cirq.Rz

A gate with matrix \(e^{-i Z t/2}\) that rotates around the Z axis of the Bloch sphere by \(t\).

Inherits From: ZPowGate, EigenGate, Gate

Used in the notebooks

Used in the tutorials

The unitary matrix of cirq.Rz(rads=t) is:

\[ e^{-i Z t /2} = \begin{bmatrix} e^{-it/2} & 0 \\ 0 & e^{it/2} \end{bmatrix} \]

This gate corresponds to the traditionally defined rotation matrices about the Pauli Z axis.

rads Radians to rotate about the Z axis of the Bloch sphere.

exponent

global_shift

Methods

controlled

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Returns a controlled ZPowGate, using a CZPowGate where possible.

The controlled method of the Gate class, of which this class is a child, returns a ControlledGate. This method overrides this behavior to return a CZPowGate or a ControlledGate of a CZPowGate, when this is possible.

The conditions for the override to occur are:

  • The global_shift of the ZPowGate is 0.
  • The control_values and control_qid_shape are compatible with the CZPowGate:
    • The last value of control_qid_shape is a qubit.
    • The last value of control_values corresponds to the control being satisfied if that last qubit is 1 and not satisfied if the last qubit is 0.

If these conditions are met, then the returned object is a CZPowGate or, in the case that there is more than one controlled qudit, a ControlledGate with the Gate being a CZPowGate. In the latter case the ControlledGate is controlled by one less qudit than specified in control_values and control_qid_shape (since one of these, the last qubit, is used as the control for the CZPowGate).

If the above conditions are not met, a ControlledGate of this gate will be returned.

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.ControlledGate (or cirq.CZPowGate if possible) representing self controlled by the given control values and qubits.

in_su2

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Returns an equal-up-global-phase gate from the group SU2.

num_qubits

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The number of qubits this gate acts on.

on

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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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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

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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.

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

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

with_canonical_global_phase

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Returns an equal-up-global-phase standardized form of the gate.

with_probability

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Creates a probabalistic 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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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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__call__

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Call self as a function.

__eq__

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__mul__

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__ne__

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__neg__

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__pow__

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__rmul__

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__sub__

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__truediv__

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