[BUG] Confusing errors when post-selection produces no valid shots.

[astralcai]

Expected behavior

When a circuit containing mid-circuit measurements with post-selection is executed with finite shots, there is always a possibility that none of the shots produced the measurement outcome that we are post-selecting on. The way we handle this scenario should be

1. Consistent across different error methods.
2. Clear to the user what is causing the error and/or invalid results.

Actual behavior

Consider the following circuit:

import pennylane as qml

dev = qml.device("default.qubit", shots=10)

def circuit():
    qml.X(0)
    m = qml.measure(0, postselect=0)
    return qml.probs(wires=[0])

When we use dynamic one-shot, the circuit executes to completion and returns nan:

>>> qml.QNode(circuit, dev, mcm_method="one-shot")()
nan

With tree-traversal, we now get an error:

>>> qml.QNode(circuit, dev, mcm_method="tree-traversal")() 
ZeroDivisionError: division by zero

With deferred measurement, we get a different error:

>>> qml.QNode(circuit, dev, mcm_method="deferred")()
ValueError: cannot reshape array of size 0 into shape (0)

This can be difficult to debug for a user with complex circuits.

Additional information

No response

Source code

No response

Tracebacks

No response

System information

Name: PennyLane
Version: 0.39.0.dev31
Summary: PennyLane is a cross-platform Python library for quantum computing, quantum machine learning, and quantum chemistry. Train a quantum computer the same way as a neural network.
Home-page: https://github.com/PennyLaneAI/pennylane
Author: 
Author-email: 
License: Apache License 2.0
Location: /Users/astral.cai/Workspace/pennylane
Requires: appdirs, autograd, autoray, cachetools, networkx, numpy, packaging, pennylane-lightning, requests, rustworkx, scipy, toml, typing_extensions
Required-by: PennyLane-Catalyst, PennyLane_Lightning, PennyLane_Lightning_Kokkos

Platform info:           macOS-15.1-arm64-arm-64bit
Python version:          3.10.14
Numpy version:           1.26.4
Scipy version:           1.12.0
Installed devices:
- default.clifford (PennyLane-0.39.0.dev31)
- default.gaussian (PennyLane-0.39.0.dev31)
- default.mixed (PennyLane-0.39.0.dev31)
- default.qubit (PennyLane-0.39.0.dev31)
- default.qutrit (PennyLane-0.39.0.dev31)
- default.qutrit.mixed (PennyLane-0.39.0.dev31)
- default.tensor (PennyLane-0.39.0.dev31)
- null.qubit (PennyLane-0.39.0.dev31)
- reference.qubit (PennyLane-0.39.0.dev31)
- lightning.qubit (PennyLane_Lightning-0.39.0.dev48)
- nvidia.custatevec (PennyLane-Catalyst-0.9.0.dev41)
- nvidia.cutensornet (PennyLane-Catalyst-0.9.0.dev41)
- oqc.cloud (PennyLane-Catalyst-0.9.0.dev41)
- softwareq.qpp (PennyLane-Catalyst-0.9.0.dev41)
- lightning.kokkos (PennyLane_Lightning_Kokkos-0.39.0.dev38)

Existing GitHub issues

• I have searched existing GitHub issues to make sure the issue does not already exist.