##### 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

performance.

” 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

synthesis.

” 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

technology.”

Sungu Erdem

Translated by Başak Arya Gençler