Optimal parent Hamiltonians for time-dependent states

TL;DR

This paper develops a method to find optimal parent Hamiltonians for arbitrary time-dependent quantum states, considering realistic interaction constraints, with applications to spin models and connections to shortcuts to adiabaticity.

Contribution

It introduces an optimization framework for identifying the best feasible Hamiltonian for evolving given quantum states over time.

Findings

Successfully applied to time-dependent ground states of Ising and p-spin models.

Demonstrated the ability to generate target states with optimized Hamiltonians.

Connected the approach to shortcuts to adiabaticity techniques.

Abstract

Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians, we find the optimal Hamiltonian once a set of realistic elementary interactions is defined. We provide three examples of this approach. We first apply the optimization protocol to the ground states of the one-dimensional Ising model and a ferromagnetic $p$-spin model but with time-dependent coefficients. We also consider a time-dependent state that interpolates between a product state and the ground state of a $p$-spin model. We determine the time-dependent optimal parent Hamiltonian for these states and analyze the capability of this Hamiltonian of generating the state evolution. Finally, we discuss the connections of our approach to shortcuts to adiabaticity.