Utilizing small quantum computers for machine learning and ground state energy approximation

Abstract

Quantum circuit partitioning (QCP) is a hybrid quantum-classical approach that aims to simulate large quantum systems on smaller quantum computers. A quantum computation is divided into smaller subsystems and results of measurements on these subsystems are combined using classical processing. In this paper, we propose a QCP strategy to measure an observable on a large quantum system by utilizing several quantum systems of smaller size. The method can be applied to both machine learning and variational ground state energy approximation, and we show that the required calculations and the variance of the gradients can be tailored to scale efficiently with the total number of qubits. Thus it can be utilized to mitigate the well-known problem of barren plateaus. Additionally, the method can be realized by performing simple measurements of Pauli-strings on the separate subsystems, and the gradients can be estimated with common methods such as the parameter-shift rule. We demonstrate the method by approximating the ground state energy of the 1D transverse-field Ising model with periodic boundary conditions, and by classifying handwritten digits. For the ground state energy approximation, we achieved a relative error within the order of 0.1\% for all the tested system sizes. When applied to the classification between the digits 3 and 6, we were able to generalize to out-of-sample data with 100\% accuracy.