cirq.XXPowGate

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

The X-parity gate, possibly raised to a power.

At exponent=1, this gate implements the following unitary:

X⊗X = [0 0 0 1]
      [0 0 1 0]
      [0 1 0 0]
      [1 0 0 0]
See also: cirq.MS (the Mølmer–Sørensen gate), which is implemented via
this class.
__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.

qubit_index_to_equivalence_group_key(index)

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

exponent

global_shift