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pauli_composer.py
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pauli_composer.py
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"""
Pauli(Diag)Composer class definition.
See: https://arxiv.org/abs/2301.00560
"""
import warnings
import numpy as np
import scipy.sparse as ss
from numbers import Number
from utils import BINARY
# Ignore ComplexWarning
warnings.simplefilter('ignore', np.ComplexWarning)
class PauliComposer:
def __init__(self, entry: str, weight: Number = None):
# Compute the number of dimensions for the given entry
n = len(entry)
self.n = n
# Compute some helpful powers
self.dim = 1<<n
# Store the entry converting the Pauli labels into uppercase
self.entry = entry.upper()
self.paulis = list(set(self.entry))
# (-i)**(0+4m)=1, (-i)**(1+4m)=-i, (-i)**(2+4m)=-1, (-i)**(3+4m)=i
mat_ent = {0: 1, 1: -1j, 2: -1, 3: 1j}
# Count the number of ny mod 4
self.ny = self.entry.count('Y') & 3
init_ent = mat_ent[self.ny]
if weight is not None:
# first non-zero entry
init_ent *= weight
self.init_entry = init_ent
self.iscomplex = np.iscomplex(init_ent)
# Reverse the input and its 'binary' representation
rev_entry = self.entry[::-1]
rev_bin_entry = ''.join([BINARY[ent] for ent in rev_entry])
# Column of the first-row non-zero entry
col_val = int(''.join([BINARY[ent] for ent in self.entry]), 2)
# Initialize an empty (2**n x 3)-matrix (rows, columns, entries)
# row = np.arange(self.dim)
col = np.empty(self.dim, dtype=np.int32)
# FIXME: storing rows and columns as np.complex64 since NumPy arrays
# must have the same data type for each entry. Consider using
# pd.DataFrame?
col[0] = col_val # first column
# The AND bit-operator computes more rapidly mods of 2**n. Check that:
# x mod 2**n == x & (2**n-1)
if weight is not None:
if self.iscomplex:
ent = np.full(self.dim, self.init_entry)
else:
ent = np.full(self.dim, float(self.init_entry))
else:
if self.iscomplex:
ent = np.full(self.dim, self.init_entry, dtype=np.complex64)
else:
ent = np.full(self.dim, self.init_entry, dtype=np.int8)
for ind in range(n):
p = 1<<int(ind) # left-shift of bits ('1' (1) << 2 = '100' (4))
p2 = p<<1
disp = p if rev_bin_entry[ind] == '0' else -p # displacements
col[p:p2] = col[0:p] + disp # compute new columns
# col[p:p2] = col[0:p] ^ p # alternative for computing column
# Store the new entries using old ones
if rev_entry[ind] in ['I', 'X']:
ent[p:p2] = ent[0:p]
else:
ent[p:p2] = -ent[0:p]
self.col = col
self.mat = ent
def to_sparse(self):
self.row = np.arange(self.dim)
return ss.csr_matrix((self.mat, (self.row, self.col)),
shape=(self.dim, self.dim))
def to_matrix(self):
return self.to_sparse().toarray()
class PauliDiagComposer:
def __init__(self, entry: str, weight: Number = None):
# Compute the number of dimensions for the given entry
n = len(entry)
self.n = n
# Compute some helpful powers
self.dim = 1<<n
# Store the entry converting the Pauli labels into uppercase
self.entry = entry.upper()
# Reverse the input and its 'binary' representation
rev_entry = self.entry[::-1]
# FIXME: storing rows and columns as np.complex64 since NumPy arrays
# must have the same data type for each entry. Consider using
# pd.DataFrame?
# mat[:, 0] = mat[:, 1] = np.arange(self.dim) # rows, columns
if weight is not None:
# first non-zero entry
mat = np.full(self.dim, weight)
else:
mat = np.ones(self.dim, dtype=np.int8)
for ind in range(n):
p = 1<<int(ind) # left-shift of bits ('1' (1) << 2 = '100' (4))
p2 = p<<1
# Store the new entries using old ones
if rev_entry[ind] == 'I':
mat[p:p2] = mat[0:p]
else:
mat[p:p2] = -mat[0:p]
self.mat = mat
def to_sparse(self):
return ss.csr_matrix((self.mat, (np.arange(self.dim), np.arange(self.dim))),
shape=(self.dim, self.dim))
def to_matrix(self):
return self.to_sparse().toarray()