Three RIKEN theoretical physicists have used neural networks to investigate
the way atoms and electrons interact with each other at finite temperatures.
This knowledge will help inform the development of future quantum
technologies for advanced computation.

Many of a material's properties, both conventional and exotic, originate
from atoms and electrons interacting with each other according to the laws
of quantum mechanics. Understanding these so-called quantum many-body
systems is critical for predicting and controlling these properties. In
addition, this knowledge will be vital for developing practically useful
devices such as quantum computers.

The large number of interactions makes modeling quantum many-body systems
challenging even for temperatures near absolute zero, but this becomes much
harder as the temperature rises. Numerical methods that can account for the
nontrivial interplay between thermal and quantum fluctuations require
prohibitively high computational costs, often becoming intractable even by
the most powerful supercomputers in the world.

"The numerical complexity of treating quantum many-body systems means that
there is a dearth of powerful methods for finite-temperature simulations,"
says Yusuke Nomura from the RIKEN Center for Emergent Matter Science. "To
overcome this difficulty, we have developed several efficient methods that
employ machine learning."

Nomura, together with RIKEN colleagues Nobuyuki Yoshioka and Franco Nori,
has now developed two mathematical techniques that use neural networks to
model thermal effects in quantum many-body systems.

A neural network is an interconnected array of nodes that is designed to
process information in a way that mimics neurons in the brain. Neural
networks have found applications in machine learning and artificial
intelligence. "The flexibility of artificial neural networks allowed us to
construct compact and accurate expressions of many-body quantum states in
thermal equilibrium," explains Nomura.

The first of the cutting-edge approaches taken by the trio was to use a
machine-learning process known as a deep Boltzmann machine to create a
mathematical description of a quantum many-body system called the Gibbs
state. Their second method employed so-called stochastic sampling to
optimize the parameters of their network.

"The ultimate goal of our approach is to reveal complex finite-temperature
phenomena that remain unexplored in a wide range of fields, including
condensed-matter physics, atomic physics, statistical mechanics and quantum
optics," says Nomura. "While we need to improve the method, we're confident
it will give us a better understanding of the thermal behavior of quantum
many-body systems, which in turn will provide a stronger foundation for
designing future quantum devices and investigating new functional
materials."

## Reference:

Yusuke Nomura et al, Purifying Deep Boltzmann Machines for Thermal Quantum
States, Physical Review Letters (2021).
DOI: 10.1103/PhysRevLett.127.060601

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