Nanotechnology Now - Press Release: Entanglement unlocks scaling for quantum machine learning: New No-Free-Lunch theorem for quantum neural networks gives hope for quantum speedup

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The No-Free-Lunch theorem for quantum data sets demonstrates that quantum entanglement, along with big data, allows for scaling up quantum machine learning. CREDIT Shutterstock

Abstract:
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.

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

Los Alamos, NM | Posted on February 25th, 2022

“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.

The Funding: U.S. Department of Energy Office of Science, the Laboratory Directed Research and Development program at Los Alamos National Laboratory, the Center for Nonlinear Studies at Los Alamos and the ASC Beyond Moore’s Law program at Los Alamos.

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About DOE/Los Alamos National Laboratory
Los Alamos National Laboratory, a multidisciplinary research institution engaged in strategic science on behalf of national security, is managed by Triad, a public service oriented, national security science organization equally owned by its three founding members: Battelle Memorial Institute (Battelle), the Texas A&M University System (TAMUS), and the Regents of the University of California (UC) for the Department of Energy’s National Nuclear Security Administration.

Los Alamos enhances national security by ensuring the safety and reliability of the U.S. nuclear stockpile, developing technologies to reduce threats from weapons of mass destruction, and solving problems related to energy, environment, infrastructure, health, and global security concerns.
LA-UR-22-21502

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Contacts:
Charles Poling
DOE/Los Alamos National Laboratory

Cell: 505-257-8006

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