Less is more: subspace reduction for counterdiabatic driving of Rydberg atom arrays

TL;DR

This paper introduces a subspace-based approach to enhance counterdiabatic driving in Rydberg atom arrays, significantly reducing computational costs while maintaining high performance for solving the MIS problem.

Contribution

The work demonstrates that restricting counterdiabatic analysis to relevant subspaces accelerates computations and optimizes cost functions, making the method more practical for quantum systems.

Findings

Subspace methods accelerate counterdiabatic matrix calculations.

Subspace techniques maintain performance while reducing computational cost.

Optimized subspace-based cost functions improve efficiency.

Abstract

This study explores the use of subspace methods in combination with counterdiabatic driving in a Rydberg atom system to solve the Maximum Independent Set (MIS) problem. Although exact counterdiabatic driving offers excellent performance, it comes at an unscalable computational cost. In this work, we demonstrate that counterdiabatic driving can be significantly improved by restricting the analysis to a relevant subspace of the system. We first show that both direct diagonalization and the Krylov method for obtaining the counterdiabatic matrix can be accelerated through the use of subspace techniques, while still maintaining strong performance. We then demonstrate that the cost function used in the standard Krylov method can be further optimized by employing a subspace-based cost function. These findings open up new possibilities for applying counterdiabatic driving in a practical and efficient manner to a variety of quantum systems.