Accelerating Many-Body Quantum State Preparation via Optimized Commutator Counterdiabatic Driving

Counterdiabatic (CD) driving enables rapid, high-fidelity state preparation, but in many-body systems it typically requires non-local terms that are difficult to compute and implement in practice. In this work, we introduce an optimized-commutator CD (OC-CD) protocol that preserves local CD operators while enlarging the classical optimization space used to determine their coefficients. This additional variational freedom shifts the workload from the quantum device to classical computation, reducing quantum resources and runtime. In one dimension, OC-CD prepares a family of matrix product states with system sizes up to N=1000 qubits at high fidelity, achieving speedups exceeding an order of magnitude compared to standard adiabatic ramps. We further demonstrate its applicability in two dimensions by preparing the AKLT state on a hexagonal lattice. These results indicate that CD-based acceleration can be made scalable and practical for large many-body systems when combined with efficient classical optimization.