I'm working in the Bravyi-Kitaev basis implemented by the openfermion.bravyi_kitaev() function to find the ground state of a fermionic operator in the BK representation. Now I want to convert this ground state from the BK basis to the occupation number basis. I couldn't find any functions implementing this, and the transformation matrix shown in arXiv:1208.5986 is not the correct one. Has anyone managed to find a transform between these two bases?
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I managed to solve the problem:
The matrix $\beta$ that transforms a binary string from the occupation number basis to the Bravyi-Kitaev basis, introduced in arXiv:1208.5986 in eq. (23), is the correct matrix. For qubit states in cirq the ordering of the qubits has to be reversed, while qubit states in Qiskit can be transformed directly.
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1$\begingroup$ This question and answer might be more helpful to other people if you spell out a few more details, such as what $\beta$ and the B-K basis are explicitly $\endgroup$ Nov 30, 2021 at 15:00