AI Article Synopsis
- The no-free-lunch theorem outlines limitations on a learning algorithm's performance based on the training dataset.
- Recent advancements in quantum machine learning raise questions about the existence of a quantum version of this theorem, especially since quantum training data can exhibit unique behaviors like entanglement.
- The study demonstrates that entangled datasets can bypass classical limits of the NFL theorem, leading to a reformulated theorem that recognizes entanglement as beneficial for learning unitary processes in quantum environments.
Article Abstract
The no-free-lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training dataset. With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process with quantum training data. However, in the quantum setting, the training data can possess entanglement, a strong correlation with no classical analog. In this Letter, we show that entangled datasets lead to an apparent violation of the (classical) NFL theorem. This motivates a reformulation that accounts for the degree of entanglement in the training set. As our main result, we prove a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. We employ Rigetti's quantum computer to test both the classical and quantum NFL theorems. Our Letter establishes that entanglement is a commodity in quantum machine learning.
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| http://dx.doi.org/10.1103/PhysRevLett.128.070501 | DOI Listing |
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