16,501 research outputs found
Learning many-body Hamiltonians with Heisenberg-limited scaling
Learning a many-body Hamiltonian from its dynamics is a fundamental problem
in physics. In this work, we propose the first algorithm to achieve the
Heisenberg limit for learning an interacting -qubit local Hamiltonian. After
a total evolution time of , the proposed algorithm
can efficiently estimate any parameter in the -qubit Hamiltonian to
-error with high probability. The proposed algorithm is robust
against state preparation and measurement error, does not require eigenstates
or thermal states, and only uses experiments.
In contrast, the best previous algorithms, such as recent works using
gradient-based optimization or polynomial interpolation, require a total
evolution time of and
experiments. Our algorithm uses ideas from quantum simulation to decouple the
unknown -qubit Hamiltonian into noninteracting patches, and learns
using a quantum-enhanced divide-and-conquer approach. We prove a matching lower
bound to establish the asymptotic optimality of our algorithm.Comment: 11 pages, 1 figure + 27-page appendi
On Training Traffic Predictors via Broad Learning Structures:A Benchmark Study
A fast architecture for real-time (i.e., minute-based) training of a traffic predictor is studied, based on the so-called broad learning system (BLS) paradigm. The study uses various traffic datasets by the California Department of Transportation, and employs a variety of standard algorithms (LASSO regression, shallow and deep neural networks, stacked autoencoders, convolutional, and recurrent neural networks) for comparison purposes: all algorithms are implemented in MATLAB on the same computing platform. The study demonstrates a BLS training process two-three orders of magnitude faster (tens of seconds against tens-hundreds of thousands of seconds), allowing unprecedented real-time capabilities. Additional comparisons with the extreme learning machine architecture, a learning algorithm sharing some features with BLS, confirm the fast training of least-square training as compared to gradient training
- …