cirq.HPowGate

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

A Gate that performs a rotation around the X+Z axis of the Bloch sphere.

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

[[(c-i·s/sqrt(2)), -i·g·s/sqrt(2)],
[-i·g·s/sqrt(2)], (c+i·s/sqrt(2))]]

where

c = cos(π·t/2)
s = sin(π·t/2)
g = exp(i·π·t/2).

Note in particular that for t=1, this gives the Hadamard matrix.

cirq.H, the Hadamard gate, is an instance of this gate at exponent=1.

__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

num_qubits()

The number of qubits this gate acts on.

on(*qubits)

Returns an application of this gate to the given qubits.

on_each(*targets)

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

validate_args(qubits)

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

wrap_in_linear_combination([coefficient])

Attributes

exponent

global_shift