def test_multiplication(self):
a = BinaryCode([[0, 1, 0], [1, 0, 1]], [
BinaryPolynomial(' w1 + w0 '),
BinaryPolynomial('w0 + 1'),
BinaryPolynomial('w1')
])
d = BinaryCode([[0, 1], [1, 0]],
[BinaryPolynomial(' w0 '),
BinaryPolynomial('w0 w1')])
b = a * d
self.assertEqual(
b.__repr__(), "[[[1, 0, 1], [0, 1, 0]],"
" '[[W0] + [W0 W1],[1] +"
" [W0],[W0 W1]]']")
b = 2 * d
self.assertEqual(
str(b), "[[[0, 1, 0, 0], [1, 0, 0, 0], "
"[0, 0, 0, 1], [0, 0, 1, 0]], "
"'[[W0],[W0 W1],[W2],[W2 W3]]']")
with self.assertRaises(BinaryCodeError):
d * a
with self.assertRaises(TypeError):
2.0 * a
with self.assertRaises(TypeError):
a *= 2.0
with self.assertRaises(ValueError):
b = 0 * a
def __init__(self, encoding, decoding):
""" Initialization of a binary code.
Args:
encoding (np.ndarray or list): nested lists or binary 2D-array
decoding (array or list): list of BinaryPolynomial(list-like or str)
Raises:
TypeError: non-list, array like encoding or decoding, unsuitable
BinaryPolynomial generators,
BinaryCodeError: in case of decoder/encoder size mismatch or
decoder size, qubits indexed mismatch
"""
if not isinstance(encoding, (numpy.ndarray, list)):
raise TypeError('encoding must be a list or array.')
if not isinstance(decoding, (numpy.ndarray, list)):
raise TypeError('decoding must be a list or array.')
self.encoder = scipy.sparse.csc_matrix(encoding)
self.n_qubits, self.n_modes = numpy.shape(encoding)
if self.n_modes != len(decoding):
raise BinaryCodeError(
'size mismatch, decoder and encoder should have the same'
' first dimension')
decoder_qubits = set()
self.decoder = []
for symbolic_binary in decoding:
if isinstance(symbolic_binary, (tuple, list, str, int,
numpy.int32, numpy.int64)):
symbolic_binary = BinaryPolynomial(symbolic_binary)
if isinstance(symbolic_binary, BinaryPolynomial):
self.decoder.append(symbolic_binary)
decoder_qubits = decoder_qubits | set(
symbolic_binary.enumerate_qubits())
else:
raise TypeError(
'decoder component provided '
'is not a suitable for BinaryPolynomial',
symbolic_binary)
if len(decoder_qubits) != self.n_qubits:
raise BinaryCodeError(
'decoder and encoder provided has different number of qubits')
if max(decoder_qubits) + 1 > self.n_qubits:
raise BinaryCodeError('decoder is not indexing some qubits. Qubits'
'indexed are: {}'.format(decoder_qubits))
def test_addition(self):
a = BinaryCode([[0, 1, 0], [1, 0, 1]],
[BinaryPolynomial(' w1 + w0 '), BinaryPolynomial('w0 + 1'),
BinaryPolynomial('w1')])
d = BinaryCode([[0, 1], [1, 0]],
[BinaryPolynomial(' w0 '), BinaryPolynomial('w0 w1')])
summation = a + d
self.assertEqual(str(summation), "[[[0, 1, 0, 0, 0],"
" [1, 0, 1, 0, 0],"
" [0, 0, 0, 0, 1],"
" [0, 0, 0, 1, 0]],"
" '[[W1] + [W0],[W0] + [1],"
"[W1],[W2],[W2 W3]]']")
with self.assertRaises(TypeError):
summation += 5
def _binary_address(digits, address):
""" Helper function to fill in an encoder column/decoder component of a
certain number.
