cirq.SingleQubitCliffordGate

Any single qubit Clifford rotation.

Inherits From: CliffordGate, Gate

cirq.SingleQubitCliffordGate(
    *,
    _clifford_tableau: cirq.CliffordTableau
) -> None

Attributes
`clifford_tableau`

Attributes

clifford_tableau

Methods

`commutes_with_pauli`

View source

commutes_with_pauli(
    pauli: cirq.Pauli
) -> bool

`commutes_with_single_qubit_gate`

View source

commutes_with_single_qubit_gate(
    gate: 'SingleQubitCliffordGate'
) -> bool

Tests if the two circuits would be equivalent up to global phase: --self--gate-- and --gate--self--

`controlled`

View source

controlled(
    num_controls: Optional[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.

`decompose_gate`

View source

decompose_gate() -> Sequence['cirq.Gate']

Decomposes this clifford into a series of H and pauli rotation gates.

Returns
A sequence of H and pauli rotation gates which are equivalent to this clifford gate if applied in order. This decomposition agrees with cirq.unitary(self), including global phase.

`decompose_rotation`

View source

decompose_rotation() -> Sequence[Tuple[Pauli, int]]

Decomposes this clifford into a series of pauli rotations.

Each rotation is given as a tuple of (axis, quarter_turns), where axis is a Pauli giving the axis to rotate about. The result will be a sequence of zero, one, or two rotations.

Note that the combined unitary effect of these rotations may differ from cirq.unitary(self) by a global phase.

`dense_pauli_string`

View source

dense_pauli_string(
    pauli: cirq.Pauli
) -> 'cirq.DensePauliString'

`equivalent_gate_before`

View source

equivalent_gate_before(
    after: 'SingleQubitCliffordGate'
) -> 'SingleQubitCliffordGate'

Returns a SingleQubitCliffordGate such that the circuits --output--self-- and --self--gate-- are equivalent up to global phase.

`from_clifford_tableau`

View source

@staticmethod
from_clifford_tableau(
    tableau: cirq.CliffordTableau
) -> 'SingleQubitCliffordGate'

Create the CliffordGate instance from Clifford Tableau.

Args
`tableau`	A CliffordTableau to define the effect of Clifford Gate applying on the stabilizer state or Pauli group. The meaning of tableau here is To X Z sign from X [ X_x Z_x \| r_x ] from Z [ X_z Z_z \| r_z ] Each row in the Clifford tableau indicates how the transformation of original Pauli gates to the new gates after applying this Clifford Gate.

Returns
A CliffordGate instance, which has the transformation defined by the input tableau.

Raises
`ValueError`	When input tableau is wrong type or the tableau does not satisfy the symplectic property.

`from_double_map`

View source

@staticmethod
from_double_map(
    pauli_map_to: Optional[Dict[Pauli, Tuple[Pauli, bool]]] = None,
    *,
    x_to: Optional[Tuple[Pauli, bool]] = None,
    y_to: Optional[Tuple[Pauli, bool]] = None,
    z_to: Optional[Tuple[Pauli, bool]] = None
) -> 'SingleQubitCliffordGate'

Returns a SingleQubitCliffordGate for the specified transform with a 90 or 180 degree rotation.

Either pauli_map_to or two of (x_to, y_to, z_to) may be specified.

Args
`pauli_map_to`	A dictionary with two key value pairs describing two transforms.
`x_to`	The transform from cirq.X
`y_to`	The transform from cirq.Y
`z_to`	The transform from cirq.Z

`from_op_list`

View source

@classmethod
from_op_list(
    operations: Sequence[cirq.Operation],
    qubit_order: Sequence[cirq.Qid]
) -> 'CliffordGate'

Construct a new Clifford gates from several known operations.

Args
`operations`	A list of cirq operations to construct the Clifford gate. The combination order is the first element in the list applies the transformation on the stabilizer state first.
`qubit_order`	Determines how qubits are ordered when decomposite the operations.

Returns
A CliffordGate instance, which has the transformation on the stabilizer state equivalent to the composition of operations.

Raises
`ValueError`	When one or more operations do not have stabilizer effect.

`from_pauli`

View source

@staticmethod
from_pauli(
    pauli: cirq.Pauli,
    sqrt: bool = False
) -> 'SingleQubitCliffordGate'

`from_quarter_turns`

View source

@staticmethod
from_quarter_turns(
    pauli: cirq.Pauli,
    quarter_turns: int
) -> 'SingleQubitCliffordGate'

`from_single_map`

View source

@staticmethod
from_single_map(
    pauli_map_to: Optional[Dict[Pauli, Tuple[Pauli, bool]]] = None,
    *,
    x_to: Optional[Tuple[Pauli, bool]] = None,
    y_to: Optional[Tuple[Pauli, bool]] = None,
    z_to: Optional[Tuple[Pauli, bool]] = None
) -> 'SingleQubitCliffordGate'

Returns a SingleQubitCliffordGate for the specified transform with a 90 or 180 degree rotation.

