Weighted Nested Commutators for Scalable Counterdiabatic State Preparation

• URL: http://arxiv.org/abs/2603.25625v1
• Date: Thu, 26 Mar 2026 16:40:11 GMT
• Title: Weighted Nested Commutators for Scalable Counterdiabatic State Preparation
• Abstract summary: We introduce a nested-commutator ansatz to approximate nonlocal adiabatic gauge potentials.<n>We 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.
• Score: 9.314730705585026
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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