Entanglement unlocks scaling for quantum machine learning
New No-Free-Lunch theorem for quantum neural networks gives hope for
quantum speedup

Date:
February 24, 2022
Source:
DOE/Los Alamos National Laboratory
Summary:
The field of machine learning on quantum computers got a boost
from new research removing a potential roadblock to the practical
implementation of quantum neural networks.



FULL STORY ==========================================================================
The field of machine learning on quantum computers got a boost from new research removing a potential roadblock to the practical implementation
of quantum neural networks. While theorists had previously believed an exponentially large training set would be required to train a quantum
neural network, the quantum No-Free-Lunch theorem developed by Los
Alamos National Laboratory shows that quantum entanglement eliminates
this exponential overhead.


==========================================================================
"Our work proves that both big data and big entanglement are valuable in quantum machine learning. Even better, entanglement leads to scalability,
which solves the roadblock of exponentially increasing the size of the
data in order to learn it," said Andrew Sornborger, a computer scientist
at Los Alamos and a coauthor of the paper published Feb. 18 in Physical
Review Letters."The theorem gives us hope that quantum neural networks
are on track towards the goal of quantum speed-up, where eventually
they will outperform their counterparts on classical computers."
The classical No-Free-Lunch theorem states that any machine-learning
algorithm is as good as, but no better than, any other when their
performance is averaged over all possible functions connecting the data
to their labels. A direct consequence of this theorem that showcases
the power of data in classical machine learning is that the more data
one has, the better the average performance. Thus, data is the currency
in machine learning that ultimately limits performance.

The new Los Alamos No-Free-Lunch theorem shows that in the quantum regime entanglement is also a currency, and one that can be exchanged for data
to reduce data requirements.

Using a Rigetti quantum computer, the team entangled the quantum data
set with a reference system to verify the new theorem.

"We demonstrated on quantum hardware that we could effectively violate
the standard No-Free-Lunch theorem using entanglement, while our new formulation of the theorem held up under experimental test," said Kunal
Sharma, the first author on the article.

"Our theorem suggests that entanglement should be considered a
valuable resource in quantum machine learning, along with big data,"
said Patrick Coles, a physicist at Los Alamos and senior author on
the article. "Classical neural networks depend only on big data."
Entanglement describes the state of a system of atomic-scale particles
that cannot be fully described independently or individually. Entanglement
is a key component of quantum computing.

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


========================================================================== Journal Reference:
1. Kunal Sharma, M. Cerezo, Zoe" Holmes, Lukasz Cincio, Andrew
Sornborger,
Patrick J. Coles. Reformulation of the No-Free-Lunch Theorem for
Entangled Datasets. Physical Review Letters, 2022; 128 (7) DOI:
10.1103/ PhysRevLett.128.070501 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2022/02/220224125214.htm

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