Optimal control for unitary preparation of many-body states: application to Luttinger liquids

TL;DR

This paper investigates optimal control strategies for preparing many-body ground states, specifically Luttinger liquids, using unitary evolution, revealing nonmonotonic protocols and a transition point for high-fidelity state preparation.

Contribution

It introduces a simulated annealing approach to find optimal time-dependent interactions for Luttinger liquids, uncovering nonmonotonic protocols and a critical ratio for near-perfect state preparation.

Findings

Optimal protocols can be obtained via simulated annealing.

The optimal interaction strength exhibits nonmonotonic time dependence.

A transition occurs when the ratio of preparation time to system size exceeds a critical value.

Abstract

Many-body ground states can be prepared via unitary evolution in cold atomic systems. Given the initial state and a fixed time for the evolution, how close can we get to a desired ground state if we can tune the Hamiltonian in time? Here we study this optimal control problem focusing on Luttinger liquids with tunable interactions. We show that the optimal protocol can be obtained by simulated annealing. We find that the optimal interaction strength of the Luttinger liquid can have a nonmonotonic time dependence. Moreover, the system exhibits a marked transition when the ratio $\tau/L$ of the preparation time to the system size exceeds a critical value. In this regime, the optimal protocols can prepare the states with almost perfect accuracy. The optimal protocols are robust against dynamical noise.