class LogicalExpressionOracle(Oracle):
r"""
The Logical Expression Quantum Oracle.
The Logical Expression Oracle, as its name suggests, constructs circuits for any arbitrary
input logical expressions. A logical expression is composed of logical operators
`&` (`AND`), `|` (`OR`), `~` (`NOT`), and `^` (`XOR`),
as well as symbols for literals (variables).
For example, `'a & b'`, and `(v0 | ~v1) ^ (~v2 & v3)`
are both valid string representation of boolean logical expressions.
For convenience, this oracle, in addition to parsing arbitrary logical expressions,
also supports input strings in the `DIMACS CNF format
<http://www.satcompetition.org/2009/format-benchmarks2009.html>`__,
which is the standard format for specifying SATisfiability (SAT) problem instances in
`Conjunctive Normal Form (CNF) <https://en.wikipedia.org/wiki/Conjunctive_normal_form>`__,
which is a conjunction of one or more clauses, where a clause is a disjunction of one
or more literals.
The following is an example of a CNF expressed in DIMACS format:
.. code:: text
c This is an example DIMACS CNF file with 3 satisfying assignments: 1 -2 3, -1 -2 -3, 1 2 -3.
p cnf 3 5
-1 -2 -3 0
1 -2 3 0
1 2 -3 0
1 -2 -3 0
-1 2 3 0
The first line, following the `c` character, is a comment. The second line specifies that the
CNF is over three boolean variables --- let us call them :math:`x_1, x_2, x_3`, and contains
five clauses. The five clauses, listed afterwards, are implicitly joined by the logical `AND`
operator, :math:`\land`, while the variables in each clause, represented by their indices,
are implicitly disjoined by the logical `OR` operator, :math:`lor`. The :math:`-` symbol
preceding a boolean variable index corresponds to the logical `NOT` operator, :math:`lnot`.
Character `0` (zero) marks the end of each clause. Essentially, the code above corresponds
to the following CNF:
:math:`(\lnot x_1 \lor \lnot x_2 \lor \lnot x_3)
\land (x_1 \lor \lnot x_2 \lor x_3)
\land (x_1 \lor x_2 \lor \lnot x_3)
\land (x_1 \lor \lnot x_2 \lor \lnot x_3)
\land (\lnot x_1 \lor x_2 \lor x_3)`.
This is an example showing how to search for a satisfying assignment to an SAT problem encoded
in DIMACS using the `Logical Expression oracle with the Grover algorithm.
<https://github.com/Qiskit/qiskit-tutorials-community/blob/master/optimization/grover.ipynb>`__
Logic expressions, regardless of the input formats, are parsed and stored as Abstract Syntax
Tree (AST) tuples, from which the corresponding circuits are constructed. The oracle circuits
can then be used with any oracle-oriented algorithms when appropriate. For example, an oracle
built from a DIMACS input can be used with the Grover's algorithm to search for a satisfying
assignment to the encoded SAT instance.
By default, the Logical Expression oracle will not try to apply any optimization when building
the circuits. For any DIMACS input, the constructed circuit truthfully recreates each inner
disjunctive clauses as well as the outermost conjunction; For other arbitrary input expression,
It only tries to convert it to a CNF or DNF (Disjunctive Normal Form, similar to CNF, but with
inner conjunctions and a outer disjunction) before constructing its circuit. This, for example,
could be good for educational purposes, where a user would like to compare a built circuit
against their input expression to examine and analyze details. However, this often leads
to relatively deep circuits that possibly also involve many ancillary qubits. The oracle
therefore, provides the option to try to optimize the input logical expression before
building its circuit.
"""
def __init__(self,
expression: str,
optimization: bool = False,
mct_mode: str = 'basic') -> None:
"""
Args:
expression: The string of the desired logical expression.
It could be either in the DIMACS CNF format,
or a general boolean logical expression, such as 'a ^ b' and 'v[0] & (~v[1] | v[2])'
optimization: Boolean flag for attempting logical expression optimization
mct_mode: The mode to use for building Multiple-Control Toffoli.
