Method Of Predicting Properties Of Complex Quantum Systems

Predicting the properties of complex quantum systems is a crucial
step in the development of advanced quantum technologies. Although
research teams around the world have developed a number of
techniques for studying the properties of quantum systems, many of
these have proven to be effective only in some cases.

Three researchers at the California Institute of Technology recently
introduced a new method that can be used to predict the multiple
properties of complex quantum systems from a limited number of
measurements.Their methods, outlined in a paper published in the
journal Nature Physics, have been found to be highly effective and
could open up new opportunities to study how machines process
quantum information.

The first step towards the development of more advanced machines
based on quantum-mechanical processes is to better understand how
existing technologies process and manipulate quantum systems and
quantum information. The standard method for doing this, known as
quantum state tomography, works by learning the entire definition of
a quantum system. However, this requires an exponential number of
measurements, as well as a significant amount of computational
memory and time.

As a result, while using quantum state tomography, machines are
currently unable to support quantum systems with dozens of qubits.
In recent years, researchers have proposed a series of techniques
based on artificial neural networks that could significantly improve
machines ‘ quantum information processing. Unfortunately, however,
these techniques are not well generalized in all cases, and the specific
requirements that allow them to work are still unclear.

” To create a rigorous basis for how machines can perceive quantum
systems, we combined my previous knowledge of statistical learning
theory with the expertise of Richard Kueng and John Preskill on a
beautiful mathematical theory known as unitary t-design, ” Huang
said. “Statistical learning theory is the theory that underlies how the
machine can learn an approximate model of how the world behaves,
while the unitary t-design is a mathematical theory based on how
quantum information is mixed.”

By combining statistical learning and unitary t-design theory, the
researchers were able to develop a rigorous and effective procedure
that enabled classical machines to produce approximate classical
definitions of quantum multibody systems. These explanations can be
used to predict the various properties of quantum systems studied by
performing a minimum number of quantum measurements.

” To create an approximate classical definition of the quantum state,
we apply a randomized measurement procedure given as follows, ”
Huang said. “We are sampling several random quantum evolutions to
be applied to the unknown quantum multi-body system. These random
quantum evolutions are typically chaotic and confuse quantum
information stored in the quantum system.”

The random quantum evolutions sampled by the researchers
ultimately enable the use of the mathematical theory of unitary tdesign
to study chaotic quantum systems such as quantum black
holes. In addition, Huang and his colleagues studied a series of
randomly mangled quantum systems using a measurement tool that
revealed a wave function collapse, a process that transforms a
quantum system into a classical one. Finally, they combined random
quantum evolutions with classical system representations derived
from their measurements, producing an approximate classical
description of the quantum system of interest.

” Intuitively, we can think of this procedure as follows, ” Huang said.
“We have an exponentially high-dimensional object, a quantum
multibody system, that is very difficult to grasp by a classical machine.
We perform several random projections of this extremely highdimensional
object into a much lower-dimensional space using
random/chaotic quantum evolution. The set of random projections
provides a rough picture of how this exponentially high-dimensional
object looks, and the classical representation allows us to predict the
various properties of the quantum multibody system.”

By combining statistical learning structures and quantum information
mixing theory, Huang and his colleagues proved that they could
accurately predict the M Properties of a quantum system based only
on logarithmic(m) measurements. In other words, his methods can
predict an exponential number of properties by repeatedly measuring
certain aspects of a quantum system for a given number.

” The traditional understanding is that when we want to Measure M
Properties, we need to measure the quantum system m Times, ” Huang
said. “This is because, after measuring a property of the quantum
system, the quantum system will collapse and become classical. Once
the quantum system becomes classical, we cannot measure other
properties with the resulting classical system. Our approach avoids this
by making randomly generated measurements and combining these
measurement data to reveal the desired property.”

The study partly describes the excellent performance achieved by
newly developed machine learning (ML) techniques in predicting
properties of quantum systems. In addition, their unique design
makes the method they developed significantly faster than existing
ML techniques, while at the same time allowing them to predict the
properties of quantum multibody systems with greater accuracy.
” Our study shows that much more information is hidden in the data
from quantum measurements than we initially expected, ” Huang said.
“By appropriately combining this data, we can extract this secret
information and learn significantly more about the quantum system.
This implies the importance of data science techniques for the
development of quantum technology.”

The results of tests conducted by the team show that to harness the
power of machine learning, it is necessary to first understand well the
intrinsic mechanisms of quantum physics. Huang and colleagues, lead
to satisfactory results although the direct implementation of standard
machine learning techniques, machine learning, organically
integrating the mathematics behind Quantum Information Processing
and quantum physics, respectively, showed that much better

” Given the rigorous backdrop for perceiving quantum systems with
classical machines, my personal plan now is to take the next step
towards creating a learning machine that can manipulate and use
quantum-mechanical processes, ” Huang said. “In particular, we want
to provide a solid understanding of how machines can solve quantum
multibody problems, such as classifying quantum phases of matter or
finding quantum multibody ground States.”

This new method for creating classical representations of quantum
systems could open up new possibilities for the use of machine
learning to solve challenging problems involving quantum multibody
systems. However, to address these problems more efficiently,
machines need to be able to simulate a series of complex calculations
that require greater synthesis between the mathematics underlying
machine learning and quantum physics. In their next study, Huang and
his colleagues plan to explore new techniques that could provide this

” We are also working to develop and develop new tools to extract
confidential information from data collected by quantum
experimenters, ” Huang said. “The physical limitation in actual systems
presents interesting challenges for developing more advanced
techniques. This will allow experimenters to see things they initially
couldn’t, helping them advance the current state of quantum

Sungu Erdem

Translated by Başak Arya Gençler



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