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We consider the problem of learning local quantum Hamiltonians given copies of their Gibbs state at a known inverse temperature, following Haah et al. [2108.04842] and Bakshi et al. [arXiv:2310.02243]. Our main technical contribution is a…

Quantum Physics · Physics 2024-02-09 Ales Wodecki , Jakub Marecek

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

Data Structures and Algorithms · Computer Science 2017-11-07 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart

As the size of quantum devices continues to grow, the development of scalable methods to characterise and diagnose noise is becoming an increasingly important problem. Recent methods have shown how to efficiently estimate Hamiltonians in…

Quantum Physics · Physics 2019-12-18 Tim J. Evans , Robin Harper , Steven T. Flammia

We study the problem of simulating the time evolution of a lattice Hamiltonian, where the qubits are laid out on a lattice and the Hamiltonian only includes geometrically local interactions (i.e., a qubit may only interact with qubits in…

Quantum Physics · Physics 2021-08-24 Jeongwan Haah , Matthew B. Hastings , Robin Kothari , Guang Hao Low

We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$.…

Quantum Physics · Physics 2026-05-11 Ainesh Bakshi , Allen Liu , Ankur Moitra , Ewin Tang

Learning the Hamiltonian governing a quantum system is a central task in quantum metrology, sensing, and device characterization. Existing Heisenberg-limited Hamiltonian learning protocols either require multi-qubit operations that are…

Quantum Physics · Physics 2026-01-16 Shrigyan Brahmachari , Shuchen Zhu , Iman Marvian , Yu Tong

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that…

Quantum Physics · Physics 2025-10-27 Hong-Ye Hu , Muzhou Ma , Weiyuan Gong , Qi Ye , Yu Tong , Steven T. Flammia , Susanne F. Yelin

Identifying unknown Hamiltonians from their quantum dynamics is a pivotal challenge in quantum technologies. In this paper, we introduce Hamiltonian recognition, a framework that bridges quantum hypothesis testing and quantum metrology,…

Quantum Physics · Physics 2026-02-26 Chengkai Zhu , Shuyu He , Yu-Ao Chen , Lei Zhang , Xin Wang

Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…

Machine Learning · Computer Science 2014-11-04 Siu-On Chan , Ilias Diakonikolas , Rocco A. Servedio , Xiaorui Sun

The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…

Quantum Physics · Physics 2017-01-06 Guang Hao Low , Isaac L. Chuang

The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series dataset. The…

Quantum Physics · Physics 2023-05-10 Rishabh Gupta , Raja Selvarajan , Manas Sajjan , Raphael D. Levine , Sabre Kais

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

Machine Learning · Computer Science 2023-07-18 Ilias Diakonikolas , Jelena Diakonikolas , Daniel M. Kane , Puqian Wang , Nikos Zarifis

To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In…

Quantum Physics · Physics 2013-04-29 Chao Zheng , Liang Hao , Gui Lu Long

In this work, we study the problems of certifying and learning quantum Ising Hamiltonians. Our main contributions are as follows: Certification of Ising Hamiltonians. We show that certifying an Ising Hamiltonian in normalized Frobenius norm…

Hamiltonian learning is a cornerstone for advancing accurate many-body simulations, improving quantum device performance, and enabling quantum-enhanced sensing. Existing readily deployable quantum metrology techniques primarily focus on…

Quantum Physics · Physics 2025-10-10 Suying Liu , Xiaodi Wu , Murphy Yuezhen Niu

A function $f : \mathbb{F}_2^n \to \mathbb{R}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. Motivated by applications to fast sparse Fourier transforms over $\mathbb{F}_2^n$, we study efficient algorithms for the…

Data Structures and Algorithms · Computer Science 2019-10-15 Grigory Yaroslavtsev , Samson Zhou

We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean…

Quantum Physics · Physics 2023-07-11 Haoya Li , Yu Tong , Hongkang Ni , Tuvia Gefen , Lexing Ying

The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence…

Data Structures and Algorithms · Computer Science 2015-12-15 Tsvi Kopelowitz , Ely Porat

We consider the problem of learning the Hamiltonian of a quantum system from estimates of Gibbs-state expectation values. Various methods for achieving this task were proposed recently, both from a practical and theoretical point of view.…

Quantum Physics · Physics 2024-10-31 Adam Artymowicz , Hamza Fawzi , Omar Fawzi , Samuel O. Scalet

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

Optimization and Control · Mathematics 2024-04-02 Ziming Wang , Xinghua Zhu