Endian representation bug in `QppCircuitSimulator::observe`

[1tnguyen]

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Describe the bug

In PR #1082, we reverted the endianness of qpp state vector but didn't adjust the QppCircuitSimulator::observe implementation, which uses spin_op::to_matrix to construct the full Hamiltonian matrix. This matrix and the state vector need to be in sync. w.r.t. endianness.

Note: this code path is not active by default

Steps to reproduce the bug

With CUDA-Q version 0.7.0,

import cudaq
import os

os.environ["CUDAQ_OBSERVE_FROM_SAMPLING"] = "0"
cudaq.set_target("qpp-cpu")
kernel = cudaq.make_kernel()
qreg = kernel.qalloc(2)
kernel.x(qreg[0])
hamiltonian = cudaq.spin.z(0)

print("<Z0> =", cudaq.observe(kernel, hamiltonian, shots_count=-1).expectation())

This is expected to print -1 but will print 1.

Change the hamiltonian to z(1) will produce -1, indicating an endian issue.

Expected behavior

Correct calculation for all modes.

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

Since PR 1082

Environment

• CUDA Quantum version: 0.7.0
• Python version: 3.10
• C++ compiler: gcc12
• Operating system: Ubuntu22.04

Suggestions

There is another implementation of this 'direct' calculation in https://github.com/NVIDIA/cuda-quantum/blob/main/unittests/backends/qpp_observe/QPPObserveBackend.cpp#L22.

Not sure why we have two different implementations. We might want to consolidate them.