Lowering <u>qubit</u> requirements for quantum simulations of <u>fermionic</u> systems

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers.
One challenge in realizing simulations on near-term quantum devices is the large number of qubits required by such mappings.
In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a non-linear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates.
We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with only a very modest increase in gate difficulty.