--- title: CPhaseGate (latest version) description: API reference for qiskit.circuit.library.CPhaseGate in the latest version of qiskit source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.CPhaseGate --- # CPhaseGate *class* `qiskit.circuit.library.CPhaseGate(theta, label=None, ctrl_state=None, *, _base_label=None)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/standard_gates/p.py#L170-L303) Bases: [`ControlledGate`](/docs/api/qiskit/qiskit.circuit.ControlledGate "qiskit.circuit.controlledgate.ControlledGate") Controlled-Phase gate. This is a diagonal and symmetric gate that induces a phase on the state of the target qubit, depending on the control state. Can be applied to a [`QuantumCircuit`](/docs/api/qiskit/qiskit.circuit.QuantumCircuit "qiskit.circuit.QuantumCircuit") with the [`cp()`](/docs/api/qiskit/qiskit.circuit.QuantumCircuit#cp "qiskit.circuit.QuantumCircuit.cp") method. Circuit symbol: ```text q_0: ─■── │θ q_1: ─■── ``` Matrix representation: $$ CPhase = I \otimes |0\rangle\langle 0| + P \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\theta} \end{pmatrix} $$ > **See also** > > `CRZGate`: Due to the global phase difference in the matrix definitions of Phase and RZ, CPhase and CRZ are different gates with a relative phase difference. Create new CPhase gate. ## Attributes **Parameters** - **theta** (*ParameterValueType*) - **label** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *| None*) - **ctrl\_state** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *|*[*int*](https://docs.python.org/3/library/functions.html#int) *| None*) ### base\_class Get the base class of this instruction. This is guaranteed to be in the inheritance tree of `self`. The “base class” of an instruction is the lowest class in its inheritance tree that the object should be considered entirely compatible with for \_all\_ circuit applications. This typically means that the subclass is defined purely to offer some sort of programmer convenience over the base class, and the base class is the “true” class for a behavioral perspective. In particular, you should *not* override [`base_class`](#qiskit.circuit.library.CPhaseGate.base_class "qiskit.circuit.library.CPhaseGate.base_class") if you are defining a custom version of an instruction that will be implemented differently by hardware, such as an alternative measurement strategy, or a version of a parametrized gate with a particular set of parameters for the purposes of distinguishing it in a [`Target`](/docs/api/qiskit/qiskit.transpiler.Target "qiskit.transpiler.Target") from the full parametrized gate. This is often exactly equivalent to `type(obj)`, except in the case of singleton instances of standard-library instructions. These singleton instances are special subclasses of their base class, and this property will return that base. For example: ```python >>> isinstance(XGate(), XGate) True >>> type(XGate()) is XGate False >>> XGate().base_class is XGate True ``` In general, you should not rely on the precise class of an instruction; within a given circuit, it is expected that `Instruction.name` should be a more suitable discriminator in most situations. ### ctrl\_state Return the control state of the gate as a decimal integer. ### decompositions Get the decompositions of the instruction from the SessionEquivalenceLibrary. ### definition Return definition in terms of other basic gates. If the gate has open controls, as determined from [`ctrl_state`](#qiskit.circuit.library.CPhaseGate.ctrl_state "qiskit.circuit.library.CPhaseGate.ctrl_state"), the returned definition is conjugated with X without changing the internal `_definition`. ### label Return instruction label ### mutable Is this instance is a mutable unique instance or not. If this attribute is `False` the gate instance is a shared singleton and is not mutable. ### name Get name of gate. If the gate has open controls the gate name will become: > \ where \ is the gate name for the default case of closed control qubits and \ is the integer value of the control state for the gate. ### num\_clbits Return the number of clbits. ### num\_ctrl\_qubits Get number of control qubits. **Returns** The number of control qubits for the gate. **Return type** [int](https://docs.python.org/3/library/functions.html#int) ### num\_qubits Return the number of qubits. ### params Get parameters from base\_gate. **Returns** List of gate parameters. **Return type** [list](https://docs.python.org/3/library/stdtypes.html#list) **Raises** [**CircuitError**](/docs/api/qiskit/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – Controlled gate does not define a base gate ## Methods ### add\_decomposition `add_decomposition(decomposition)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/instruction.py#L318-L323) Add a decomposition of the instruction to the SessionEquivalenceLibrary. ### broadcast\_arguments `broadcast_arguments(qargs, cargs)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/gate.py#L206-L263) Validation and handling of the arguments and its relationship. For example, `cx([q[0],q[1]], q[2])` means `cx(q[0], q[2]); cx(q[1], q[2])`. This method yields the arguments in the right grouping. In the given example: ```python in: [[q[0],q[1]], q[2]],[] outs: [q[0], q[2]], [] [q[1], q[2]], [] ``` The general broadcasting rules are: > - If len(qargs) == 1: > > ```python > [q[0], q[1]] -> [q[0]],[q[1]] > ``` > > - If len(qargs) == 2: > > ```python > [[q[0], q[1]], [r[0], r[1]]] -> [q[0], r[0]], [q[1], r[1]] > [[q[0]], [r[0], r[1]]] -> [q[0], r[0]], [q[0], r[1]] > [[q[0], q[1]], [r[0]]] -> [q[0], r[0]], [q[1], r[0]] > ``` > > - If len(qargs) >= 3: > > ```python > [q[0], q[1]], [r[0], r[1]], ...] -> [q[0], r[0], ...], [q[1], r[1], ...] > ``` **Parameters** - **qargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)) – List of quantum bit arguments. - **cargs** ([*list*](https://docs.python.org/3/library/stdtypes.html#list)) – List of classical bit arguments. **Returns** A tuple with single arguments. **Raises** [**CircuitError**](/docs/api/qiskit/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If the input is not valid. For example, the number of arguments does not match the gate expectation. **Return