Characterizing convergence speed of dissipative ground state preparation algorithms*

Ground state preparation is a fundamental problem in physics, which stands challenging even for quantum computers. In the context of near-term devices, dissipative preparation methods have gained attention due to their resilience to noise. These methods imitate natural energy dissipation utilizing partial measurements and conditioned operations to gradually prepare the desired state. Although they stand out as a promising approach for NISQ devices, analyzing their performance presents a unique set of challenges.

As previous research in quantum channels has primarily focused on determining the impact of noise, it has often neglected pure state fixed points and characterizing convergence speed - crucial aspects for quantum algorithms. In this presentation, I redirect the interest focus by introducing mathematical techniques for analyzing the distance between the target and prepared states and the convergence speed. I apply them in the context of channel composition, which naturally arises in algorithms implemented as the iteration over a dissipative subroutine. In particular, I study whether introducing mixing channels can accelerate these algorithms and the behavior of an algorithm where the dissipative subroutine is slowly varied, which describes simulated annealing algorithms.