Args:
digits (int): number of digits, which is the qubit number
address (int): column index, decoder component
Returns (tuple): encoder column, decoder component
"""
binary_expression = BinaryPolynomial('1')
# isolate the binary number and fill up the mismatching digits
address = bin(address)[2:]
address = ('0' * (digits - len(address))) + address
for index in numpy.arange(digits):
binary_expression *= BinaryPolynomial('w' + str(index) + ' + 1 + ' +
address[index])
return list(map(int, list(address))), binary_expression
def _decoder_checksum(modes, odd):
""" Helper function for checksum_code that outputs the decoder.
Args:
modes (int): number of modes
odd (int or bool): 1 (True) or 0 (False), if odd,
we encode all states with odd Hamming weight
Returns (list): list of BinaryPolynomial
"""
if odd:
all_in = BinaryPolynomial('1')
else:
all_in = BinaryPolynomial()
for mode in range(modes - 1):
all_in += BinaryPolynomial('w' + str(mode))
djw = linearize_decoder(numpy.identity(modes - 1, dtype=int))
djw.append(all_in)
return djw
def test_init_errors(self):
with self.assertRaises(TypeError):
BinaryCode(1,
[BinaryPolynomial(' w1 + w0 '), BinaryPolynomial('w0 + 1')])
with self.assertRaises(TypeError):
BinaryCode([[0, 1], [1, 0]], '1+w1')
with self.assertRaises(BinaryCodeError):
BinaryCode([[0, 1], [1, 0]], [BinaryPolynomial(' w1 + w0 ')])
with self.assertRaises(TypeError):
BinaryCode([[0, 1, 1], [1, 0, 0]], ['1 + w1',
BinaryPolynomial('1 + w0'),
2.0])
with self.assertRaises(BinaryCodeError):
BinaryCode([[0, 1], [1, 0]], [BinaryPolynomial(' w0 '),
BinaryPolynomial('w0 + 1')])
with self.assertRaises(BinaryCodeError):
BinaryCode([[0, 1], [1, 0]], [BinaryPolynomial(' w5 '),
BinaryPolynomial('w0 + 1')])
def make_parity_list(code):
"""Create the parity list from the decoder of the input code.
The output parity list has a similar structure as code.decoder.
Args:
code (BinaryCode): the code to extract the parity list from.
Returns (list): list of BinaryPolynomial, the parity list
Raises:
TypeError: argument is not BinaryCode
"""
if not isinstance(code, BinaryCode):
raise TypeError('argument is not BinaryCode')
parity_binaries = [BinaryPolynomial()]
for index in numpy.arange(code.n_modes - 1):
parity_binaries += [parity_binaries[-1] + code.decoder[index]]
return parity_binaries
def linearize_decoder(matrix):
""" Outputs linear decoding function from input matrix
Args:
matrix (np.ndarray or list): list of lists or 2D numpy array
to derive the decoding function from
Returns (list): list of BinaryPolynomial
"""
matrix = numpy.array(list(map(numpy.array, matrix)))
system_dim, code_dim = numpy.shape(matrix)
decoder = [] * system_dim
for row_idx in numpy.arange(system_dim):
dec_str = ''
for col_idx in numpy.arange(code_dim):
if matrix[row_idx, col_idx] == 1:
dec_str += 'W' + str(col_idx) + ' + '
dec_str = dec_str.rstrip(' + ')
decoder.append(BinaryPolynomial(dec_str))
return decoder
def double_decoding(decoder_1, decoder_2):
""" Concatenates two decodings
Args:
decoder_1 (iterable): list of BinaryPolynomial
decoding of the outer code layer
decoder_2 (iterable): list of BinaryPolynomial
decoding of the inner code layer
Returns (list): list of BinaryPolynomial the decoding defined by
w -> decoder_1( decoder_2(w) )
"""
doubled_decoder = []
for entry in decoder_1:
tmp_sum = 0
for summand in entry.terms:
tmp_term = BinaryPolynomial('1')
for factor in summand:
if isinstance(factor, (numpy.int32, numpy.int64, int)):
tmp_term *= decoder_2[factor]
tmp_sum = tmp_term + tmp_sum
doubled_decoder += [tmp_sum]
return doubled_decoder
def test_shift(self):
decoder = [BinaryPolynomial('1'), BinaryPolynomial('1 + w1 w0')]
with self.assertRaises(TypeError):
shift_decoder(decoder, 2.5)
def binary_code_transform(hamiltonian, code):
""" Transforms a Hamiltonian written in fermionic basis into a Hamiltonian
written in qubit basis, via a binary code.
