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298 | class TIHamiltonian :
""" The time-independent Hamiltonian
The underlying data-structure to store it is a list of
tuples (h, c). Here h is a product Hamiltonian,
represented by a list of site operators on the sites.
c is the coefficient corresponding to h, and can either
be a real number or an Expression.
The site operator algebras are symbolically dealt with
here, since fermionic operators' algebra is position-related.
We can also test commutativity of Hamiltonians, and
calculate the sites the Hamiltonian is acting non-
trivially on.
"""
def __init__(self, sites_type, ham) :
self.sites_type = sites_type
self.ham = ham
self.saved_t_sites = None
self.cleanHam()
@classmethod
def empty(cls, sites_type) :
ham = []
return cls(sites_type, ham)
@classmethod
def identity(cls, sites_type) :
num_sites = len(sites_type)
prod = ['' for i in range(num_sites)]
ham = [(prod, 1)]
return cls(sites_type, ham)
@classmethod
def op(cls, sites_type, index, op) :
num_sites = len(sites_type)
prod = ['' for i in range(num_sites)]
prod[index] = op
ham = [(prod, 1)]
return cls(sites_type, ham)
def operAlgebra(self) :
self.extend_ham_by_sites()
i = 0
while i < len(self.ham) :
(h, coef) = self.ham[i]
for j in range(len(h)) :
if self.sites_type[j] == 'qubit' :
if h[j] == 'XX' or h[j] == 'YY' or h[j] == 'ZZ' :
h[j] = ''
elif h[j] == 'XY' :
h[j] = 'Z'
coef *= 1j
elif h[j] == 'YX' :
h[j] = 'Z'
coef *= -1j
elif h[j] == 'YZ' :
h[j] = 'X'
coef *= 1j
elif h[j] == 'ZY' :
h[j] = 'X'
coef *= -1j
elif h[j] == 'ZX' :
h[j] = 'Y'
coef *= 1j
elif h[j] == 'XZ' :
h[j] = 'Y'
coef *= -1j
self.ham[i]
for j in range(len(h)) :
if self.sites_type[j] == 'boson' :
s = h[j].find('ac')
while s != -1 :
h_copy = h.copy()
h_copy[j] = h_copy[j].replace('ac', 'ca', 1)
h[j] = h[j].replace('ac', '', 1)
self.ham.append((h_copy, coef))
s = h[j].find('ac')
elif self.sites_type[j] == 'fermion' :
s = h[j].find('ac')
while s != -1 :
h_copy = h.copy()
h_copy[j] = h_copy[j].replace('ac', 'ca', 1)
h[j] = h[j].replace('ac', '', 1)
self.ham.append((h_copy, -coef))
s = h[j].find('ac')
self.ham[i] = (h, coef)
i += 1
def cleanHam(self, tol = 1e-10) :
self.operAlgebra()
i = 0
while i < len(self.ham) :
for j in range(i) :
if self.ham[j][0] == self.ham[i][0] :
self.ham[j] = (self.ham[j][0], self.ham[j][1] + self.ham[i][1])
del self.ham[i]
i -= 1
break
i += 1
i = 0
while i < len(self.ham) :
if isinstance(self.ham[i][1], Expression) :
break
if abs(self.ham[i][1]) < tol :
del self.ham[i]
continue
i += 1
def extend_ham_by_sites(self) :
for i in range(len(self.ham)) :
(h, coef) = self.ham[i]
if len(h) < len(self.sites_type) :
h += [''] * (len(self.sites_type) - len(h))
self.ham[i] = (h, coef)
def extend_sites(self, new_sites_type) :
if len(new_sites_type) <= len(self.sites_type) :
return
for i in range(len(self.sites_type)) :
if self.sites_type[i] != new_sites_type[i] :
raise Exception("Sites type inconsistent!")
