
# Number of applications of the unitary to get ground state
svect_LANZ[ib + 1] = svect_LANZ[ib] + np.log(dnorm)
fout.write("QITE gs wfn \n")
print_state(psi_QITE, nbit, fout)
dump_state(psi_QITE, nbit, 'qite.psi')
dump_lanz_vecs(hvect_LANZ[:nbeta], svect_LANZ[:nbeta], 'qlanz.vecs')
fout.close()
return data, hpauli
def QITE(H_,
db,
bmax,
lanczos=False,
psi0=None,
omega=None,
ncheck=1,
davidson=True):
if (davidson):
N = H_[0][2].shape[1]
nbit = int(np.log2(N))
hdiag = np.zeros(N, dtype=complex)
for i in range(N):
hdiag[i] = Hii(H_, i)
print i, hdiag[i]
precond = lambda x, e, *args: x / (hdiag - e + 1e-4)
def hop(c_):
return Hpsi(H_, c_)
if (psi0 is None):
i0 = np.argmin(hdiag)
psi0 = np.zeros(N, dtype=complex)
psi0[i0] = 1.0
from pyscf.lib import davidson
epsm0, Um0 = davidson(hop, psi0, precond)
else:
Hm = Hmat(H_)
N = Hm.shape[0]
nbit = int(np.log2(N))
eps, U = SciLA.eigh(Hm)
m0 = np.argmin(eps)
epsm0 = eps[m0]
Um0 = U[:, m0]
zeta = np.exp(-db * (eps - eps[m0]))
fide = 1.0
fout = open('QITE.out', 'w')
fout.write("FCI gs energy %.6f \n" % epsm0)
fout.write("FCI gs wfn \n")
print_state(Um0, nbit, fout)
psi_QITE = psi0[:]
nbeta = int(bmax / db) + 1
hvect_LANZ = np.zeros(nbeta + 1)
svect_LANZ = np.zeros(nbeta + 1)
xv = None
fout.write("QITE\n")
for ib in range(nbeta):
ea, ev = Hmoms(H_, psi_QITE)
hvect_LANZ[ib] = ea
if (omega is None): fide = fidelity(psi_QITE, Um0)
else: fide = LA.norm(psi_QITE[omega])**2
if (lanczos):
ea_ = Lanczos_QITE(hvect_LANZ[:ib + 1], svect_LANZ[:ib + 1], db)
fout.write("%.6f %.6f %.6f %.6f %.6f \n" %
(ib * db, ea, ev, fide, ea_))
else:
fout.write("%.6f %.6f %.6f %.6f \n" % (ib * db, ea, ev, fide))
fout.flush()
if (ncheck > 0): check = (ib % ncheck == 0)
else: check = False
psi_QITE, dnorm, xv = QITE_step(H_, psi_QITE, db, xv, check)
svect_LANZ[ib + 1] = svect_LANZ[ib] + np.log(dnorm)
fout.write("QITE gs wfn \n")
print_state(psi_QITE, nbit, fout)
dump_state(psi_QITE, nbit, 'qite.psi')
dump_lanz_vecs(hvect_LANZ[:nbeta], svect_LANZ[:nbeta], 'qlanz.vecs')
fout.close()