Quantum machine learning models are kernel methods
- URL: http://arxiv.org/abs/2101.11020v1
- Date: Tue, 26 Jan 2021 19:00:04 GMT
- Title: Quantum machine learning models are kernel methods
- Authors: Maria Schuld
- Abstract summary: This technical manuscript summarises, formalises and extends the link by systematically rephrasing quantum models as a kernel method.
It shows that most near-term and fault-tolerant quantum models can be replaced by a general support vector machine.
In particular, kernel-based training is guaranteed to find better or equally good quantum models than variational circuit training.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: With near-term quantum devices available and the race for fault-tolerant
quantum computers in full swing, researchers became interested in the question
of what happens if we replace a machine learning model with a quantum circuit.
While such "quantum models" are sometimes called "quantum neural networks", it
has been repeatedly noted that their mathematical structure is actually much
more closely related to kernel methods: they analyse data in high-dimensional
Hilbert spaces to which we only have access through inner products revealed by
measurements. This technical manuscript summarises, formalises and extends the
link by systematically rephrasing quantum models as a kernel method. It shows
that most near-term and fault-tolerant quantum models can be replaced by a
general support vector machine whose kernel computes distances between
data-encoding quantum states. In particular, kernel-based training is
guaranteed to find better or equally good quantum models than variational
circuit training. Overall, the kernel perspective of quantum machine learning
tells us that the way that data is encoded into quantum states is the main
ingredient that can potentially set quantum models apart from classical machine
learning models.
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