# cirq.CCZPowGate¶

class cirq.CCZPowGate(*, exponent: Union[float, sympy.core.basic.Basic] = 1.0, global_shift: float = 0.0)[source]

A doubly-controlled-Z that can be raised to a power.

The matrix of CCZ**t is diag(1, 1, 1, 1, 1, 1, 1, exp(i pi t)).

__init__(*, exponent: Union[float, sympy.core.basic.Basic] = 1.0, global_shift: float = 0.0) → None

Initializes the parameters used to compute the gate’s matrix.

The eigenvalue of each eigenspace of a gate is computed by

1. Starting with an angle in half turns as returned by the gate’s
_eigen_components method:
θ

2. Shifting the angle by global_shift:

θ + s

3. Scaling the angle by exponent:

(θ + s) * e

4. Converting from half turns to a complex number on the unit circle:

exp(i * pi * (θ + s) * e)

Parameters
• exponent – The t in gate**t. Determines how much the eigenvalues of the gate are scaled 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.

Methods

 controlled([num_controls, control_values, …]) Returns a controlled version of this gate. If no arguments are The number of qubits this gate acts on. on(*qubits) Returns an application of this gate to the given qubits. Returns a key that differs between non-interchangeable qubits. validate_args(qubits) Checks if this gate can be applied to the given qubits. wrap_in_linear_combination([coefficient])

Attributes