cirq.EigenGate

A gate with a known eigendecomposition.

Inherits From: Gate

cirq.EigenGate(
    *,
    exponent: cirq.TParamVal = 1.0,
    global_shift: float = 0.0
) -> None

EigenGate is particularly useful when one wishes for different parts of the same eigenspace to be extrapolated differently. For example, if a gate has a 2-dimensional eigenspace with eigenvalue -1, but one wishes for the square root of the gate to split this eigenspace into a part with eigenvalue i and a part with eigenvalue -i, then EigenGate allows this functionality to be unambiguously specified via the _eigen_components method.

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)

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:

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.

ValueError If the supplied exponent is a complex number with an imaginary component.

exponent

global_shift

Methods

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.

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.

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: Union[float, sympy.Symbol]
) -> 'EigenGate'

__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'