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class qiskit.circuit.library.PhaseOracle(expression, synthesizer=None, var_order=None)

GitHub(opens in a new tab)

Bases: QuantumCircuit

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(opens in a new tab), which is the standard format for specifying SATisfiability (SAT) problem instances in Conjunctive Normal Form (CNF)(opens in a new tab), which is a conjunction of one or more clauses, where a clause is a disjunction of one or more literals. See qiskit.circuit.library.phase_oracle.PhaseOracle.from_dimacs_file().

From 16 variables on, possible performance issues should be expected when using the default synthesizer.

Creates a PhaseOracle object


  • expression (Union[str(opens in a new tab), ClassicalElement]) – A Python-like boolean expression.
  • synthesizer (Optional[Callable[[BooleanExpression], QuantumCircuit]]) – Optional. A function to convert a BooleanExpression into a QuantumCircuit If None is provided, Tweedledum’s pkrm_synth with phase_esop will be used.
  • var_order (list(opens in a new tab)) – A list with the order in which variables will be created. (default: by appearance)



Returns a list of ancilla bits in the order that the registers were added.


Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}


Returns a list of classical bits in the order that the registers were added.


Return the circuit data (instructions and context).


a list-like object containing the CircuitInstructions for each instruction.

Return type



Default value: 'include "";'


Return the global phase of the current circuit scope in radians.

Default value: 'OPENQASM 2.0;'


Default value: 266


Return any associated layout information about the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.


The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.


Return the number of ancilla qubits.


Return number of classical bits.


The number of parameter objects in the circuit.


Return number of qubits.


Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.


List of integers representing instruction start times. The index corresponds to the index of instruction in


AttributeError(opens in a new tab) – When circuit is not scheduled.


The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.


The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])

To respect numerical sorting, a ParameterVector can be used.

>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])


The sorted Parameter objects in the circuit.


Default value: 'circuit'


Returns a list of quantum bits in the order that the registers were added.




Evaluate the oracle on a bitstring. This evaluation is done classically without any quantum circuit.


bitstring (str(opens in a new tab)) – The bitstring for which to evaluate. The input bitstring is expected to be in little-endian order.


True if the bitstring is a good state, False otherwise.

Return type

bool(opens in a new tab)


classmethod from_dimacs_file(filename)

Create a PhaseOracle from the string in the DIMACS format.

It is possible to build a PhaseOracle from a file in DIMACS CNF format(opens in a new tab), which is the standard format for specifying SATisfiability (SAT) problem instances in Conjunctive Normal Form (CNF)(opens in a new tab), 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:

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 x1,x2,x3x_1, x_2, x_3, and contains five clauses. The five clauses, listed afterwards, are implicitly joined by the logical AND operator, \land, while the variables in each clause, represented by their indices, are implicitly disjoined by the logical OR operator, lorlor. The - symbol preceding a boolean variable index corresponds to the logical NOT operator, lnotlnot. Character 0 (zero) marks the end of each clause. Essentially, the code above corresponds to the following CNF:

(¬x1¬x2¬x3)(x1¬x2x3)(x1x2¬x3)(x1¬x2¬x3)(¬x1x2x3)(\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).


filename (str(opens in a new tab)) – A file in DIMACS format.


A quantum circuit with a phase oracle.

Return type


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