Determining the ground-state probability of a quantum simulation with product-state measurements

TL;DR

This paper presents methods to estimate the probability of a quantum system being in its ground state after diabatic evolution using only product-state measurements, without prior knowledge of the Hamiltonian.

Contribution

It introduces techniques to determine ground-state probabilities from product-state measurements during quantum simulations, bypassing the need for Hamiltonian eigenstate information.

Findings

Methods successfully estimate ground-state probability from measurements.

Techniques applicable to various quantum platforms like trapped ions.

No prior Hamiltonian knowledge required for estimation.

Abstract

One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the evolution is adiabatic and the initial and final ground states are connected due to having the same symmetry, then the simulation will be successful. But in most experiments, adiabatic simulation is not possible because it would take too long, and the system has some level of diabatic excitation. In this work, we quantify the extent of the diabatic excitation even if we do not know {\it a priori} what the complicated ground state is. Since many quantum simulator platforms, like trapped ions, can measure the probabilities to be in a product state, we describe techniques that can employ these measurements to estimate the probability of being in the ground state of the system after the diabatic evolution. These techniques do not require one to know any properties about the Hamiltonian itself, nor to calculate its eigenstate properties. All the information is derived by analyzing the product-state measurements as functions of time.