Adiabatic preparation of many-body quantum states: getting the beginning and ending right

TL;DR

This paper investigates how smooth scheduling functions in adiabatic processes can reduce errors in preparing many-body quantum states, with theoretical and experimental insights into error scaling.

Contribution

It introduces the use of differentiable schedule functions to suppress end-to-end transfer errors in adiabatic quantum state preparation.

Findings

Smooth schedule functions improve transfer fidelity.

Error scales as 1/T^{n+1} with schedule differentiability.

Experimental results confirm theoretical predictions.

Abstract

We present numerical calculations, and simulations performed on a Rydberg atom quantum simulator, of the adiabatic evolution of many-body quantum systems around a quantum phase transition. We demonstrate that the end-to-end transfer error, for a given process duration and dissipative losses, can be suppressed by adopting smooth initial and final scheduling functions for the Hamiltonian. We consider a one-dimensional mixed-field Ising model, as well as a chain of Rydberg atoms, and compare numerical calculations and experimental results for the end-to-end transfer error with different schedule functions. We show, in particular, that if the time dependent Hamiltonian is $n$ times differentiable with vanishing $1^{st}$ to $n^{th}$ order derivatives in the beginning and in the end, the infidelity with respect to the final adiabatic eigenstate scales as $1/T^{n+1}$ when evolving for time $T$.