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Assume, I'm using a system of qubits to simulate a fermionic system.

If I'm using the second-quantized formalism (e.g. orbitals in quantum chemistry), the anti-symmetric nature of the fermionic wave functions can be taken into account by means of the Jordan-Wigner or Brayi-Kitaev transformation. Roughly speaking, this gives a 1-to-1 correspondence between the physical (fermionic) and logical (bosonic) DOFs, with operators of certain locality. So, in terms of qubits resources, this is as efficient as can be.

Now, could anyone please elaborate how the issue of the wave function anti-symmetry is typically resolved within the first-quantized approach? (In other words, when doing lattice simulations.)

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