The role of the binary code is to relate the occupation vectors (v0 v1 v2
... vN-1) that span the fermionic basis, to the qubit basis, spanned by
binary vectors (w0, w1, w2, ..., wn-1).
The binary code has to provide an analytic relation between the binary
vectors (v0, v1, ..., vN-1) and (w0, w1, ..., wn-1), and possibly has the
property N>n, when the Fermion basis is smaller than the fermionic Fock
space. The binary_code_transform function can transform Fermion operators
to qubit operators for custom- and qubit-saving mappings.
Note:
Logic multi-qubit operators are decomposed into Pauli-strings (e.g.
CPhase(1,2) = 0.5 * (1 + Z1 + Z2 - Z1 Z2 ) ), which might increase
the number of Hamiltonian terms drastically.
Args:
hamiltonian (FermionOperator): the fermionic Hamiltonian
code (BinaryCode): the binary code to transform the Hamiltonian
Returns (QubitOperator): the transformed Hamiltonian
Raises:
TypeError: if the hamiltonian is not a FermionOperator or code is not
a BinaryCode
"""
if not isinstance(hamiltonian, FermionOperator):
raise TypeError('hamiltonian provided must be a FermionOperator'
'received {}'.format(type(hamiltonian)))
if not isinstance(code, BinaryCode):
raise TypeError('code provided must be a BinaryCode'
'received {}'.format(type(code)))
new_hamiltonian = QubitOperator()
parity_list = make_parity_list(code)
# for each term in hamiltonian
for term, term_coefficient in hamiltonian.terms.items():
""" the updated parity and occupation account for sign changes due
changed occupations mid-way in the term """
updated_parity = 0 # parity sign exponent
parity_term = BinaryPolynomial()
changed_occupation_vector = [0] * code.n_modes
transformed_term = QubitOperator(())
# keep track of indices appeared before
fermionic_indices = numpy.array([])
# for each multiplier
for op_idx, op_tuple in enumerate(reversed(term)):
# get count exponent, parity exponent addition
fermionic_indices = numpy.append(fermionic_indices, op_tuple[0])
count = numpy.count_nonzero(
fermionic_indices[:op_idx] == op_tuple[0])
updated_parity += numpy.count_nonzero(
fermionic_indices[:op_idx] < op_tuple[0])
# update term
extracted = extractor(code.decoder[op_tuple[0]])
extracted *= (((-1) ** count) * ((-1) ** (op_tuple[1])) * 0.5)
transformed_term *= QubitOperator((), 0.5) - extracted
# update parity term and occupation vector
changed_occupation_vector[op_tuple[0]] += 1
parity_term += parity_list[op_tuple[0]]
# the parity sign and parity term
transformed_term *= QubitOperator((), (-1) ** updated_parity)
transformed_term *= extractor(parity_term)
# the update operator
changed_qubit_vector = numpy.mod(code.encoder.dot(
changed_occupation_vector), 2)
update_operator = QubitOperator(())
for index, q_vec in enumerate(changed_qubit_vector):
if q_vec:
update_operator *= QubitOperator('X' + str(index))
# append new term to new hamiltonian
new_hamiltonian += term_coefficient * update_operator * \
transformed_term
new_hamiltonian.compress()
return new_hamiltonian