# A semi-agnostic ansatz with variable structure for quantum machine learning

arXiv: https://arxiv.org/abs/2103.06712 · HTML: https://mlsanity.com/paper/2103.06712/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 106 references that are in the map.
- First posted on arXiv 11 Mar 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [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)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [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)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus](https://mlsanity.com/paper/2102.01828/) (2021)
- [Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm](https://mlsanity.com/paper/1910.02071/) (2019)
- [A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver](https://mlsanity.com/paper/1910.09694/) (2019)
- [Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers](https://mlsanity.com/paper/2102.05566/) (2021)
- [Quantum Circuit Design Search](https://mlsanity.com/paper/2012.04046/) (2020)
- [Non-trivial symmetries in quantum landscapes and their resilience to quantum noise](https://mlsanity.com/paper/2011.08763/) (2020)
- [Long-time simulations with high fidelity on quantum hardware](https://mlsanity.com/paper/2102.04313/) (2021)

## Built on by (most cited first, 15 of 15)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Reinforcement Learning for Variational Quantum Circuits Design](https://mlsanity.com/paper/2409.05475/) (2024)
- [TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search](https://mlsanity.com/paper/2505.09371/) (2025)
- [Coreset selection can accelerate quantum machine learning models with provable generalization](https://mlsanity.com/paper/2309.10441/) (2023)
- [Provably efficient variational generative modeling of quantum many-body systems via quantum-probabilistic information geometry](https://mlsanity.com/paper/2206.04663/) (2022)
- [The role of data embedding in quantum autoencoders for improved anomaly detection](https://mlsanity.com/paper/2409.04519/) (2024)
- [Expressivity of deterministic quantum computation with one qubit](https://mlsanity.com/paper/2411.02751/) (2024)
- [Sub-universal variational circuits for combinatorial optimization problems](https://mlsanity.com/paper/2308.14981/) (2023)
- [Multi-channel convolutional neural quantum embedding](https://mlsanity.com/paper/2509.22355/) (2025)
- [Quantum Circuit Pre-Synthesis: Learning Local Edits to Reduce T-count](https://mlsanity.com/paper/2601.19738/) (2026)
- [Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketches](https://mlsanity.com/paper/2407.06416/) (2024)
- [Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networks](https://mlsanity.com/paper/2410.09470/) (2024)
- [Toward Joint Optimization of Circuit Depth and Training Data Size in Adaptively Grown Quantum Classifiers](https://mlsanity.com/paper/2610.12428/) (2026)

## Abstract (arXiv)

Quantum machine learning -- and specifically Variational Quantum Algorithms (VQAs) -- offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data science, and mathematics. Here, one trains an ansatz, in the form of a parameterized quantum circuit, to accomplish a task of interest. However, challenges have recently emerged suggesting that deep ansatzes are difficult to train, due to flat training landscapes caused by randomness or by hardware noise. This motivates our work, where we present a variable structure approach to build ansatzes for VQAs. Our approach, called VAns (Variable Ansatz), applies a set of rules to both grow and (crucially) remove quantum gates in an informed manner during the optimization. Consequently, VAns is ideally suited to mitigate trainability and noise-related issues by keeping the ansatz shallow. We employ VAns in the variational quantum eigensolver for condensed matter and quantum chemistry applications, in the quantum autoencoder for data compression and in unitary compilation problems showing successful results in all cases.