cirq.PhasedFSimGate

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General excitation-preserving two-qubit gate.

Inherits From: InterchangeableQubitsGate, Gate

cirq.PhasedFSimGate(
    theta: 'cirq.TParamVal',
    zeta: 'cirq.TParamVal' = 0.0,
    chi: 'cirq.TParamVal' = 0.0,
    gamma: 'cirq.TParamVal' = 0.0,
    phi: 'cirq.TParamVal' = 0.0
) -> None

Used in the notebooks

Used in the tutorials
Coherent vs Incoherent Error with XEB

The unitary matrix of PhasedFSimGate(θ, ζ, χ, γ, φ) is:

\[ \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{-i \gamma - i \zeta} \cos(\theta) & -i e^{-i \gamma + i\chi} \sin(\theta) & 0 \\ 0 & -i e^{-i \gamma - i \chi} \sin(\theta) & e^{-i \gamma + i \zeta} \cos(\theta) & 0 \\ 0 & 0 & 0 & e^{-2i \gamma - i \phi} \end{bmatrix} \]

This parametrization follows eq (18) in https://arxiv.org/abs/2010.07965 See also eq (43) in https://arxiv.org/abs/1910.11333 for an older variant which uses the same θ and φ parameters, but has three phase angles that have different names and opposite sign. Specifically, ∆+ angle corresponds to -γ, ∆- corresponds to -ζ and ∆-,off corresponds to -χ.

Another useful parametrization of PhasedFSimGate is based on the fact that the gate is equivalent up to global phase to the following circuit:

0: ───Rz(α0)───FSim(θ, φ)───Rz(β0)───
               │
1: ───Rz(α1)───FSim(θ, φ)───Rz(β1)───

where α0 and α1 are Rz angles to be applied before the core FSimGate, β0 and β1 are Rz angles to be applied after FSimGate and θ and φ specify the core FSimGate. Use the static factory function from_fsim_rz to instantiate the gate using this parametrization.

Note that the θ and φ parameters in the two parametrizations are the same.

The matrix above is block diagonal where the middle block may be any element of U(2) and the bottom right block may be any element of U(1). Consequently, five real parameters are required to specify an instance of PhasedFSimGate. Therefore, the second parametrization is not injective. Indeed, for any angle δ

cirq.PhasedFSimGate.from_fsim_rz(θ, φ, (α0, α1), (β0, β1))

and

cirq.PhasedFSimGate.from_fsim_rz(θ, φ,
                                 (α0 + δ, α1 + δ),
                                 (β0 - δ, β1 - δ))

specify the same gate and therefore the two instances will compare as equal up to numerical error. Another consequence of the non-injective character of the second parametrization is the fact that the properties rz_angles_before and rz_angles_after may return different Rz angles than the ones used in the call to from_fsim_rz.

This gate is generally not symmetric under exchange of qubits. It becomes symmetric if both of the following conditions are satisfied:

• ζ = kπ or θ = π/2 + lπ for k and l integers,
• χ = kπ or θ = lπ for k and l integers.

Args
theta	Swap angle on the |01⟩ |10⟩ subspace, in radians. See class docstring above for details.
zeta	One of the phase angles, in radians. See class docstring above for details.
chi	One of the phase angles, in radians. See class docstring above for details.
gamma	One of the phase angles, in radians. See class docstring above for details.
phi	Controlled phase angle, in radians. See class docstring above for details.

Attributes
chi
gamma
phi
rz_angles_after	Returns 2-tuple of phase angles applied to qubits after FSimGate.
rz_angles_before	Returns 2-tuple of phase angles applied to qubits before FSimGate.
theta
zeta

Methods

controlled

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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.

from_fsim_rz

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@staticmethod
from_fsim_rz(
    theta: 'cirq.TParamVal',
    phi: 'cirq.TParamVal',
    rz_angles_before: Tuple['cirq.TParamVal', 'cirq.TParamVal'],
    rz_angles_after: Tuple['cirq.TParamVal', 'cirq.TParamVal']
) -> 'PhasedFSimGate'

Creates PhasedFSimGate using an alternate parametrization.

Args
theta	Swap angle on the |01⟩ |10⟩ subspace, in radians. See class docstring above for details.
phi	Controlled phase angle, in radians. See class docstring above for details.
rz_angles_before	2-tuple of phase angles to apply to each qubit before the core FSimGate. See class docstring for details.
rz_angles_after	2-tuple of phase angles to apply to each qubit after the core FSimGate. See class docstring for details.

num_qubits

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num_qubits() -> int

The number of qubits this gate acts on.

on

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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

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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.

qubit_index_to_equivalence_group_key

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qubit_index_to_equivalence_group_key(
    index: int
) -> int

Returns a key that differs between non-interchangeable qubits.

validate_args

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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

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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

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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__

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

__call__

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__call__(
    *qubits, **kwargs
)

Call self as a function.

__eq__

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__eq__(
    other: _SupportsValueEquality
) -> bool

__mul__

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

__ne__

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__ne__(
    other: _SupportsValueEquality
) -> bool

__neg__

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__neg__() -> 'cirq.LinearCombinationOfGates'

__pow__

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__pow__(
    power
)

__rmul__

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

__sub__

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

__truediv__

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