Allow reusing and reseting wires after a mid-circuit measurement

[mudit2812]

Context:
Making mid-circuit measurements more feature rich.

Description of the Change:

• qml.defer_measurements no longer raises an error if a qubit is reused after measurement, and includes functionality to reset qubits.
• Updated qml.measure to include a reset keyword argument for reseting qubits to the $|0\rangle$ computational basis state after measurement.

Qubit reuse is enabled by by applying a CNOT gate controlled on the measured wire to an auxiliary target wire to store the measurement state on the auxiliary wire. Using CNOT will cause entanglement between the measured wire and the rest of the wires to be "copied" to the auxiliary wire. Hence, the measured wire can be reused while still preserving the measurement state in the auxiliary wire, which, defer_measurements uses as the control wires for controlled operations created by qml.cond.

For qubit reset, qml.defer_measurements applies a CNOT gate controlled on the auxiliary wire to the target measured wire. A CNOT between two wires in the same state reduces the target wire to the $|0\rangle$ state.

Benefits:

• Qubit reuse and reset is possible on PennyLane

Possible Drawbacks:

• Until defer_measurements is ported over to the new transforms API, custom wire labels will not be allowed.
• Users need to remember to initialize old-gen devices with n extra wires for n mid-circuit measurements, and make sure that the last n wires are reserved for mid-circuit measurement states.
• Space complexity for circuits with mid-circuit measurements will scale as $O(2^n)$ for n mid-circuit measurements, as a new wire will be added for each mid-circuit measurement.
• Since new wires will be added, old-gen devices will need to be initialized with as many extra wires as the number of mid-circuit measurements.

Related GitHub Issues:

[mudit2812]

[sc-36565] [sc-38882]

[lillian542]

Looks good! 🚀 I left a few very minor suggestions/questions wrt tests, but that's all from me.

[trbromley]

Thanks @mudit2812! Will we have a follow up PR to update the docs here?

[trbromley]

What does this mean?