Efficiently architecting VQAs: Expressibility--Trainability--Resources Pareto-Optimality

TL;DR

This paper systematically explores the design space of parametrized quantum circuits for variational quantum algorithms, balancing expressibility, trainability, and resource costs to identify Pareto-optimal solutions.

Contribution

It introduces a multi-metric, multi-objective framework for ansatz selection, providing quantitative insights into the expressibility-trainability-resource trade-offs.

Findings

Identifies Pareto-optimal PQCs balancing expressibility and trainability.

Provides a systematic approach for ansatz design space exploration.

Clarifies the interplay between expressibility and barren plateaus.

Abstract

Ansatz selection is a key factor in the performance of variational quantum algorithms (VQAs). While much of the state-of-the-art still relies on heuristic choices, an inadequate circuit structure can compromise both the expressive power and the trainability of the resulting model. Recent results have also established theoretical connections between expressibility and the onset of barren plateaus, highlighting the need for systematic criteria for ansatz selection. In this work, the ansatz is treated as a design feature to be optimized rather than a fixed block, and a design space exploration (DSE) is performed over a diverse set of parametrized quantum circuits (PQCs). Three complementary metrics -- expressibility, trainability, and resource cost -- are evaluated and used to analyze the trade-offs that emerge across different PQCs. Beyond identifying Pareto-optimal candidates, this multi-objective perspective helps clarify the interplay between these metrics and contributes quantitative evidence toward understanding the expressibility--trainability tension in variational circuits.