Hybrid Parameterized Quantum States for Variational Quantum Learning

TL;DR

This paper introduces Hybrid Parameterized Quantum States (HPQS), a versatile framework combining quantum and classical models to improve variational quantum learning's efficiency, scalability, and noise resilience in NISQ devices.

Contribution

The paper proposes HPQS, a novel hybrid modeling approach that integrates quantum measurements with neural estimators, enhancing performance and scalability in quantum machine learning tasks.

Findings

HPQS outperforms pure PQC and NQS in classification accuracy with limited measurements.

HPQS efficiently generates classical network parameters with polylogarithmic variables.

HPQS improves perplexity in fine-tuning large language models under low-shot conditions.

Abstract

Variational quantum learning faces practical challenges in the noisy intermediate-scale quantum (NISQ) era. Parameterized quantum circuit (PQC) models suffer from statistical uncertainty due to finite-shot measurements and are highly sensitive to quantum noise, while purely classical approximations like neural quantum states (NQS) lack access to genuine quantum correlations and are limited in scalability. This work introduces Hybrid Parameterized Quantum States (HPQS), a general-purpose modeling framework that interpolates between quantum and classical parameterizations. HPQS combines PQC-based measurements with neural estimators via a blending mechanism and postprocessing functions, enabling enhanced, shot-efficient evaluation under hardware constraints. We demonstrate HPQS across three representative quantum learning tasks: (1) Expectation-based QML, where HPQS yields higher classification accuracy than PQC-only and NQS-only baselines under limited quantum measurements. (2) Quantum-Train, where HPQS generates the entire parameter set of classical networks using polylogarithmic trainable variables; and (3) Quantum Parameter Adaptation (QPA), where HPQS produces LoRA adapter parameters for fine-tuning large language models like GPT-2 and Gemma-2 with improved perplexity under low-shot conditions; Together, these results position HPQS as a scalable, noise-resilient approach for variational quantum learning, compatible with both current NISQ hardware and future fault-tolerant architectures.