Reducing Qubit Requirements for Quantum Simulations Using Molecular Point Group Symmetries

Simulating molecules is believed to be one of the early stage applications for quantum computers. Current state-of-the-art quantum computers are limited in size and coherence; therefore, optimizing resources to execute quantum algorithms is crucial. In this work, we develop the second quantization representation of spatial symmetries, which are then transformed to their qubit operator representation. These qubit operator representations are used to reduce the number of qubits required for simulating molecules. We present our results for various molecules and elucidate a formal connection of this work with a previous technique that analyzed generic Z2 Pauli symmetries.