CNOT(0,1).to_matrix() returns unexpected value

[Lknadfodr]

Describe the bug
CNOT(0,1).to_matrix() returns

$$ \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \end{pmatrix} $$

but I expect it to be

$$ \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{pmatrix} $$

In comparison, SWAP(0,1), H(0)+H(1) are as expected, and when rewriting CZ(0,1) with H(1)+CX(0,1)+H(1) it also is as expected.

The behaviour of the cirquit itself however is correct, so when CNOT(0,1) is applied to |10>, one gets |11> instead of |10> as the matrix would imply.

Note also that CNOT(1,0).to_matrix() returns the expected matrix of CNOT(0,1), and vice versa, so the control and target seem to be swapped.

To Reproduce

import tequila as tq

U = tq.gates.CNOT(control=0, target=1)
print(U.to_matrix().real)

for b in [tq.QubitWaveFunction.from_string(b) for b in ["|00>", "|01>", "|10>", "|11>"]]:
    print(f"{b} -> {tq.simulate(objective=U, initial_state=b)}")

Expected behavior

Computer (please complete the following information):
tequila version: 1.9.10
python version: 3.10.12 (main, Nov 4 2025, 08:48:33) [GCC 11.4.0]
platform: #88~22.04.1-Ubuntu SMP PREEMPT_DYNAMIC Tue Oct 14 14:03:14 UTC 2

Additional context
I am trying to verify excercise 1 from Quantum Computing sheet 8, which resulted in a different matrix than I calculated by hands.

[kottmanj]

thanks for noticing. Will take a look.

the to_matrix feature in the circuits is quite new and won't affect any other part in tequila.
It's basically an isolated function that uses quimb to get the matrices.
For some reason, it is inverting the qubit counts (i.e. 0,1 will become 1,0), which is not the desired behaviour.

[kottmanj]

Planning some refactoring on the to_matrix function anyways, will notify once implemented :-)