Reducing the qubit requirement of Jordan-Wigner encodings of N-mode, K-fermion systems from N to log(N choose K)

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