# Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation

arXiv: https://arxiv.org/abs/2003.02183 · HTML: https://mlsanity.com/paper/2003.02183/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 7 of 7)

- [Deep reinforcement learning for quantum multiparameter estimation](https://mlsanity.com/paper/2209.00671/) (2022)
- [Social learning spontaneously emerges by searching optimal heuristics with deep reinforcement learning](https://mlsanity.com/paper/2204.12371/) (2022)
- [A Two-stage Optimization Method for Wide-range Single-electron Quantum Magnetic Sensing](https://mlsanity.com/paper/2506.13469/) (2025)
- [Quantum Bayesian Networks Can Speed up Reinforcement Learning in Partially Observable Environments](https://mlsanity.com/paper/2507.18606/) (2025)
- [Machine learning enabled experimental design and parameter estimation for ultrafast spin dynamics](https://mlsanity.com/paper/2306.02015/) (2023)
- [SymQNet: Amortized Acquisition for Low-Latency Adaptive Hamiltonian Learning](https://mlsanity.com/paper/2606.12808/) (2026)
- [Rethinking Quantum Continual Learning with Quantum Fisher Information](https://mlsanity.com/paper/2607.16030/) (2026)

## Abstract (arXiv)

Quantum metrology promises unprecedented measurement precision but suffers in practice from the limited availability of resources such as the number of probes, their coherence time, or non-classical quantum states. The adaptive Bayesian approach to parameter estimation allows for an efficient use of resources thanks to adaptive experiment design. For its practical success fast numerical solutions for the Bayesian update and the adaptive experiment design are crucial. Here we show that neural networks can be trained to become fast and strong experiment-design heuristics using a combination of an evolutionary strategy and reinforcement learning. Neural-network heuristics are shown to outperform established heuristics for the technologically important example of frequency estimation of a qubit that suffers from dephasing. Our method of creating neural-network heuristics is very general and complements the well-studied sequential Monte-Carlo method for Bayesian updates to form a complete framework for adaptive Bayesian quantum estimation.