How to find expressible and trainable parameterized quantum circuits?

arXiv (Cornell University)

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.

Authors 3

1. Peter Röseler

   Forschungszentrum Jülich · University of Cologne · Jülich Supercomputing Centre

   Affiliation as printed

   Jülich Supercomputing Centre , Forschungszentrum Jülich , 52425 Jülich , Germany

   Universität zu Köln , 50923 Köln , Germany

2. Dennis Willsch Aachen Faculty of Medical Engineering and Technomathematics

   FH Aachen · Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Faculty of Medical Engineering and Technomathematics , University of Applied Sciences Aachen , 52428 Jülich , Germany

   Jülich Supercomputing Centre , Forschungszentrum Jülich , 52425 Jülich , Germany

3. Kristel F. L. Michielsen