How to find expressible and trainable parameterized quantum circuits?

2026-03-15

AI Summary

This work addresses the fundamental trade-off in parametrized quantum circuits (PQCs) between expressibility and trainability: highly expressive circuits are prone to barren plateaus, while trainable architectures may be classically simulable. The authors derive a finite-sample, dimension-independent concentration bound on the variance of the cost function, establishing the first rigorous theoretical guarantee for trainability and revealing an inverse relationship between trainability and expressibility. Leveraging this insight, they propose a property-driven variational circuit search framework that jointly optimizes both criteria. Experimental validation on real quantum hardware demonstrates that the discovered circuits achieve over sixfold reduction in parameter count while exhibiting higher effective dimensionality. In the VQE task for the H₂ molecule, these circuits attain accuracy comparable to UCCSD with significantly lower computational complexity.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit efficient classical simulation. We address this question by deriving a finite-sample, dimension-independent concentration bound for estimating the variance of a PQC cost function, yielding explicit trainability guarantees. Across commonly used ansätze, we observe an anticorrelation between trainability and expressibility, consistent with theoretical insights. Building on this observation, we propose a property-based ansatz-search framework for identifying circuits that combine trainability and expressibility. We demonstrate its practical viability on a real quantum computer and apply it to variational quantum algorithms. We identify quantum neural network ansätze with improved effective dimension using over $6 \times$ fewer parameters, and for VQE on $\mathrm{H}_2$ we achieve UCCSD-like accuracy at substantially reduced circuit complexity.

Problem

• parameterized quantum circuits
• expressibility
• trainability
• barren plateaus
• quantum ansätze

Innovation

• parameterized quantum circuits
• trainability
• expressibility
• ansatz search
• barren plateaus