Generalizing commuting operators for ADAPT-VQE
By Olivia
EXTERNAL MENTOR: Dr. Bharath Sambasivam, Virginia Tech
Introduction
The proposed research aims to improve the traditional approach of Variational Quantum Eigensolver (VQE) for finding the ground state of many-body systems. Used in quantum chemistry and molecule simulations, VQE is a hybrid quantum-classical algorithm that works by taking energy as the cost function. VQE relies on an ansatz, or parametrized guess wave function, which has led to much research regarding the goal of creating a compact ansatz that provides high accuracy with few parameters and shallow circuits.
Intellectual Merit
One major advance, ADAPT-VQE, introduced adaptivity into ansatz construction by iteratively selecting operators from a predefined pool based on gradient magnitudes, leading to more compact and circuits. Building on this, TETRIS-ADAPT-VQE relaxes the sequential one-operator rule by adding multiple operators to act on different qubits simultaneously, significantly reducing circuit depth. TETRIS-ADAPT-VQE highlights the role of operator selection. The use of commuting operators is something we plan to look into to extend this line of improvement. By partitioning Hamiltonian terms and excitation operators into commuting sets, we can potentially enhance parallelism in operator insertion and reduce circuit depth.
Broader Impact
Incorporating commuting operators into adaptive VQE frameworks such as TETRIS-ADAPT-VQE has the potential to substantially improve the scalability of quantum simulations on noisy intermediate-scale quantum (NISQ) devices. These advances directly target the primary bottlenecks of circuit depth and measurement cost. If successful, this research could pave the way for near-term quantum advantage in simulating materials, thereby expanding the reach of quantum computing in science and engineering.