Holography relates gravitational theories in five dimensions to
four-dimensional quantum field theories in flat space. Under this map, the
equation of state of the field theory is encoded in the black hole solutions of
the gravitational theory. Solving the five-dimensional Einstein's equations to
determine the equation of state is an algorithmic, direct problem. Determining
the gravitational theory that gives rise to a prescribed equation of state is a
much more challenging, inverse problem. We present a novel approach to solve
this problem based on physics-informed neural networks. The resulting algorithm
is not only data-driven but also informed by the physics of the Einstein's
equations. We successfully apply it to theories with crossovers, first- and
second-order phase transitions.

用物理信息的神经网络来解决将五维引力理论与四维量子场论联系起来的反问题。

方程状态中的引力对偶

Gravitational Duals from Equations of State

It has been proposed that random wide neural networks near Gaussian process
are quantum field theories around Gaussian fixed points. In this paper, we
provide a novel map with which a wide class of quantum mechanical systems can
be cast into the form of a neural network with a statistical summation over
network parameters. Our simple idea is to use the universal approximation
theorem of neural networks to generate arbitrary paths in the Feynman's path
integral. The map can be applied to interacting quantum systems / field
theories, even away from the Gaussian limit. Our findings bring machine
learning closer to the quantum world.

通过使用神经网络的通用逼近定理，本文提出了一种新的映射方法，将广义的量子力学系统转化为带有网络参数统计求和的神经网络形式，从而将机器学习与量子世界更加紧密地联系起来。

量子系统的神经网络表示

Neural network representation of quantum systems

We employ quantum circuit learning to simulate quantum field theories (QFTs).
Typically, when simulating QFTs with quantum computers, we encounter
significant challenges due to the technical limitations of quantum devices when
implementing the Hamiltonian using Pauli spin matrices. To address this
challenge, we leverage quantum circuit learning, employing a compact
configuration of qubits and low-depth quantum circuits to predict real-time
dynamics in quantum field theories. The key advantage of this approach is that
a single-qubit measurement can accurately forecast various physical parameters,
including fully-connected operators. To demonstrate the effectiveness of our
method, we use it to predict quench dynamics, chiral dynamics and jet
production in a 1+1-dimensional model of quantum electrodynamics. We find that
our predictions closely align with the results of rigorous classical
calculations, exhibiting a high degree of accuracy. This hybrid
quantum-classical approach illustrates the feasibility of efficiently
simulating large-scale QFTs on cutting-edge quantum devices.

我们利用量子电路学习来模拟量子场论，通过使用紧凑的量子比特配置和低深度的量子电路来预测量子场论中的实时动态，从而准确地预测各种物理参数，包括全连接算符。通过在一个 1+1 维的量子电动力学模型中预测淬火动力学、手性动力学和喷注产生，我们发现我们的预测与严格的经典计算结果十分吻合，显示了利用现代量子设备高效模拟大规模量子场论的可行性。

量子电路学习实现量子场论的量子 - 经典模拟

Quantum-classical simulation of quantum field theory by quantum circuit  learning

We explain how to use diffusion models to learn inverse renormalization group
flows of statistical and quantum field theories. Diffusion models are a class
of machine learning models which have been used to generate samples from
complex distributions, such as the distribution of natural images, by learning
the inverse process to a diffusion process which adds noise to the data until
the distribution of the data is pure noise. Nonperturbative renormalization
group schemes can naturally be written as diffusion processes in the space of
fields. We combine these observations in a concrete framework for building
ML-based models for studying field theories, in which the models learn the
inverse process to an explicitly-specified renormalization group scheme. We
detail how these models define a class of adaptive bridge (or parallel
tempering) samplers for lattice field theory. Because renormalization group
schemes have a physical meaning, we provide explicit prescriptions for how to
compare results derived from models associated to several different
renormalization group schemes of interest. We also explain how to use diffusion
models in a variational method to find ground states of quantum systems. We
apply some of our methods to numerically find RG flows of interacting
statistical field theories. From the perspective of machine learning, our work
provides an interpretation of multiscale diffusion models, and gives
physically-inspired suggestions for diffusion models which should have novel
properties.

使用扩散模型学习统计场论和量子场论的逆重整化群流。