cirq.ArithmeticGate

A helper gate for implementing reversible classical arithmetic.

Inherits From: Gate

Used in the notebooks

Used in the tutorials

Child classes must override the registers, with_registers, and apply methods.

This class handles the details of ensuring that the scaling of implementing the gate is O(2^n) instead of O(4^n) where n is the number of qubits being acted on, by implementing an _apply_unitary_ function in terms of the registers and the apply function of the child class.

Examples:

class Add(cirq.ArithmeticGate):
    def __init__(
        self,
        target_register: '[int, Sequence[int]]',
        input_register: 'Union[int, Sequence[int]]',
    ):
        self.target_register = target_register
        self.input_register = input_register

    def registers(self) -> 'Sequence[Union[int, Sequence[int]]]':
        return self.target_register, self.input_register

    def with_registers(
        self, *new_registers: 'Union[int, Sequence[int]]'
    ) -> 'Add':
        return Add(*new_registers)

    def apply(self, *register_values: int) -> 'Union[int, Iterable[int]]':
        return sum(register_values)
cirq.unitary(
    Add(target_register=[2, 2],
        input_register=1).on(*cirq.LineQubit.range(2))
).astype(np.int32)
array([[0, 0, 0, 1],
       [1, 0, 0, 0],
       [0, 1, 0, 0],
       [0, 0, 1, 0]], dtype=int32)
c = cirq.Circuit(
   cirq.X(cirq.LineQubit(3)),
   cirq.X(cirq.LineQubit(2)),
   cirq.X(cirq.LineQubit(6)),
   cirq.measure(*cirq.LineQubit.range(4, 8), key='before_in'),
   cirq.measure(*cirq.LineQubit.range(4), key='before_out'),

   Add(target_register=[2] * 4,
       input_register=[2] * 4).on(*cirq.LineQubit.range(8)),

   cirq.measure(*cirq.LineQubit.range(4, 8), key='after_in'),
   cirq.measure(*cirq.LineQubit.range(4), key='after_out'),
)
cirq.sample(c).data
   before_in  before_out  after_in  after_out
0          2           3         2          5

Methods

apply

View source

@abc.abstractmethod
apply(
    *register_values
) -> Union[int, Iterable[int]]

Returns the result of the gate operating on classical values.

For example, an addition takes two values (the target and the source), adds the source into the target, then returns the target and source as the new register values.

The apply method is permitted to be sloppy in three ways:

  1. The apply method is permitted to return values that have more bits than the registers they will be stored into. The extra bits are simply dropped. For example, if the value 5 is returned for a 2 qubit register then 5 % 22 = 1 will be used instead. Negative values are also permitted. For example, for a 3 qubit register the value -2 becomes -2 % 23 = 6.
  2. When the value of the last k registers is not changed by the gate, the apply method is permitted to omit these values from the result. That is to say, when the length of the output is less than the length of the input, it is padded up to the intended length by copying from the same position in the input.
  3. When only the first register's value changes, the apply method is permitted to return an int instead of a sequence of ints.

The apply method must be reversible. Otherwise the gate will not be unitary, and incorrect behavior will result.

Examples
A fully detailed adder:

def apply(self, target, offset):
    return (target + offset) % 2**len(self.target_register), offset

The same adder, with less boilerplate due to the details being handled by the ArithmeticGate class:

def apply(self, target, offset):
    return target + offset

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.

registers

View source

@abc.abstractmethod
registers() -> Sequence[Union[int, Sequence[int]]]

The data acted upon by the arithmetic gate.

Each register in the list can either be a classical constant (an int), or else a list of qubit/qudit dimensions. Registers that are set to a classical constant must not be mutated by the arithmetic gate (their value must remain fixed when passed to apply).

Registers are big endian. The first qubit is the most significant, the last qubit is the 1s qubit, the before last qubit is the 2s qubit, etc.

Returns
A list of constants and qubit groups that the gate will act upon.

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.

with_registers

View source

@abc.abstractmethod
with_registers(
    *new_registers
) -> Self

Returns the same fate targeting different registers.

Args
*new_registers The new values that should be returned by the registers method.

Returns
An instance of the same kind of gate, but acting on different registers.

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.

__mul__

View source

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

__neg__

View source

__neg__() -> 'cirq.LinearCombinationOfGates'

__pow__

View source

__pow__(
    power
)

__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'