# openfermion.circuits.FSwapPowGate

The FSWAP gate, possibly raised to a power.

FSwapPowGate()**t = FSwapPowGate(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, p]]
``````

where:

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

`openfermion.FSWAP` is an instance of this gate at exponent=1. It swaps adjacent fermionic modes under the Jordan-Wigner Transform.

`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.

`exponent`

`global_shift`

## Methods

### `controlled`

Returns a controlled version of this gate. If no arguments are specified, defaults to a single qubit control.

num_controls: Total number of control qubits. control_values: For which control qubit values to apply the sub gate. A sequence of length `num_controls` where each entry is an integer (or set of integers) corresponding to the qubit value (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.

### `num_qubits`

View source

The number of qubits this gate acts on.

### `on`

Returns an application of this gate to the given qubits.

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

### `qubit_index_to_equivalence_group_key`

Returns a key that differs between non-interchangeable qubits.

### `validate_args`

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.

#### Throws:

• `ValueError`: The gate can't be applied to the qubits.

### `__call__`

Call self as a function.

### `__truediv__`

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