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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 log 2 N K . This will improve the feasibility of simulation of molecules and many-body systems on near-term quantum computers with limited qubit number.