  We develop theoretical methods for the implementation of creation and
destruction operators in separate registers of a quantum computer, allowing for
a transparent and dynamical creation and destruction of particle modes in
second quantization in problems with variable particle number. We establish
theorems for the commutation (anticommutation) relations on a finite memory
bank and provide the needed symmetrizing and antisymmetrizing operators.
Finally, we provide formulae in terms of these operators for unitary evolution
under conventional two- and four-body Hamiltonian terms, as well as terms
varying the particle number. In this formalism, the number of qubits needed to
codify $n$ particles with $N_p$ modes each is of order $n\log_2 N_p$. Such
scaling is more efficient than the Jordan-Wigner transformation which requires
$O(N_p)$ qubits, whenever there are a modest number of particles with a large
number of states available to each (and less advantageous for a large number of
particles with few states available to each). And although less efficient, it
is also less cumbersome than compact encoding.
