## RQC Seminar

### 9th RQC Seminar

#### 講演者

桑原 知剛 理研白眉TL（量子複雑性解析理研白眉研究チーム）

#### 日程

2022年6月8日（水）16:00-17:00（JST）

#### 開催場所

ハイブリッド（Zoom ・ 理研 和光事業所 本部棟２階大会議室）

#### 講演タイトル

ハミルトニアン学習のサンプル複雑性

#### お問合せ

rqc_colloquium_inquiry[at]ml.riken.jp

**講演概要**

The properties of a system of interacting quantum particles (quantum many-body
system) are completely determined by the Hamiltonian of the system. With the
recent development of experimental techniques, observation of the microscopic
structure of quantum systems becomes possible. With this background, the
Hamiltonian learning, i.e., estimating the Hamiltonian from observational data, has
attracted considerable attention from theoretical and experimental fields in
materials science, quantum machine learning, and quantum information theory. On
the other hand, most of the currently proposed algorithms for Hamiltonian learning
have been heuristic, and guaranteeing accuracy is usually a challenging problem. In
the present study, we analyzed sample complexity, i.e., "the number of data
sufficient to learn a Hamiltonian up to desired precision." Specifically, we consider a
quantum Gibbs distribution with inverse temperature β. The question is how
accurately one can estimate the Hamiltonian from the data obtained by measuring
the quantum state N times. In classical cases, recent studies have solved this
problem qualitatively. However, in quantum cases, the sample complexity has not
been solved in spite that there have been various studies on the estimation of the
Gibbs state itself. Here, we have solved the sample complexity problem of
Hamiltonian learning. We clarified the sufficient and necessary conditions regarding
the number of samples to achieve the estimation with the accuracy ε, where the
Poly(n) (n: system size) sample complexity is qualitatively optimal. I will provide a
more detailed research background and explain the key property (strong convexity)
in deriving the sample complexity.
[ References ]
[1] A. Anshu S. Arunachalam T. Kuwahara and M. Soleimanifar Nature Physics 17 931-935 (2021)
[2] V. Dunjko Nature Physics 17 880-881 (2021)

Flyer: 9th RQC Seminar Flyer