Shallow-circuit Supervised Learning on a Quantum Processor

TL;DR

This paper introduces a quantum machine learning approach using Hamiltonian ground states and Krylov diagonalization, enabling efficient data representation and training on near-term quantum hardware with up to 50 qubits.

Contribution

It presents a novel Hamiltonian-based quantum learning method that overcomes data loading and trainability issues in quantum machine learning.

Findings

Successful implementation on IBM quantum hardware with 50 qubits

Efficient low-energy state computation via Krylov diagonalization

Effective classical data representation through quantum ground states

Abstract

Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor trainability of many quantum machine learning algorithms designed for near-term quantum hardware. In this work, we show that one can overcome these obstacles by using a linear Hamiltonian-based machine learning method which provides a compact quantum representation of classical data via ground state problems for k-local Hamiltonians. We use the recent sample-based Krylov quantum diagonalization method to compute low-energy states of the data Hamiltonians, whose parameters are trained to express classical datasets through local gradients. We demonstrate the efficacy and scalability of the methods by performing experiments on benchmark datasets using up to 50 qubits of an IBM Heron quantum processor.