How to find expressible and trainable parameterized quantum circuits?
This addresses a critical bottleneck in variational quantum algorithms for quantum computing researchers, offering a systematic approach to balance trainability and expressibility, though it is incremental in building on existing theoretical insights.
The paper tackles the challenge of constructing parameterized quantum circuits (PQCs) that are both trainable and expressive, by deriving a concentration bound for cost function variance and proposing an ansatz-search framework. They demonstrate practical viability on a quantum computer, achieving UCCSD-like accuracy for VQE on H2 with reduced circuit complexity and identifying quantum neural network ansätze with improved effective dimension using over 6× fewer parameters.
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.