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A unitary qubit or qudit gate defined entirely by its matrix.

Inherits From: Gate

Used in the notebooks

Used in the tutorials

matrix The matrix that defines the gate.
name The optional name of the gate to be displayed.
qid_shape The shape of state tensor that the matrix applies to. If not specified, this value is inferred by assuming that the matrix is supposed to apply to qubits.
unitary_check_rtol The relative tolerance for checking whether the supplied matrix is unitary. See cirq.is_unitary.
unitary_check_atol The absolute tolerance for checking whether the supplied matrix is unitary. See cirq.is_unitary.

ValueError If the matrix is not a square numpy array, if the matrix does not match the qid_shape, if qid_shape is not supplied and the matrix dimension is not a power of 2, or if the matrix not unitary (to the supplied precisions).



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Returns a controlled version of this gate. If no arguments are specified, defaults to a single qubit control.

num_controls: Total number of control qubits. control_values: For which control qubit values to apply the sub gate. A sequence of length num_controls where each entry is an integer (or set of integers) corresponding to the qubit value (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.


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The number of qubits this gate acts on.


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Returns an application of this gate to the given qubits.

*qubits The collection of qubits to potentially apply the gate to.


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Returns a list of operations applying the gate to all targets.

*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.

Operations applying this gate to the target qubits.

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.


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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.

qubits The sequence of qubits to potentially apply the gate to.


  • ValueError: The gate can't be applied to the qubits.


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Call self as a function.


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Return self==value.


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Return self!=value.


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