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fix ordering of alpha and beta spins in example notebook #9

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kevinsung
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In the LUCJ circuit, alpha qubits come before beta qubits. In Qiskit, qubits are ordered from right to left. Therefore, the alpha qubits are on the right part of the bitstring, and the beta qubits are on the left. In this particular case the numbers of alpha and beta electrons are the same, which is why there is no error, but the distinction is material in the open-shell case.

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Thanks for bringing this up @kevinsung . This is a bit deeper of a problem with the API. I have opened #11 to bring more consistency to the API and a bit more clarity in the docs.

@caleb-johnson caleb-johnson added the stable backport potential Doesn't affect the API label Sep 13, 2024
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I believe we will merge #11 and do a quick release to improve the workflow. Thanks again 🚀

@kevinsung kevinsung deleted the bitstring-order branch September 17, 2024 14:55
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