I am having some trouble understanding how the number of simulation qubits are chosen when finding the eigenvalue of a fermionic Hamiltonian.
For the phase-estimation algorithm, is the number of simulation qubits the same as the number of particles you want to simulate, or is it the number of orthogonal single-particle states you want to include?
For example: If I want to find the eigenvalues for a two-particle system and have 10 qubits to spare, do I initialize the 10 qubits to for example $|0011111111\rangle$ or $|1100111111\rangle$ (1s are un-occupied and 0s are occupied states) and let the time evolution operator act on this system? Or do I simply go for a random two-qubit state, for example, $|00\rangle$ and let the time-evolution operator act on this state?