Shallow-circuit Supervised Learning on a Quantum Processor

2026-01-06

AI Summary

This work addresses the high quantum overhead of classical data loading and the poor trainability of quantum machine learning models on near-term hardware by proposing a supervised learning framework based on encoding classical data into the ground states of k-local Hamiltonians. The approach compactly maps input data to low-energy eigenstates of parameterized Hamiltonians, which are efficiently approximated using sample-based Krylov quantum diagonalization. Shallow quantum circuits are then trained via local gradient-based optimization to prepare these states. By circumventing explicit data-encoding circuits, the method substantially reduces circuit depth, alleviates the data-loading bottleneck, and enhances model trainability. Empirical validation on up to 50 qubits using IBM’s Heron processor demonstrates the framework’s effectiveness and scalability on standard benchmark datasets.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Humans and AI: Human-in-the-loop Machine Learning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• quantum machine learning
• shallow quantum circuits
• classical data loading
• trainability
• near-term quantum hardware

Innovation

• shallow-circuit quantum learning
• Hamiltonian-based representation
• Krylov quantum diagonalization
• quantum data encoding
• trainable quantum models