Raises:
AquaError: Invalid input
"""
validate_in_set(
'mct_mode', mct_mode,
{'basic', 'basic-dirty-ancilla', 'advanced', 'noancilla'})
super().__init__()
self._mct_mode = mct_mode.strip().lower()
self._optimization = optimization
expression = re.sub('(?i)' + re.escape(' and '), ' & ', expression)
expression = re.sub('(?i)' + re.escape(' xor '), ' ^ ', expression)
expression = re.sub('(?i)' + re.escape(' or '), ' | ', expression)
expression = re.sub('(?i)' + re.escape('not '), '~', expression)
orig_expression = expression
# try parsing as normal logical expression that sympy recognizes
try:
raw_expr = parse_expr(expression)
except Exception: # pylint: disable=broad-except
# try parsing as dimacs cnf
try:
expression = LogicalExpressionOracle._dimacs_cnf_to_expression(
expression)
raw_expr = parse_expr(expression)
except Exception:
raise AquaError(
'Failed to parse the input expression: {}.'.format(
orig_expression))
self._expr = raw_expr
self._process_expr()
self.construct_circuit()
@staticmethod
def _dimacs_cnf_to_expression(dimacs):
lines = [
ll
for ll in [l.strip().lower() for l in dimacs.strip().split('\n')]
if len(ll) > 0 and not ll[0] == 'c'
]
if not lines[0][:6] == 'p cnf ':
raise AquaError('Unrecognized dimacs cnf header {}.'.format(
lines[0]))
def create_var(cnf_tok):
return ('~v' + cnf_tok[1:]) if cnf_tok[0] == '-' else ('v' +
cnf_tok)
clauses = []
for line in lines[1:]:
toks = line.split()
if not toks[-1] == '0':
raise AquaError('Unrecognized dimacs line {}.'.format(line))
clauses.append('({})'.format(' | '.join(
[create_var(t) for t in toks[:-1]])))
return ' & '.join(clauses)
def _process_expr(self):
self._num_vars = len(self._expr.binary_symbols)
self._lit_to_var = [None] + sorted(self._expr.binary_symbols, key=str)
self._var_to_lit = dict(
zip(self._lit_to_var[1:], range(1, self._num_vars + 1)))
cnf = to_cnf(self._expr, simplify=self._optimization)
if isinstance(cnf, BooleanTrue):
ast = 'const', 1
elif isinstance(cnf, BooleanFalse):
ast = 'const', 0
else:
ast = get_ast(self._var_to_lit, cnf)
if ast[0] == 'or':
self._nf = DNF(ast, num_vars=self._num_vars)
else:
self._nf = CNF(ast, num_vars=self._num_vars)
@property
def variable_register(self):
""" returns variable register """
return self._variable_register
@property
def ancillary_register(self):
""" returns ancillary register """
return self._ancillary_register
@property
def output_register(self):
""" returns output register """
return self._output_register
def construct_circuit(self):
""" construct circuit """
if self._circuit is None:
if self._nf is not None:
self._circuit = self._nf.construct_circuit(
mct_mode=self._mct_mode)
self._variable_register = self._nf.variable_register
self._output_register = self._nf.output_register
self._ancillary_register = self._nf.ancillary_register
else:
self._variable_register = QuantumRegister(self._num_vars,
name='v')
self._output_register = QuantumRegister(1, name='o')
self._ancillary_register = None
self._circuit = QuantumCircuit(self._variable_register,
self._output_register)
return self._circuit
def evaluate_classically(self, measurement):
""" evaluate classically """
assignment = [
(var + 1) * (int(tf) * 2 - 1)
for tf, var in zip(measurement[::-1], range(len(measurement)))
]
assignment_dict = dict()
for v in assignment:
assignment_dict[self._lit_to_var[abs(v)]] = bool(v > 0)
return self._expr.subs(assignment_dict), assignment
class LogicalExpressionOracle(Oracle):
CONFIGURATION = {
'name': 'LogicalExpressionOracle',
'description': 'Logical Expression Oracle',
'input_schema': {
'$schema': 'http://json-schema.org/schema#',
'id': 'logical_expression_oracle_schema',
'type': 'object',
'properties': {
'expression': {
'type': ['string', 'null'],
'default': None
},
"optimization": {
"type": "boolean",
"default": False,
},
'mct_mode': {
'type':
'string',
'default':
'basic',
'enum':
['basic', 'basic-dirty-ancilla', 'advanced', 'noancilla']
},
},
'additionalProperties': False
}
}
def __init__(self, expression=None, optimization=False, mct_mode='basic'):
"""
Constructor.
