# Maximising Quantum-Computing Expressive Power through Randomised Circuits

arXiv: https://arxiv.org/abs/2312.01947 · HTML: https://mlsanity.com/paper/2312.01947/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 84 references that are in the map.
- First posted on arXiv 4 Dec 2023.

## Builds on (most cited first, 12 of 12)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [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)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [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)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)

## Abstract (arXiv)

In the noisy intermediate-scale quantum era, variational quantum algorithms (VQAs) have emerged as a promising avenue to obtain quantum advantage. However, the success of VQAs depends on the expressive power of parameterised quantum circuits, which is constrained by the limited gate number and the presence of barren plateaus. In this work, we propose and numerically demonstrate a novel approach for VQAs, utilizing randomised quantum circuits to generate the variational wavefunction. We parameterize the distribution function of these random circuits using artificial neural networks and optimize it to find the solution. This random-circuit approach presents a trade-off between the expressive power of the variational wavefunction and time cost, in terms of the sampling cost of quantum circuits. Given a fixed gate number, we can systematically increase the expressive power by extending the quantum-computing time. With a sufficiently large permissible time cost, the variational wavefunction can approximate any quantum state with arbitrary accuracy. Furthermore, we establish explicit relationships between expressive power, time cost, and gate number for variational quantum eigensolvers. These results highlight the promising potential of the random-circuit approach in achieving a high expressive power in quantum computing.