type** [*Iterable*](https://docs.python.org/3/library/collections.abc.html#collections.abc.Iterable)\[[tuple](https://docs.python.org/3/library/stdtypes.html#tuple)\[[list](https://docs.python.org/3/library/stdtypes.html#list), [list](https://docs.python.org/3/library/stdtypes.html#list)]] ### control `control(num_ctrl_qubits=1, label=None, ctrl_state=None, annotated=None)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/standard_gates/p.py#L246-L279) Return a controlled version of the CPhase gate. The controlled gate is implemented as [`MCPhaseGate`](/docs/api/qiskit/qiskit.circuit.library.MCPhaseGate "qiskit.circuit.library.MCPhaseGate"), regardless of the value of `annotated`. **Parameters** - **num\_ctrl\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int)) – Number of controls to add. Defaults to `1`. - **label** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *| None*) – Optional gate label. Defaults to `None`. - **ctrl\_state** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *|*[*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – The control state of the gate, specified either as an integer or a bitstring (e.g. `"110"`). If `None`, defaults to the all-ones state `2**num_ctrl_qubits - 1` - **annotated** ([*bool*](https://docs.python.org/3/library/functions.html#bool) *| None*) – Ignored. **Returns** A controlled version of this gate. ### copy `copy(name=None)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/instruction.py#L428-L443) Copy of the instruction. **Parameters** **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str)) – name to be given to the copied circuit, if `None` then the name stays the same. **Returns** a copy of the current instruction, with the name updated if it was provided **Return type** [qiskit.circuit.Instruction](/docs/api/qiskit/qiskit.circuit.Instruction "qiskit.circuit.Instruction") ### inverse `inverse(annotated=False)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/standard_gates/p.py#L281-L283) Return inverted CPhase gate ($CPhase(\lambda)^{\dagger} = CPhase(-\lambda)$) **Parameters** **annotated** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) ### is\_parameterized `is_parameterized()` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/instruction.py#L283-L288) Return whether the `Instruction` contains [compile-time parameters](/docs/api/qiskit/circuit#circuit-compile-time-parameters). ### power `power(exponent, annotated=False)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/library/standard_gates/p.py#L296-L298) Raise this gate to the power of `exponent`. Implemented either as a unitary gate (ref. [`UnitaryGate`](/docs/api/qiskit/qiskit.circuit.library.UnitaryGate "qiskit.circuit.library.UnitaryGate")) or as an annotated operation (ref. [`AnnotatedOperation`](/docs/api/qiskit/qiskit.circuit.AnnotatedOperation "qiskit.circuit.AnnotatedOperation")). In the case of several standard gates, such as [`RXGate`](/docs/api/qiskit/qiskit.circuit.library.RXGate "qiskit.circuit.library.RXGate"), when the power of a gate can be expressed in terms of another standard gate that is returned directly. **Parameters** - **exponent** ([*float*](https://docs.python.org/3/library/functions.html#float)) – the power to raise the gate to - **annotated** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – indicates whether the power gate can be implemented as an annotated operation. In the case of several standard gates, such as [`RXGate`](/docs/api/qiskit/qiskit.circuit.library.RXGate "qiskit.circuit.library.RXGate"), this argument is ignored when the power of a gate can be expressed in terms of another standard gate. **Returns** An operation implementing `gate^exponent` **Raises** [**CircuitError**](/docs/api/qiskit/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If gate is not unitary ### repeat `repeat(n)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/instruction.py#L491-L521) Creates an instruction with `self` repeated $n$ times. **Parameters** **n** ([*int*](https://docs.python.org/3/library/functions.html#int)) – Number of times to repeat the instruction **Returns** Containing the definition. **Return type** [qiskit.circuit.Instruction](/docs/api/qiskit/qiskit.circuit.Instruction "qiskit.circuit.Instruction") **Raises** [**CircuitError**](/docs/api/qiskit/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If n \< 1. ### reverse\_ops `reverse_ops()` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/instruction.py#L345-L369) For a composite instruction, reverse the order of sub-instructions. This is done by recursively reversing all sub-instructions. It does not invert any gate. **Returns** **a new instruction with** sub-instructions reversed. **Return type** [qiskit.circuit.Instruction](/docs/api/qiskit/qiskit.circuit.Instruction "qiskit.circuit.Instruction") ### soft\_compare `soft_compare(other)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/instruction.py#L214-L254) Soft comparison between gates. Their names, number of qubits, and classical bit numbers must match. The number of parameters must match. Each parameter is compared. If one is a ParameterExpression then it is not taken into account. **Parameters** **other** (*instruction*) – other instruction. **Returns** are self and other equal up to parameter expressions. **Return type** [bool](https://docs.python.org/3/library/functions.html#bool) ### to\_matrix `to_matrix()` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/gate.py#L49-L61) Return a Numpy.array for the gate unitary matrix. **Returns** if the Gate subclass has a matrix definition. **Return type** np.ndarray **Raises** [**CircuitError**](/docs/api/qiskit/circuit#qiskit.circuit.CircuitError "qiskit.circuit.CircuitError") – If a Gate subclass does not implement this method an exception will be raised when this base class method is called. ### to\_mutable `to_mutable()` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/instruction.py#L144-L152) Return a mutable copy of this gate. This method will return a new mutable copy of this gate instance. If a singleton instance is being used this will be a new unique instance that can be mutated. If the instance is already mutable it will be a deepcopy of that instance. ### validate\_parameter `validate_parameter(parameter)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.5/qiskit/circuit/gate.py#L265-L279) Gate parameters should be int, float, or ParameterExpression