Args:
expression (str): The string of the desired logical expression.
It could be either in the DIMACS CNF format,
or a general boolean logical expression, such as 'a ^ b' and 'v[0] & (~v[1] | v[2])'
optimization (bool): Boolean flag for attempting logical expression optimization
mct_mode (str): The mode to use for building Multiple-Control Toffoli.
"""
self.validate(locals())
super().__init__()
if expression is None:
raise AquaError('Missing logical expression.')
self._mct_mode = mct_mode.strip().lower()
self._optimization = optimization
expression = re.sub('(?i)' + re.escape(' and '), ' & ', expression)
expression = re.sub('(?i)' + re.escape(' xor '), ' ^ ', expression)
expression = re.sub('(?i)' + re.escape(' or '), ' | ', expression)
expression = re.sub('(?i)' + re.escape('not '), '~', expression)
orig_expression = expression
# try parsing as normal logical expression that sympy recognizes
try:
raw_expr = parse_expr(expression)
except Exception:
# try parsing as dimacs cnf
try:
expression = LogicalExpressionOracle._dimacs_cnf_to_expression(
expression)
raw_expr = parse_expr(expression)
except Exception:
raise AquaError(
'Failed to parse the input expression: {}.'.format(
orig_expression))
self._expr = raw_expr
self._process_expr()
self.construct_circuit()
@staticmethod
def _dimacs_cnf_to_expression(dimacs):
lines = [
ll
for ll in [l.strip().lower() for l in dimacs.strip().split('\n')]
if len(ll) > 0 and not ll[0] == 'c'
]
if not lines[0][:6] == 'p cnf ':
raise AquaError('Unrecognized dimacs cnf header {}.'.format(
lines[0]))
def create_var(cnf_tok):
return ('~v' + cnf_tok[1:]) if cnf_tok[0] == '-' else ('v' +
cnf_tok)
clauses = []
for line in lines[1:]:
toks = line.split()
if not toks[-1] == '0':
raise AquaError('Unrecognized dimacs line {}.'.format(line))
else:
clauses.append('({})'.format(' | '.join(
[create_var(t) for t in toks[:-1]])))
return ' & '.join(clauses)
def _process_expr(self):
self._num_vars = len(self._expr.binary_symbols)
self._lit_to_var = [None] + sorted(self._expr.binary_symbols, key=str)
self._var_to_lit = {
v: l
for v, l in zip(self._lit_to_var[1:], range(1, self._num_vars + 1))
}
cnf = to_cnf(self._expr, simplify=self._optimization)
if isinstance(cnf, BooleanTrue):
ast = 'const', 1
elif isinstance(cnf, BooleanFalse):
ast = 'const', 0
else:
ast = get_ast(self._var_to_lit, cnf)
if ast[0] == 'or':
self._nf = DNF(ast, num_vars=self._num_vars)
else:
self._nf = CNF(ast, num_vars=self._num_vars)
@property
def variable_register(self):
return self._variable_register
@property
def ancillary_register(self):
return self._ancillary_register
@property
def output_register(self):
return self._output_register
def construct_circuit(self):
if self._circuit is None:
if self._nf is not None:
self._circuit = self._nf.construct_circuit(
mct_mode=self._mct_mode)
self._variable_register = self._nf.variable_register
self._output_register = self._nf.output_register
self._ancillary_register = self._nf.ancillary_register
else:
self._variable_register = QuantumRegister(self._num_vars,
name='v')
self._output_register = QuantumRegister(1, name='o')
self._ancillary_register = None
self._circuit = QuantumCircuit(self._variable_register,
self._output_register)
return self._circuit
def evaluate_classically(self, measurement):
assignment = [
(var + 1) * (int(tf) * 2 - 1)
for tf, var in zip(measurement[::-1], range(len(measurement)))
]
assignment_dict = dict()
for v in assignment:
assignment_dict[self._lit_to_var[abs(
v)]] = True if v > 0 else False
return self._expr.subs(assignment_dict), assignment
class LogicalExpressionOracle(Oracle):
""" Logical expression Oracle """
def __init__(self,
expression: str,
optimization: bool = False,
mct_mode: str = 'basic') -> None:
"""
Constructor.
Args:
expression: The string of the desired logical expression.
It could be either in the DIMACS CNF format,
or a general boolean logical expression, such as 'a ^ b' and 'v[0] & (~v[1] | v[2])'
optimization: Boolean flag for attempting logical expression optimization
mct_mode: The mode to use for building Multiple-Control Toffoli.
Raises:
AquaError: invalid input
"""
validate_in_set(
'mct_mode', mct_mode,
{'basic', 'basic-dirty-ancilla', 'advanced', 'noancilla'})
super().__init__()
self._mct_mode = mct_mode.strip().lower()
self._optimization = optimization
expression = re.sub('(?i)' + re.escape(' and '), ' & ', expression)
expression = re.sub('(?i)' + re.escape(' xor '), ' ^ ', expression)
expression = re.sub('(?i)' + re.escape(' or '), ' | ', expression)
expression = re.sub('(?i)' + re.escape('not '), '~', expression)
orig_expression = expression
# try parsing as normal logical expression that sympy recognizes
try:
raw_expr = parse_expr(expression)
except Exception: # pylint: disable=broad-except
# try parsing as dimacs cnf
try:
expression = LogicalExpressionOracle._dimacs_cnf_to_expression(
expression)
raw_expr = parse_expr(expression)
except Exception:
raise AquaError(
'Failed to parse the input expression: {}.'.format(
orig_expression))
self._expr = raw_expr
self._process_expr()
self.construct_circuit()
@staticmethod
def _dimacs_cnf_to_expression(dimacs):
lines = [
ll
for ll in [l.strip().lower() for l in dimacs.strip().split('\n')]
if len(ll) > 0 and not ll[0] == 'c'
]
if not lines[0][:6] == 'p cnf ':
raise AquaError('Unrecognized dimacs cnf header {}.'.format(
lines[0]))
def create_var(cnf_tok):
return ('~v' + cnf_tok[1:]) if cnf_tok[0] == '-' else ('v' +
cnf_tok)
clauses = []
for line in lines[1:]:
toks = line.split()
if not toks[-1] == '0':
raise AquaError('Unrecognized dimacs line {}.'.format(line))
clauses.append('({})'.format(' | '.join(
[create_var(t) for t in toks[:-1]])))
return ' & '.join(clauses)
def _process_expr(self):
self._num_vars = len(self._expr.binary_symbols)
self._lit_to_var = [None] + sorted(self._expr.binary_symbols, key=str)
self._var_to_lit = dict(
zip(self._lit_to_var[1:], range(1, self._num_vars + 1)))
cnf = to_cnf(self._expr, simplify=self._optimization)
if isinstance(cnf, BooleanTrue):
ast = 'const', 1
elif isinstance(cnf, BooleanFalse):
ast = 'const', 0
else:
ast = get_ast(self._var_to_lit, cnf)
if ast[0] == 'or':
self._nf = DNF(ast, num_vars=self._num_vars)
else:
self._nf = CNF(ast, num_vars=self._num_vars)
@property
def variable_register(self):
""" returns variable register """
return self._variable_register
@property
def ancillary_register(self):
""" returns ancillary register """
return self._ancillary_register
@property
def output_register(self):
""" returns output register """
return self._output_register
def construct_circuit(self):
""" construct circuit """
if self._circuit is None:
if self._nf is not None:
self._circuit = self._nf.construct_circuit(
mct_mode=self._mct_mode)
self._variable_register = self._nf.variable_register
self._output_register = self._nf.output_register
self._ancillary_register = self._nf.ancillary_register
else:
self._variable_register = QuantumRegister(self._num_vars,
name='v')
self._output_register = QuantumRegister(1, name='o')
self._ancillary_register = None
self._circuit = QuantumCircuit(self._variable_register,
self._output_register)
return self._circuit
def evaluate_classically(self, measurement):
""" evaluate classically """
assignment = [
(var + 1) * (int(tf) * 2 - 1)
for tf, var in zip(measurement[::-1], range(len(measurement)))
]
assignment_dict = dict()
for v in assignment:
assignment_dict[self._lit_to_var[abs(v)]] = bool(v > 0)
return self._expr.subs(assignment_dict), assignment