Adaptive Variational Quantum Dynamics Simulations with the TETRIS method*

Adaptive variational quantum dynamics simulation (AVQDS) [1] has been developed as a near-term quantum algorithm to accurately simulate dynamical quantum systems using automatically generated unitaries that are more compressed than Trotterized circuits. Here we report an improved version of AVQDS by porting the Tiling Efficient Trial circuits with Rotations Implemented Simultaneously (TETRIS) technique [2], which adaptively adds layers of disjoint unitary gates to the ansatz to keep the McLachlan distance below a threshold. We apply TETRIS AVQDS to simulate the quench dynamics of local spin lattice models and demonstrate that it significantly reduces the quantum circuit depth and the number of 2-qubit operators. We also study the dynamical response of a BH molecule in an oscillating electric field and evaluate the first and second order polarizability, showing that TETRIS AVQDS can be applied to problems with a time-dependent Hamiltonians.

[1] Y.-X. Yao, N. Gomes, F. Zhang, T. Iadecola, C.-Z. Wang, K.-M. Ho, and P. P. Orth, Adaptive variational quantum dynamics simulations, Phys. Rev. X Quantum 2, 030307 (2021).

[2] P. G. Anastasiou, Y. Chen, N. J. Mayhall, E. Barnes, and S. E. Economou, Tetris-adapt-vqe: An adaptive algorithm that yields shallower, denser circuit ansätze, arXiv:2209.10562 (2022).