cudaq.observe with a list of multi-term operators drops term coefficients, and fails when arguments are broadcast #5679

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Describe the bug

When cudaq.observe gets a list of operators and one element has more than one term, the result for that element ignores the term coefficients. Identity terms still add their coefficient, so the number is neither the raw Pauli expectation nor the operator expectation. With broadcast kernel arguments the same list raises instead.

Steps to reproduce the bug

import numpy as np, cudaq
from cudaq import spin

@cudaq.kernel
def k(t: float):
    q = cudaq.qvector(2)
    x(q[0])
    rx(t, q[1])

Z0 = spin.z(0); Z1 = spin.z(1)
ops = [2*Z0 + 3*Z1, 0.5*Z0*Z1 + 1.0, spin.x(0) + 4*Z1]
print([cudaq.observe(k, o, 0.7).expectation() for o in ops])
print([r.expectation() for r in cudaq.observe(k, ops, 0.7)])
cudaq.observe(k, ops, [0.0, 0.7])

Output, rounded to six places, with only the last line of the traceback

[0.294527, 0.617579, 3.059369]
[-0.235158, 0.235158, 0.764842]
ValueError: expecting a spin op with a single term

-0.235158 is <Z0> + <Z1> = -1 + cos(0.7), while 2*Z0 + 3*Z1 has expectation -2 + 3*cos(0.7) = 0.294527.

Expected behavior

The second line should match the first, and the broadcast call should return one such row per argument value.

The list path came in with #3835 for #3745. It sums observe_result.expectation(term) over the terms of each element, and that method returns the raw Pauli string expectation without the coefficient. The test added there only puts a coefficient on the identity term, so it passes either way. The broadcast path in the same function still calls p.expectation(o) on the whole operator, which is the error from #3745.

Is this a regression? If it is, put the last known working version (or commit) here.

Not a regression

Environment

• CUDA-Q version: 0.16.0.post1 (cuda-quantum-cu13 wheel, qpp-cpu target). python/cudaq/runtime/observe.py on main is identical to the one in this wheel.
• Python version: 3.12.15
• Operating system: Debian 13 (python:3.12-slim container), aarch64

Suggestions

Single-term elements return the raw Pauli expectation. With the kernel above, [2*Z0, -3*Z1] at t = 0.7 gives [-1.0, 0.764842]. That matches the C++ term list overload and test_observe_list, so I would leave it alone and only change the multi-term case. I have a small patch with a test and can open a PR if that sounds right.