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

Reducing the qubit requirement of Jordan-Wigner encodings of $N$-mode, $K$-fermion systems from $N$ to $\lceil \log_2 {N \choose K} \rceil$