The arguments are exclusive, only one may be specified.

Args
`pauli_map_to`	A dictionary with a single key value pair describing the transform.
`x_to`	The transform from cirq.X
`y_to`	The transform from cirq.Y
`z_to`	The transform from cirq.Z

`from_unitary`

View source

@staticmethod
from_unitary(
    u: np.ndarray
) -> Optional['SingleQubitCliffordGate']

Creates Clifford gate with given unitary (up to global phase).

Args
`u`	2x2 unitary matrix of a Clifford gate.

Returns
SingleQubitCliffordGate, whose matrix is equal to given matrix (up to global phase), or `None` if `u` is not a matrix of a single-qubit Clifford gate.

`from_unitary_with_global_phase`

View source

@classmethod
from_unitary_with_global_phase(
    u: np.ndarray
) -> Optional[Tuple['SingleQubitCliffordGate', complex]]

Creates Clifford gate with given unitary, including global phase.

Args
`u`	2x2 unitary matrix of a Clifford gate.

Returns
A tuple of a SingleQubitCliffordGate and a global phase, such that the gate unitary (as given by `cirq.unitary`) times the global phase is identical to the given unitary `u`; or `None` if `u` is not the matrix of a single-qubit Clifford gate.

`from_xz_map`

View source

@staticmethod
from_xz_map(
    x_to: Tuple[cirq.Pauli, bool],
    z_to: Tuple[cirq.Pauli, bool]
) -> 'SingleQubitCliffordGate'

Returns a SingleQubitCliffordGate for the specified transforms. The Y transform is derived from the X and Z.

Args
`x_to`	Which Pauli to transform X to and if it should negate.
`z_to`	Which Pauli to transform Z to and if it should negate.

`merged_with`

View source

merged_with(
    second: 'SingleQubitCliffordGate'
) -> 'SingleQubitCliffordGate'

Returns a SingleQubitCliffordGate such that the circuits --output-- and --self--second-- are equivalent up to global phase.

`num_qubits`

View source

num_qubits() -> int

The number of qubits this gate acts on.

`on`

View source

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`

View source

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.

`pauli_tuple`

View source

pauli_tuple(
    pauli: cirq.Pauli
) -> Tuple[cirq.Pauli, bool]

Returns a tuple of a Pauli operator and a boolean.

The pauli is the operator of the transform and the boolean determines whether the operator should be flipped. For instance, it is True if the coefficient is -1, and False if the coefficient is 1.

`to_phased_xz_gate`

View source

to_phased_xz_gate() -> cirq.PhasedXZGate

Convert this gate to a PhasedXZGate instance.

The rotation can be categorized by {axis} * {degree}:

* Identity: I
* {x, y, z} * {90, 180, 270}  --- {X, Y, Z} + 6 Quarter turn gates
* {+/-xy, +/-yz, +/-zx} * 180  --- 6 Hadamard-like gates
* {middle point of xyz in 4 Quadrant} * {120, 240} --- swapping axis

note 1 + 9 + 6 + 8 = 24 in total.

To associate with Clifford Tableau, it can also be grouped by 4:

* {I,X,Y,Z} is [[1 0], [0, 1]]
* {+/- X_sqrt, 2 Hadamard-like gates acting on the YZ plane} is [[1, 0], [1, 1]]
* {+/- Z_sqrt, 2 Hadamard-like gates acting on the XY plane} is [[1, 1], [0, 1]]
* {+/- Y_sqrt, 2 Hadamard-like gates acting on the XZ plane} is [[0, 1], [1, 0]]
* {middle point of xyz in 4 Quadrant} * 120 is [[0, 1], [1, 1]]
* {middle point of xyz in 4 Quadrant} * 240 is [[1, 1], [1, 0]]

`validate_args`

View source

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_probability`

View source

with_probability(
    probability: 'cirq.TParamVal'
) -> 'cirq.Gate'

Creates a probabilistic 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`

View source

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`.

`add`

View source

__add__(
    other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'

`call`

View source

__call__(
    *qubits, **kwargs
)

Call self as a function.

`eq`

View source

__eq__(
    other: _SupportsValueEquality
) -> bool

`mul`

View source

__mul__(
    other: Union[complex, float, int]
) -> 'cirq.LinearCombinationOfGates'

`ne`

View source

__ne__(
    other: _SupportsValueEquality
) -> bool

`neg`

View source

__neg__() -> 'cirq.LinearCombinationOfGates'

`pow`

View source

__pow__(
    exponent
) -> 'SingleQubitCliffordGate'

`rmul`

View source

__rmul__(
    other: Union[complex, float, int]
) -> 'cirq.LinearCombinationOfGates'

`sub`

View source

__sub__(
    other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'

`truediv`

View source

__truediv__(
    other: Union[complex, float, int]
) -> 'cirq.LinearCombinationOfGates'