# Enhancing variational quantum state diagonalization using reinforcement learning techniques

arXiv: https://arxiv.org/abs/2306.11086 · HTML: https://mlsanity.com/paper/2306.11086/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 19 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Quantum Architecture Search via Continual Reinforcement Learning](https://mlsanity.com/paper/2112.05779/) (2021)
- [Reinforcement Learning Assisted Recursive QAOA](https://mlsanity.com/paper/2207.06294/) (2022)

## Built on by (most cited first, 11 of 11)

- [KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search](https://mlsanity.com/paper/2406.17630/) (2024)
- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning](https://mlsanity.com/paper/2407.18202/) (2024)
- [Quantum Machine Learning Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2407.20147/) (2024)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search](https://mlsanity.com/paper/2505.09371/) (2025)
- [Improving thermal state preparation of Sachdev-Ye-Kitaev model with reinforcement learning on quantum hardware](https://mlsanity.com/paper/2501.11454/) (2025)
- [BenchRL-QAS: Benchmarking reinforcement learning algorithms for quantum architecture search](https://mlsanity.com/paper/2507.12189/) (2025)
- [Self-Modulating Quantum Fast-Weight Programmers for Efficient Adaptive Sequential Learning](https://mlsanity.com/paper/2606.24933/) (2026)
- [Neural Architecture Search Algorithms for Quantum Autoencoders](https://mlsanity.com/paper/2509.15451/) (2025)
- [Generative Quantum Data Embeddings for Supervised Learning](https://mlsanity.com/paper/2605.30866/) (2026)

## Abstract (arXiv)

The variational quantum algorithms are crucial for the application of NISQ computers. Such algorithms require short quantum circuits, which are more amenable to implementation on near-term hardware, and many such methods have been developed. One of particular interest is the so-called variational quantum state diagonalization method, which constitutes an important algorithmic subroutine and can be used directly to work with data encoded in quantum states. In particular, it can be applied to discern the features of quantum states, such as entanglement properties of a system, or in quantum machine learning algorithms. In this work, we tackle the problem of designing a very shallow quantum circuit, required in the quantum state diagonalization task, by utilizing reinforcement learning (RL). We use a novel encoding method for the RL-state, a dense reward function, and an ε-greedy policy to achieve this. We demonstrate that the circuits proposed by the reinforcement learning methods are shallower than the standard variational quantum state diagonalization algorithm and thus can be used in situations where hardware capabilities limit the depth of quantum circuits. The methods we propose in the paper can be readily adapted to address a wide range of variational quantum algorithms.