In this thesis, we explore a number of topics aimed at bringing quantum simulation closer to realization. We present two encodings, Bravyi-Kitaev superfast encoding (BKSF) and the generalized superfast encoding (GSE). These encodings map a target Fermionic Hamiltonian with two-body interactions on a graph of degree d to a qubit simulator Hamiltonian composed of Pauli operators of weight O(d). A system of M Fermionic modes gets mapped to n = O(M d) qubits.
We show that both these encodings have inherent quantum error correction properties. We prove that BKSF encoding in general cannot correct all single qubit errors. In certain systems, auxiliary Fermionic modes could be introduced to guarantee single qubit error correction. In contrast, if the degree of the interaction graph is greater or equal to six, the GSE guarantees single qubit error correction without any auxiliary Fermionic modes. Further, we describe a GSE that reduces the Pauli weight of the simulator Hamiltonian from O(d) to O(log d).
In chapter 8 of this thesis, we present different techniques to use the point group symmetries in the molecules to reduce the number of qubits required for quantum simulation. Error robustness and the simplified structure of the simulator Hamiltonian offered by GSEs can make the simulation of Fermionic systems within the reach of near-term quantum devices.