cirq.SwapPowGate

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

The SWAP gate, possibly raised to a power. Exchanges qubits.

SwapPowGate()**t = SwapPowGate(exponent=t) and acts on two qubits in the
computational basis as the matrix:
[[1, 0, 0, 0],
 [0, g·c, -i·g·s, 0],
 [0, -i·g·s, g·c, 0],
 [0, 0, 0, 1]]

where:

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

cirq.SWAP, the swap 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.