# Active Learning of Quantum System Hamiltonians yields Query Advantage

arXiv: https://arxiv.org/abs/2112.14553 · HTML: https://mlsanity.com/paper/2112.14553/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 94 references that are in the map.
- First posted on arXiv 29 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Reinforcement Learning in Large Discrete Action Spaces](https://mlsanity.com/paper/1512.07679/) (2015)
- [Learn What Not to Learn: Action Elimination with Deep Reinforcement Learning](https://mlsanity.com/paper/1809.02121/) (2018)
- [Reinforcement Learning with Parameterized Actions](https://mlsanity.com/paper/1509.01644/) (2015)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [Meta-Learning Transferable Active Learning Policies by Deep Reinforcement Learning](https://mlsanity.com/paper/1806.04798/) (2018)
- [Convergence Rates of Active Learning for Maximum Likelihood Estimation](https://mlsanity.com/paper/1506.02348/) (2015)
- [Exploring Representativeness and Informativeness for Active Learning](https://mlsanity.com/paper/1904.06685/) (2019)
- [Asymptotic Analysis of Objectives based on Fisher Information in Active Learning](https://mlsanity.com/paper/1605.08798/) (2016)
- [Extraction of instantaneous frequencies and amplitudes in nonstationary time-series data](https://mlsanity.com/paper/2104.01293/) (2021)

## Built on by (most cited first, 3 of 3)

- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Learning Neural Hamiltonian Dynamics: A Methodological Overview](https://mlsanity.com/paper/2203.00128/) (2022)
- [Active Learning with Variational Quantum Circuits for Quantum Process Tomography](https://mlsanity.com/paper/2412.20925/) (2024)

## Abstract (arXiv)

Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard techniques for Hamiltonian learning require careful design of queries and O(ε-2) queries in achieving learning error ε due to the standard quantum limit. With the goal of efficiently and accurately estimating the Hamiltonian parameters within learning error ε through minimal queries, we introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data. We formally specify and experimentally assess the performance of this Hamiltonian active learning (HAL) algorithm for learning the six parameters of a two-qubit cross-resonance Hamiltonian on four different superconducting IBM Quantum devices. Compared with standard techniques for the same problem and a specified learning error, HAL achieves up to a 99.8% reduction in queries required, and a 99.1% reduction over the comparable non-adaptive learning algorithm. Moreover, with access to prior information on a subset of Hamiltonian parameters and given the ability to select queries with linearly (or exponentially) longer system interaction times during learning, HAL can exceed the standard quantum limit and achieve Heisenberg (or super-Heisenberg) limited convergence rates during learning.