Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer

TL;DR

This paper introduces a method to halve the qubit resources needed for quantum chemistry simulations by exploiting Hamiltonian block diagonality, enabling simulations of complex molecules with fewer qubits.

Contribution

It presents a classical pre-computational scheme that reduces qubit requirements by leveraging Hamiltonian structure, improving quantum resource efficiency.

Findings

Reduced qubit count for Fermi-Hubbard model

Reduced qubit count for hydrogen molecule

Enables two-qubit quantum simulations

Abstract

Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the fermionic problem in a bosonic system of qubits. By exploiting the block diagonality of a fermionic Hamiltonian, we show that the number of required qubits can be reduced by a factor of two or more. There is no need to go into the basis of the Hilbert space for this reduction because all operations can be performed in the operator space. The scheme is conceived as a pre-computational step that would be performed on a classical computer prior to the actual quantum simulation. We apply this scheme to reduce the number of qubits necessary to simulate both the Hamiltonian of the two-site Fermi-Hubbard model and the hydrogen molecule. Both quantum systems can then be simulated with a two-qubit quantum computer.