cirq.CZPowGate

A gate that applies a phase to the |11⟩ state of two qubits.

Inherits From: InterchangeableQubitsGate, EigenGate, Gate

cirq.CZPowGate(
    *,
    exponent: cirq.TParamVal = 1.0,
    global_shift: float = 0.0
) -> None

Used in the notebooks

Used in the tutorials

The unitary matrix of CZPowGate(exponent=t) is:

\[ \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i \pi t} \\ \end{bmatrix} \]

cirq.CZ, the controlled Z gate, is an instance of this gate at exponent=1.

exponent The t in gate**t. Determines how much the eigenvalues of the gate are phased by. For example, eigenvectors phased by -1 when gate**1 is applied will gain a relative phase of e^{i pi exponent} when gate**exponent is applied (relative to eigenvectors unaffected by gate**1).
global_shift Offsets the eigenvalues of the gate at exponent=1. In effect, this controls a global phase factor on the gate's unitary matrix. The factor is:

exp(i * pi * global_shift * exponent)

For example, cirq.X**t uses a global_shift of 0 but cirq.rx(t) uses a global_shift of -0.5, which is why cirq.unitary(cirq.rx(pi)) equals -iX instead of X.

ValueError If the supplied exponent is a complex number with an imaginary component.

exponent

global_shift

Methods

controlled

View source

controlled(
    num_controls: Optional[int] = None,
    control_values: Optional[Union[cv.AbstractControlValues, Sequence[Union[int, Collection[int]]]]
        ] = None,
    control_qid_shape: Optional[Tuple[int, ...]] = None
) -> cirq.Gate

Returns a controlled CZPowGate, using a CCZPowGate where possible.

The controlled method of the Gate class, of which this class is a child, returns a ControlledGate. This method overrides this behavior to return a CCZPowGate or a ControlledGate of a CCZPowGate, when this is possible.

The conditions for the override to occur are:

  • The global_shift of the CZPowGate is 0.
  • The control_values and control_qid_shape are compatible with the CCZPowGate:
    • The last value of control_qid_shape is a qubit.
    • The last value of control_values corresponds to the control being satisfied if that last qubit is 1 and not satisfied if the last qubit is 0.

If these conditions are met, then the returned object is a CCZPowGate or, in the case that there is more than one controlled qudit, a ControlledGate with the Gate being a CCZPowGate. In the latter case the ControlledGate is controlled by one less qudit than specified in control_values and control_qid_shape (since one of these, the last qubit, is used as the control for the CCZPowGate).

If the above conditions are not met, a ControlledGate of this gate will be returned.

Args
num_controls Total number of control qubits.
control_values Which control computational basis state to apply the sub gate. A sequence of length num_controls where each entry is an integer (or set of integers) corresponding to the computational basis state (or set of possible values) where that control is enabled. When all controls are enabled, the sub gate is applied. If unspecified, control values default to 1.
control_qid_shape The qid shape of the controls. A tuple of the expected dimension of each control qid. Defaults to (2,) * num_controls. Specify this argument when using qudits.

Returns
A cirq.ControlledGate (or cirq.CCZPowGate if possible) representing self controlled by the given control values and qubits.

num_qubits

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num_qubits() -> int

The number of qubits this gate acts on.

on

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on(
    *qubits
) -> 'Operation'

Returns an application of this gate to the given qubits.

Args
*qubits The collection of qubits to potentially apply the gate to.

Returns: a cirq.Operation which is this gate applied to the given qubits.

on_each

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on_each(
    *targets
) -> List['cirq.Operation']

Returns a list of operations applying the gate to all targets.

Args
*targets The qubits to apply this gate to. For single-qubit gates this can be provided as varargs or a combination of nested iterables. For multi-qubit gates this must be provided as an Iterable[Sequence[Qid]], where each sequence has num_qubits qubits.

Returns
Operations applying this gate to the target qubits.

Raises
ValueError If targets are not instances of Qid or Iterable[Qid]. If the gate qubit number is incompatible.
TypeError If a single target is supplied and it is not iterable.

qubit_index_to_equivalence_group_key

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qubit_index_to_equivalence_group_key(
    index: int
) -> int

Returns a key that differs between non-interchangeable qubits.

validate_args

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validate_args(
    qubits: Sequence['cirq.Qid']
) -> None

Checks if this gate can be applied to the given qubits.

By default checks that:

  • inputs are of type Qid
  • len(qubits) == num_qubits()
  • qubit_i.dimension == qid_shape[i] for all qubits

Child classes can override. The child implementation should call super().validate_args(qubits) then do custom checks.

Args
qubits The sequence of qubits to potentially apply the gate to.

Raises
ValueError The gate can't be applied to the qubits.

with_probability

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with_probability(
    probability: 'cirq.TParamVal'
) -> 'cirq.Gate'

Creates a probabilistic channel with this gate.

Args
probability floating point value between 0 and 1, giving the probability this gate is applied.

Returns
cirq.RandomGateChannel that applies self with probability probability and the identity with probability 1-p.

wrap_in_linear_combination

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wrap_in_linear_combination(
    coefficient: 'cirq.TParamValComplex' = 1
) -> 'cirq.LinearCombinationOfGates'

Returns a LinearCombinationOfGates with this gate.

Args
coefficient number coefficient to use in the resulting cirq.LinearCombinationOfGates object.

Returns
cirq.LinearCombinationOfGates containing self with a coefficient of coefficient.

__add__

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__add__(
    other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'

__call__

View source

__call__(
    *qubits, **kwargs
)

Call self as a function.

__eq__

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__eq__(
    other: _SupportsValueEquality
) -> bool

__mul__

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__mul__(
    other: complex
) -> 'cirq.LinearCombinationOfGates'

__ne__

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__ne__(
    other: _SupportsValueEquality
) -> bool

__neg__

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__neg__() -> 'cirq.LinearCombinationOfGates'

__pow__

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__pow__(
    exponent: Union[float, sympy.Symbol]
) -> 'EigenGate'

__rmul__

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__rmul__(
    other: complex
) -> 'cirq.LinearCombinationOfGates'

__sub__

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__sub__(
    other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'

__truediv__

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__truediv__(
    other: complex
) -> 'cirq.LinearCombinationOfGates'