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qml.ftqc.measure_arbitrary_basis

measure_arbitrary_basis(wires, angle, plane, reset=False, postselect=None)[source]

Perform a mid-circuit measurement in the basis defined by the plane and angle on the supplied qubit.

The measurements are performed using the 0, 1 convention rather than the ±1 convention.

If a device doesn’t support mid-circuit measurements natively, then the desired mcm_method for executing mid-circuit measurements should be passed to the QNode.

Warning

Measurements should be diagonalized before execution for any device that only natively supports mid-circuit measurements in the computational basis. To diagonalize, the diagonalize_mcms transform can be applied.

Skipping diagonalization for a circuit containing parametric mid-circuit measurements may result in a completed execution with incorrect results.

Parameters:

  • wires (Wires) – The wire to measure.

  • angle (float) – The angle of rotation defining the axis, specified in radians.

  • plane (str) – The plane the measurement basis lies in. Options are “XY”, “YZ” and “ZX”

  • reset (Optional[bool]) – Whether to reset the wire to the \(|0 \rangle\) state after measurement.

  • postselect (Optional[int]) – Which basis state to postselect after a mid-circuit measurement. None by default. If postselection is requested, only the post-measurement state that is used for postselection will be considered in the remaining circuit.

Returns:

The mid-circuit measurement result linked to the created MidMeasureMP.

Return type:

MeasurementValue

Raises:

QuantumFunctionError – if multiple wires were specified

Note

Reset behaviour will depend on the execution method for mid-circuit measurements, and may not work for all configurations.

Example:

import pennylane as qml
from pennylane.ftqc import diagonalize_mcms, measure_arbitrary_basis

dev = qml.device("default.qubit", wires=3)

@diagonalize_mcms
@qml.qnode(dev, mcm_method="tree-traversal")
def func(x, y):
    qml.RY(x, wires=0)
    qml.CNOT(wires=[0, 1])
    m_0 = measure_arbitrary_basis(1, angle=np.pi/3, plane="XY")

    qml.cond(m_0, qml.RY)(y, wires=0)
    return qml.probs(wires=[0])

Executing this QNode:

>>> pars = np.array([0.643, 0.246])
>>> func(*pars)
array([0.91237915, 0.08762085])

The plane and angle are related to the axis of measurement by the following formulas:

\[M_{XY}(\phi) =\frac{1}{\sqrt{2}} (|0\rangle + e^{i\phi} |1\rangle),\]
\[M_{YZ}(\theta) =\cos{\frac{\theta}{2}}|0\rangle + i \sin{\frac{\theta}{2}} |1\rangle,\text{ and}\]
\[M_{ZX}(\theta) = \cos{\frac{\theta}{2}}|0\rangle + \sin{\frac{\theta}{2}} |1\rangle\]

where, in terms of spherical coordinates in the physics convention, the angles \(\phi\) and \(\theta\) are the azimuthal and polar angles, respectively.

Measurement outcomes can be used to conditionally apply operations, and measurement statistics can be gathered and returned by a quantum function. Measurement outcomes can also be manipulated using arithmetic operators like +, -, *, /, etc. with other mid-circuit measurements or scalars.

See the qml.measure function for details on the available arithmetic operators for mid-circuit measurement results.

Mid-circuit measurement results can be processed with the usual measurement functions such as expval(). For QNodes with finite shots, sample() applied to a mid-circuit measurement result will return a binary sequence of samples. See here for more details.

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