Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning quantum many-body systems from a few copies   Estimating physical properties of quantum states from measurements is one of
the most fundamental tasks in quantum science. In this work, we identify
conditions on states under which it is possible to infer the expectation values
of all quasi-local observables of a given locality up to a relative error from
a number of samples that grows polylogarithmically with the system's size and
polynomially on the locality of the target observables. This constitutes an
exponential improvement over known tomography methods in some regimes. We
achieve our results by combining one of the most well-established techniques to
learn quantum states, namely the maximum entropy method, with tools from the
emerging fields of quantum optimal transport and classical shadows. We
conjecture that our condition holds for all states exhibiting some form of
decay of correlations and establish it for several subsets thereof. These
include widely studied classes of states such as one-dimensional thermal and
high-temperature Gibbs states of local commuting Hamiltonians on arbitrary
hypergraphs or outputs of shallow circuits. Moreover, we show improvements of
the maximum entropy method beyond the sample complexity of independent
interest. These include identifying regimes in which it is possible to perform
the postprocessing efficiently as well as novel bounds on the condition number
of covariance matrices of many-body states.

7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex