# Source code for qiskit.circuit.library.phase_oracle

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2021.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""Phase Oracle object."""
from typing import Union, Callable, Optional
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.classicalfunction.boolean_expression import BooleanExpression
from qiskit.circuit.classicalfunction.classical_element import ClassicalElement
[docs]class PhaseOracle(QuantumCircuit):
r"""Phase Oracle.
The Phase Oracle object 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. See :meth:`qiskit.circuit.library.phase_oracle.PhaseOracle.from_dimacs_file`.
From 16 variables on, possible performance issues should be expected when using the
default synthesizer.
"""
def __init__(
self,
expression: Union[str, ClassicalElement],
synthesizer: Optional[Callable[[BooleanExpression], QuantumCircuit]] = None,
) -> None:
"""Creates a PhaseOracle object
Args:
expression: A Python-like boolean expression.
synthesizer: Optional. A function to convert a BooleanExpression into a QuantumCircuit
If None is provided, Tweedledum's `pkrm_synth` with `phase_esop` will be used.
"""
if not isinstance(expression, ClassicalElement):
expression = BooleanExpression(expression)
self.boolean_expression = expression
if synthesizer is None:
def synthesizer(boolean_expression):
from tweedledum.synthesis import pkrm_synth # pylint: disable=no-name-in-module
from qiskit.circuit.classicalfunction.utils import tweedledum2qiskit
truth_table = boolean_expression._tweedledum_bool_expression.truth_table(
output_bit=0
)
tweedledum_circuit = pkrm_synth(truth_table, {"pkrm_synth": {"phase_esop": True}})
return tweedledum2qiskit(tweedledum_circuit)
oracle = expression.synth(synthesizer=synthesizer)
super().__init__(oracle.num_qubits, name="Phase Oracle")
self.compose(oracle, inplace=True)
[docs] def evaluate_bitstring(self, bitstring: str) -> bool:
"""Evaluate the oracle on a bitstring.
This evaluation is done classically without any quantum circuit.
Args:
bitstring: The bitstring for which to evaluate. The input bitstring is expected to be
in little-endian order.
Returns:
True if the bitstring is a good state, False otherwise.
"""
return self.boolean_expression.simulate(bitstring[::-1])
[docs] @classmethod
def from_dimacs_file(cls, filename: str):
r"""Create a PhaseOracle from the string in the DIMACS format.
It is possible to build a PhaseOracle from a file in `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 the DIMACS format:
.. code:: text
c 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)`.
Args:
filename: A file in DIMACS format.
Returns:
PhaseOracle: A quantum circuit with a phase oracle.
"""
expr = BooleanExpression.from_dimacs_file(filename)
return cls(expr)
```