# How to find expressible and trainable parameterized quantum circuits?

arXiv: https://arxiv.org/abs/2603.14451 · HTML: https://mlsanity.com/paper/2603.14451/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 95 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 29 of 29)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees](https://mlsanity.com/paper/2305.01588/) (2023)
- [On the Generalization Benefit of Noise in Stochastic Gradient Descent](https://mlsanity.com/paper/2006.15081/) (2020)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Curriculum reinforcement learning for quantum architecture search under hardware errors](https://mlsanity.com/paper/2402.03500/) (2024)
- [On barren plateaus and cost function locality in variational quantum algorithms](https://mlsanity.com/paper/2011.10530/) (2020)
- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2204.13751/) (2022)
- [Quantum Neural Architecture Search with Quantum Circuits Metric and Bayesian Optimization](https://mlsanity.com/paper/2206.14115/) (2022)
- [Automated Quantum Circuit Design with Nested Monte Carlo Tree Search](https://mlsanity.com/paper/2207.00132/) (2022)
- [Stochastic noise can be helpful for variational quantum algorithms](https://mlsanity.com/paper/2210.06723/) (2022)
- [Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Survey](https://mlsanity.com/paper/2407.17706/) (2024)
- [Efficient Quantum Convolutional Neural Networks for Image Classification: Overcoming Hardware Constraints](https://mlsanity.com/paper/2505.05957/) (2025)
- [Quantum Deep Learning: A Comprehensive Review](https://mlsanity.com/paper/2603.06644/) (2026)

## Built on by (most cited first, 2 of 2)

- [Mitigating Bias in Low-SNR Financial Reinforcement Learning via Quantum Representations](https://mlsanity.com/paper/2606.10448/) (2026)
- [Circuit Hypernetworks for Quantum-Augmented Diffusion Language Models](https://mlsanity.com/paper/2609.24657/) (2026)

## Abstract (arXiv)

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 ans"atze, 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 ans"atze with improved effective dimension using over 6 × fewer parameters, and for VQE on H2 we achieve UCCSD-like accuracy at substantially reduced circuit complexity.