add_num = len(new_sites_type) - len(self.sites_type)
new_ham = [(self.ham[i][0] + [''] * add_num, self.ham[i][1]) for i in range(len(self.ham))]
self.sites_type = new_sites_type
self.ham = new_ham
if self.saved_t_sites is not None :
self.saved_t_sites += [0 for j in range(add_num)]
def __neg__(self) :
ham = copy(self.ham)
for i in range(len(ham)) :
ham[i] = (ham[i][0], -ham[i][1])
h = TIHamiltonian(self.sites_type, ham)
return h
def __add__(self, other) :
# need more typing restrictions
if type(other) == int or type(other) == float or type(other) == complex or isinstance(other, Expression) :
other = other * TIHamiltonian.empty()
if self.sites_type != other.sites_type :
self.extend_sites(other.sites_type)
other.extend_sites(self.sites_type)
ham = copy(self.ham)
ham += other.ham
h = TIHamiltonian(self.sites_type, ham)
h.cleanHam()
return h
def __radd__(self, other) :
if type(other) == int or type(other) == float or type(other) == complex or isinstance(other, Expression) :
return self.__add__(other * TIHamiltonian.empty(self.sites_type))
else :
return NotImplemented
def __sub__(self, other) :
# need more typing restrictions
if type(other) == int or type(other) == float or type(other) == complex or isinstance(other, Expression) :
other = other * TIHamiltonian.empty(self.sites_type)
if self.sites_type != other.sites_type :
self.extend_sites(other.sites_type)
other.extend_sites(self.sites_type)
ham = copy(self.ham)
ham += other.__neg__().ham
h = TIHamiltonian(self.sites_type, ham)
h.cleanHam()
return h
def __rsub__(self, other) :
if type(other) == int or type(other) == float or type(other) == complex or isinstance(other, Expression) :
return (other * TIHamiltonian.empty(self.sites_type)) - self
else :
return NotImplemented
@staticmethod
def strlist_mul(sites_type, a, b) :
c = []
coef = 1
# Use a suffix sum to calculate the number of fermionic operators after site i.
num_ferm_ope_backward = [0 for i in range(len(sites_type))]
for i in range(len(sites_type) - 1, 1, -1) :
num_ferm_ope_backward[i - 1] = num_ferm_ope_backward[i]
if sites_type[i] == 'fermion' :
num_ferm_ope_backward[i - 1] += len(a[i])
for i in range(len(sites_type)) :
if sites_type[i] == 'qubit' :
c.append(a[i] + b[i])
elif sites_type[i] == 'boson' :
c.append(a[i] + b[i])
elif sites_type[i] == 'fermion' :
c.append(a[i] + b[i])
if num_ferm_ope_backward[i] % 2 == 1 and len(b[i]) % 2 == 1 :
coef *= -1
return (c, coef)
def scalar_mul(self, other) :
ham = copy(self.ham)
for i in range(len(ham)) :
ham[i] = (ham[i][0], ham[i][1] * other)
h = TIHamiltonian(self.sites_type, ham)
return h
def __mul__(self, other) :
# need more typing restrictions
if type(other) == int or type(other) == float or type(other) == complex or isinstance(other, Expression) :
return self.scalar_mul(other)
self.extend_ham_by_sites()
other.extend_ham_by_sites()
if self.sites_type != other.sites_type :
self.extend_sites(other.sites_type)
other.extend_sites(self.sites_type)
ham = []
for (prod1, coef1) in self.ham :
for (prod2, coef2) in other.ham :
(prod, coef3) = self.strlist_mul(self.sites_type, prod1, prod2)
ham.append((prod, coef1 * coef2 * coef3))
h = TIHamiltonian(self.sites_type, ham)
h.cleanHam()
return h
def __truediv__(self, other) :
if type(other) == int or type(other) == float or type(other) == complex or isinstance(other, Expression) :
return self.scalar_mul(1/other)
else :
return NotImplemented
def __rmul__(self, other) :
if type(other) == int or type(other) == float or type(other) == complex or isinstance(other, Expression) :
return self.scalar_mul(other)
else :
return NotImplemented
def exp_eval(self, gvars, lvars) :
ham = copy(self.ham)
for i in range(len(ham)) :
ham[i] = (ham[i][0], ham[i][1].exp_eval(gvars, lvars))
h = TIHamiltonian(self.sites_type, ham)
return h
def is_empty(self) :
abs_sum = 0
for (prod, c) in self.ham :
abs_sum += abs(c)
if abs_sum < 1e-8 :
return True
else :
return False
@staticmethod
def commutativity_test(h1, h2, derived = False) :
if derived :
t_sites1 = h1.touched_sites()
t_sites2 = h2.touched_sites()
for i in range(len(h1.sites_type)) :
if t_sites1[i] == 1 and t_sites2[i] == 1 :
return False
return True
return (h1 * h2 - h2 * h1).is_empty()
def touched_sites(self) :
if self.saved_t_sites != None :
return self.saved_t_sites
ret = [0 for i in range(len(self.sites_type))]
for (prod, t) in self.ham :
for i in range(len(self.sites_type)) :
if prod[i] != '' :
ret[i] = 1
self.saved_t_sites = ret
return ret
|