Randomness and symmetries in ADAPT
By Anish, Ibrahim, Clinton
External Mentor: Karunya Shirali, Virginia Tech Center for Quantum Information Science and Engineering
The proposed research aims to explore the role symmetry plays in the convergence of the ADAPT-VQE algorithm, a variational quantum eigensolver which iteratively constructs an ansatz (a parameterized quantum circuit designed to approximate the ground state) by drawing from operators present in a predefined pool. The predefined operator pool is the collection of operator definitions that will be used to construct the ansatz. Building on the principal that symmetries can often be essential to solving computational physics problems, such as the rotational symmetry present within a rotating top in classical physics or conserving particle numbers in quantum states, we will analyze the creation of symmetries in the adaptive construction of the ansatz and whether the point at which these symmetries are fully established coincides with the algorithm's convergence to the ground state. In particular, we will explore the surprising observation that operator pools leading to unphysical spaces (parts of the Hilbert curve that violate conserved quantities in the system, such as particle number or total spin) can, nevertheless, lead to correct final states. By extending this analysis to randomized variants of ADAPT-VQE, which alter ansatz growth and coefficient optimization strategies, we hypothesize that the rate at which symmetries accumulate may be conducive to convergence. Finally, we will try to assess the quantum resources required, such as two-qubit gates, to quantify the practical impact of symmetry enforcement on near-term quantum hardware.