# cirq.ops.Ry

A gate, with matrix e^{-i Y rads/2}, that rotates around the Y axis of the Bloch sphere.

The unitary matrix of `Ry(rads=t)` is:

exp(-i Y t/2) = [cos(t/2) -sin(t/2)] [sin(t/2) cos(t/2) ]

The gate corresponds to the traditionally defined rotation matrices about the Pauli Y axis.

`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`

`phase_exponent`

## Methods

### `controlled`

View source

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.

### `in_su2`

View source

Returns an equal-up-global-phase gate from the group SU2.

### `num_qubits`

View source

The number of qubits this gate acts on.

### `on`

View source

Returns an application of this gate to the given qubits.

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

### `on_each`

View source

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

Args
`*targets` The qubits to apply this gate to.

Returns
Operations applying this gate to the target qubits.

Raises
ValueError if targets are not instances of Qid or List[Qid]. ValueError if the gate operates on two or more Qids.

### `validate_args`

View source

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.

### `with_canonical_global_phase`

View source

Returns an equal-up-global-phase standardized form of the gate.

View source

View source

View source

### `__call__`

View source

Call self as a function.

View source

View source

View source

View source

View source

View source

View source

View source