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()
def ITE(H_,db,bmax,lanczos=False,psi0=None):
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)
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)
fout = open('ITE.out','w')
fout.write("FCI gs energy %.6f \n" % epsm0)
fout.write("FCI gs wfn \n")
print_state(Um0,nbit,fout)
if(psi0 is None):
i0 = np.argmin(hdiag)
psi_ITE = np.zeros(N,dtype=complex)
psi_ITE[i0] = 1.0
else:
psi_ITE = psi0.copy()
nbeta = int(bmax/db)+1
hvect_LANZ = np.zeros(nbeta+1)
svect_LANZ = np.zeros(nbeta+1)
if(lanczos):
space_LANZ = np.zeros((N,nbeta),dtype=complex)
fout.write("ITE\n")
for ib in range(nbeta):
ea,ev = Hmoms(H_,psi_ITE)
hvect_LANZ[ib] = ea
fide = fidelity(psi_ITE,Um0)
if(lanczos):
space_LANZ[:,ib] = psi_ITE.copy()
psi_LANZ = Lanczos_kernel(UH,space_LANZ[:,:ib+1])
ea_,ev_ = Hmoms(H_,psi_LANZ)
fide_ = fidelity(psi_LANZ,Um0)
fout.write("%.6f %.6f %.6f %.6f %.6f %.6f %.6f \n" % (ib*db,ea,ev,fide,ea_,ev_,fide_))
else:
fout.write("%.6f %.6f %.6f %.6f \n" % (ib*db,ea,ev,fide))
psi_ITE,dn = ExpmbH(H_,psi_ITE,db)
svect_LANZ[ib+1] = svect_LANZ[ib]+np.log(dn)
fout.write("ITE gs wfn \n")
print_state(psi_ITE,nbit,fout)
dump_state(psi_ITE,nbit,'ite.psi')
dump_lanz_vecs(hvect_LANZ[:nbeta],svect_LANZ[:nbeta],'qlanz.vecs')
fout.close()
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()