Breakthrough proof clears path for quantum AI
Novel theorem demonstrates convolutional neural networks can always be
trained on quantum computers, overcoming threat of `barren plateaus' in optimization problems

Date:
October 18, 2021
Source:
DOE/Los Alamos National Laboratory
Summary:
Convolutional neural networks running on quantum computers have
generated significant buzz for their potential to analyze quantum
data better than classical computers can.



FULL STORY ========================================================================== Convolutional neural networks running on quantum computers have generated significant buzz for their potential to analyze quantum data better than classical computers can. While a fundamental solvability problem known as "barren plateaus" has limited the application of these neural networks
for large data sets, new research overcomes that Achilles heel with a
rigorous proof that guarantees scalability.


==========================================================================
"The way you construct a quantum neural network can lead to a barren
plateau - - or not," said Marco Cerezo, coauthor of the paper titled
"Absence of Barren Plateaus in Quantum Convolutional Neural Networks," published today by a Los Alamos National Laboratory team in Physical
Review X. Cerezo is a physicist specializing in quantum computing,
quantum machine learning, and quantum information at Los Alamos. "We
proved the absence of barren plateaus for a special type of quantum
neural network. Our work provides trainability guarantees for this architecture, meaning that one can generically train its parameters."
As an artificial intelligence (AI) methodology, quantum convolutional
neural networks are inspired by the visual cortex. As such, they involve
a series of convolutional layers, or filters, interleaved with pooling
layers that reduce the dimension of the data while keeping important
features of a data set.

These neural networks can be used to solve a range of problems, from
image recognition to materials discovery. Overcoming barren plateaus
is key to extracting the full potential of quantum computers in AI
applications and demonstrating their superiority over classical computers.

Until now, Cerezo said, researchers in quantum machine learning analyzed
how to mitigate the effects of barren plateaus, but they lacked a
theoretical basis for avoiding it altogether. The Los Alamos work shows
how some quantum neural networks are, in fact, immune to barren plateaus.

"With this guarantee in hand, researchers will now be able to sift through quantum-computer data about quantum systems and use that information for studying material properties or discovering new materials, among other applications," said Patrick Coles, a quantum physicist at Los Alamos
and a coauthor of the paper.



==========================================================================
Many more applications for quantum AI algorithms will emerge, Coles
thinks, as researchers use near-term quantum computers more frequently
and generate more and more data -- all machine learning programs are data-hungry.

Avoiding the Vanishing Gradient "All hope of quantum speedup or advantage
is lost if you have a barren plateau," Cerezo said.

The crux of the problem is a "vanishing gradient" in the optimization landscape. The landscape is composed of hills and valleys, and the goal
is to train the model's parameters to find the solution by exploring the geography of the landscape. The solution usually lies at the bottom of the lowest valley, so to speak. But in a flat landscape one cannot train the parameters because it's difficult to determine which direction to take.

That problem becomes particularly relevant when the number of data
features increases. In fact, the landscape becomes exponentially flat
with the feature size. Hence, in the presence of a barren plateau,
the quantum neural network cannot be scaled up.



==========================================================================
The Los Alamos team developed a novel graphical approach for analyzing
the scaling within a quantum neural network and proving its trainability.

For more than 40 years, physicists have thought quantum computers
would prove useful in simulating and understanding quantum systems of particles, which choke conventional classical computers. The type of
quantum convolutional neural network that the Los Alamos research has
proved robust is expected to have useful applications in analyzing data
from quantum simulations.

"The field of quantum machine learning is still young," Coles
said. "There's a famous quote about lasers, when they were first
discovered, that said they were a solution in search of a problem. Now
lasers are used everywhere. Similarly, a number of us suspect that
quantum data will become highly available, and then quantum machine
learning will take off." For instance, research is focusing on ceramic materials as high-temperature superconductors, Coles said, which
could improve frictionless transportation, such as magnetic levitation
trains. But analyzing data about the material's large number of phases,
which are influenced by temperature, pressure, and impurities in these materials, and classifying the phases is a huge task that goes beyond
the capabilities of classical computers.

Using a scalable quantum neural network, a quantum computer could sift
through a vast data set about the various states of a given material
and correlate those states with phases to identify the optimal state
for high-temperature superconducting.

========================================================================== Story Source: Materials provided by
DOE/Los_Alamos_National_Laboratory. Note: Content may be edited for
style and length.


========================================================================== Journal Reference:
1. Arthur Pesah, M. Cerezo, Samson Wang, Tyler Volkoff, Andrew T.

Sornborger, Patrick J. Coles. Absence of Barren Plateaus in Quantum
Convolutional Neural Networks. Physical Review X, 2021; 11 (4)
DOI: 10.1103/PhysRevX.11.041011 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/10/211018154236.htm

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