View source on GitHub
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A gate that rotates around the Y axis of the Bloch sphere.
Inherits From: EigenGate, Gate
cirq.YPowGate(
*,
exponent: cirq.TParamVal = 1.0,
global_shift: float = 0.0
) -> None
Used in the notebooks
| Used in the tutorials |
|---|
The unitary matrix of cirq.YPowGate(exponent=t) is:
\[ \begin{bmatrix} e^{i \pi t /2} \cos(\pi t /2) & - e^{i \pi t /2} \sin(\pi t /2) \\ e^{i \pi t /2} \sin(\pi t /2) & e^{i \pi t /2} \cos(\pi t /2) \end{bmatrix} \]
Note in particular that this gate has a global phase factor of
\(e^{i \pi t / 2}\) vs the traditionally defined rotation matrices
about the Pauli Y axis. See cirq.Ry for rotations without the global
phase. The global phase factor can be adjusted by using the global_shift
parameter when initializing.
cirq.Y, the Pauli Y gate, is an instance of this gate at exponent=1.
Unlike cirq.XPowGate and cirq.ZPowGate, this gate has no generalization
to qudits and hence does not take the dimension argument. Ignoring the
global phase all generalized Pauli operators on a d-level system may be
written as Xa Zb for a,b=0,1,...,d-1. For a qubit, there is only one
"mixed" operator: XZ, conventionally denoted -iY. However, when d > 2 there
are (d-1)*(d-1) > 1 such "mixed" operators (still ignoring the global phase).
Due to this ambiguity, qudit Y gate is not well defined. The "mixed" operators
for qudits are generally not referred to by name, but instead are specified in
terms of X and Z.
Args | |
|---|---|
exponent
|
The t in gate**t. Determines how much the eigenvalues of
the gate are phased 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:
For example, |
Raises | |
|---|---|
ValueError
|
If the supplied exponent is a complex number with an imaginary component. |
Attributes | |
|---|---|
exponent
|
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global_shift
|
|
phase_exponent
|
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Methods
controlled
controlled(
num_controls: int = None,
control_values: Optional[Union[cv.AbstractControlValues, Sequence[Union[int, Collection[int]]]]
] = None,
control_qid_shape: Optional[Tuple[int, ...]] = None
) -> 'Gate'
Returns a controlled version of this gate. If no arguments are specified, defaults to a single qubit control.
| Args | |
|---|---|
num_controls
|
Total number of control qubits. |
control_values
|
Which control computational basis state to apply the
sub gate. A sequence of length num_controls where each
entry is an integer (or set of integers) corresponding to the
computational basis state (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.
|
| Returns | |
|---|---|
A cirq.Gate representing self controlled by the given control values
and qubits. This is a cirq.ControlledGate in the base
implementation, but subclasses may return a different gate type.
|
in_su2
in_su2() -> 'Ry'
Returns an equal-up-global-phase gate from the group SU2.
num_qubits
num_qubits() -> int
The number of qubits this gate acts on.
on
on(
*qubits
) -> 'Operation'
Returns an application of this gate to the given qubits.
| Args | |
|---|---|
*qubits
|
The collection of qubits to potentially apply the gate to. |
Returns: a cirq.Operation which is this gate applied to the given
qubits.
on_each
on_each(
*targets
) -> List['cirq.Operation']
Returns a list of operations applying the gate to all targets.
| Args | |
|---|---|
*targets
|
The qubits to apply this gate to. For single-qubit gates
this can be provided as varargs or a combination of nested
iterables. For multi-qubit gates this must be provided as an
Iterable[Sequence[Qid]], where each sequence has num_qubits
qubits.
|
| Returns | |
|---|---|
| Operations applying this gate to the target qubits. |
| Raises | |
|---|---|
ValueError
|
If targets are not instances of Qid or Iterable[Qid]. If the gate qubit number is incompatible. |
TypeError
|
If a single target is supplied and it is not iterable. |
validate_args
validate_args(
qubits: Sequence['cirq.Qid']
) -> None
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. |
| Raises | |
|---|---|
ValueError
|
The gate can't be applied to the qubits. |
with_canonical_global_phase
with_canonical_global_phase() -> 'YPowGate'
Returns an equal-up-global-phase standardized form of the gate.
with_probability
with_probability(
probability: 'cirq.TParamVal'
) -> 'cirq.Gate'
Creates a probabalistic channel with this gate.
| Args | |
|---|---|
probability
|
floating point value between 0 and 1, giving the probability this gate is applied. |
| Returns | |
|---|---|
cirq.RandomGateChannel that applies self with probability
probability and the identity with probability 1-p.
|
wrap_in_linear_combination
wrap_in_linear_combination(
coefficient: Union[complex, float, int] = 1
) -> 'cirq.LinearCombinationOfGates'
Returns a LinearCombinationOfGates with this gate.
| Args | |
|---|---|
coefficient
|
number coefficient to use in the resulting
cirq.LinearCombinationOfGates object.
|
| Returns | |
|---|---|
cirq.LinearCombinationOfGates containing self with a
coefficient of coefficient.
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__add__
__add__(
other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'
__call__
__call__(
*qubits, **kwargs
)
Call self as a function.
__eq__
__eq__(
other: _SupportsValueEquality
) -> bool
__mul__
__mul__(
other: Union[complex, float, int]
) -> 'cirq.LinearCombinationOfGates'
__ne__
__ne__(
other: _SupportsValueEquality
) -> bool
__neg__
__neg__() -> 'cirq.LinearCombinationOfGates'
__pow__
__pow__(
exponent: Union[float, sympy.Symbol]
) -> 'EigenGate'
__rmul__
__rmul__(
other: Union[complex, float, int]
) -> 'cirq.LinearCombinationOfGates'
__sub__
__sub__(
other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'
__truediv__
__truediv__(
other: Union[complex, float, int]
) -> 'cirq.LinearCombinationOfGates'