# Universal Effectiveness of High-Depth Circuits in Variational Eigenproblems

arXiv: https://arxiv.org/abs/2010.00157 · HTML: https://mlsanity.com/paper/2010.00157/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2020.

## Built on by (most cited first, 10 of 10)

- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric](https://mlsanity.com/paper/2303.13462/) (2023)
- [Double descent in quantum kernel methods](https://mlsanity.com/paper/2501.10077/) (2025)
- [Variational Quantum Classifiers Through the Lens of the Hessian](https://mlsanity.com/paper/2105.10162/) (2021)
- [Quantum approximate optimization via learning-based adaptive optimization](https://mlsanity.com/paper/2303.14877/) (2023)
- [Resource-efficient equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2410.01252/) (2024)
- [Entanglement Diagnostics for Efficient Quantum Computation](https://mlsanity.com/paper/2102.12534/) (2021)
- [Variational Optimization for Quantum Problems using Deep Generative Networks](https://mlsanity.com/paper/2404.18041/) (2024)

## Abstract (arXiv)

We explore the effectiveness of variational quantum circuits in simulating the ground states of quantum many-body Hamiltonians. We show that generic high-depth circuits, performing a sequence of layer unitaries of the same form, can accurately approximate the desired states. We demonstrate their universal success by using two Hamiltonian systems with very different properties: the transverse field Ising model and the Sachdev-Ye-Kitaev model. The energy landscape of the high-depth circuits has a proper structure for the gradient-based optimization, i.e. the presence of local extrema -- near any random initial points -- reaching the ground level energy. We further test the circuit's capability of replicating random quantum states by minimizing the Euclidean distance.