# qml.transforms.measurement_grouping¶

measurement_grouping(tape, obs_list, coeffs_list)[source]

Returns a list of measurement optimized tapes, and a classical processing function, for evaluating the expectation value of a provided Hamiltonian.

Parameters
• tape (QuantumTape) – input tape

• obs_list (Sequence[Observable]) – The list of observables to measure the expectation values of after executing the tape.

• coeffs_list (Sequence[float]) – Coefficients of the Hamiltonian expression. Must be of the same length as obs_list.

Returns

Returns a tuple containing a list of quantum tapes to be evaluated, and a function to be applied to these tape results to compute the Hamiltonian expectation value.

Return type

tuple[list[QuantumTape], func]

Example

Given the following quantum tape,

>>> with qml.tape.QuantumTape() as tape:
...     qml.RX(0.1, wires=0)
...     qml.RX(0.2, wires=1)
...     qml.CNOT(wires=[0, 1])
...     qml.CNOT(wires=[1, 2])


and list of observables with coefficients,

>>> obs = [qml.PauliZ(0), qml.PauliX(0) @ qml.PauliZ(1), qml.PauliX(2)]
>>> coeffs = [2.0, -0.54, 0.1]


We can generate generate measurement optimized tapes corresponding to a qubit-wise commuting grouping of the provided observables:

>>> tapes, fn = qml.transforms.measurement_grouping(tape, obs, coeffs)
>>> print(tapes)
[<QuantumTape: wires=[0, 1, 2], params=2>,
<QuantumTape: wires=[0, 1, 2], params=2>]
>>> print(fn)
<function measurement_grouping.<locals>.processing_fn at 0x7f1af81287a0>


The output are the optimized tapes, and a processing function to apply to the results of the evaluated tapes to construct the expectation value of the Hamiltonian.

Note that only two tapes have been returned, rather than three (one for each observable); this is because qml.PauliZ(0) and qml.PauliX(2) are qubit-wise commuting, and can be extracted from a single tape evaluation.

We can now evaluate these tapes, and apply the processing function:

>>> dev = qml.device("default.qubit", wires=3)
>>> res = fn(dev.batch_execute(tapes))
>>> print(res)
2.0007186031172046