The role of symmetries in the ADAPT variational quantum eigensolver

Variational quantum eigensolvers (VQEs) are a class of hybrid classical-quantum computing methods which prepare and measure a parameterized state on quantum hardware and optimize the wavefunction parameters on classical hardware. While many VQEs begin with a predetermined wavefunction ansatz, ADAPT-VQE builds a problem-tailored ansatz starting from a reference state and adaptively adding operators to the ansatz from a pool of operators. This flexibility to choose shorter circuits is preferable in the current noisy intermediate-scale quantum regime of quantum computing for simulating molecular systems as it can lead to shorter circuits to initialize a state on the quantum device. In this work we investigate the role of different symmetries when constructing a reference and operator pool play in the convergence behavior of ADAPT-VQE.