Weighted Nested Commutators for Scalable Counterdiabatic State Preparation

TL;DR

This paper introduces a weighted nested-commutator ansatz to efficiently approximate adiabatic gauge potentials for counterdiabatic driving, enabling scalable quantum state preparation in large many-body systems.

Contribution

The authors propose the WNC ansatz that generalizes nested commutators with variational weights, improving approximation of gauge potentials for large systems.

Findings

WNC ansatz outperforms standard nested-commutator approach in state preparation.

Efficient local optimization scheme for WNC ansatz.

Demonstrated acceleration in preparing 1D MPS and 2D AKLT states for large system sizes.

Abstract

Counterdiabatic (CD) driving enables efficient quantum state preparation, but it requires implementing highly nonlocal adiabatic gauge potentials (AGP) that are impractical to compute and realize in large many-body systems. We introduce a \textit{weighted nested-commutator} (WNC) ansatz to approximate AGP using local operators. The WNC ansatz generalizes the standard nested-commutator ansatz by assigning independent variational weights to commutators of local Hamiltonian terms, thereby enlarging the variational space while preserving a fixed operator range. We show that the WNC ansatz can be efficiently optimized using a local optimization scheme. Moreover, it systematically outperforms the nested-commutator ansatz in preparing one-dimensional matrix product states (MPS) and the ground state of a nonintegrable quantum Ising model. We then numerically demonstrate that CD driving based on the WNC ansatz significantly accelerates the preparation of 1D MPS for system sizes up to $N = 1000$ qubits, as well as the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a hexagonal lattice with up to $N = 3 \times 10$ sites.