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

Frontiers in Physics

Yoshimura, Bryce¹  Freericks, J. K.¹ 

[1] Department of Physics, Georgetown University, Washington, DC, USA

关键词: quantum simulation;    ion trap;    adiabatic state preparation;    Transverse field Ising model;    ground state probability;   

DOI  :  10.3389/fphy.2015.00085

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

.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 simple 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.

【 授权许可】

CC BY