  To simulate a fermionic system on a quantum computer, it is necessary to
encode the state of the fermions onto qubits. Fermion-to-qubit mappings such as
the Jordan-Wigner and Bravyi-Kitaev transformations do this using $N$ qubits to
represent systems of $N$ fermionic modes. In this work, we demonstrate that for
particle number conserving systems of $K$ fermions and $N$ modes, the qubit
requirement can be reduced to the information theoretic minimum of $\lceil
\log_2 {N \choose K} \rceil$. This will improve the feasibility of simulation
of molecules and many-body systems on near-term quantum computers with limited
qubit number.
