
Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry
We derive symmetric and antisymmetric kernels by symmetrizing and antisy...
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Largescale quantum machine learning
Quantum computers promise to enhance machine learning for practical appl...
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Quantum machine learning models are kernel methods
With nearterm quantum devices available and the race for faulttolerant...
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Training Quantum Embedding Kernels on NearTerm Quantum Computers
Kernel methods are a cornerstone of classical machine learning. The idea...
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Power of data in quantum machine learning
The use of quantum computing for machine learning is among the most exci...
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Importance of Kernel Bandwidth in Quantum Machine Learning
Quantum kernel methods are considered a promising avenue for applying qu...
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Nonparametric Active Learning and Rate Reduction in Manybody Hilbert Space with Rescaled Logarithmic Fidelity
In quantum and quantuminspired machine learning, the very first step is...
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The Inductive Bias of Quantum Kernels
It has been hypothesized that quantum computers may lend themselves well to applications in machine learning. In the present work, we analyze function classes defined via quantum kernels. Quantum computers offer the possibility to efficiently compute inner products of exponentially large density operators that are classically hard to compute. However, having an exponentially large feature space renders the problem of generalization hard. Furthermore, being able to evaluate inner products in high dimensional spaces efficiently by itself does not guarantee a quantum advantage, as already classically tractable kernels can correspond to high or infinitedimensional reproducing kernel Hilbert spaces (RKHS). We analyze the spectral properties of quantum kernels and find that we can expect an advantage if their RKHS is low dimensional and contains functions that are hard to compute classically. If the target function is known to lie in this class, this implies a quantum advantage, as the quantum computer can encode this inductive bias, whereas there is no classically efficient way to constrain the function class in the same way. However, we show that finding suitable quantum kernels is not easy because the kernel evaluation might require exponentially many measurements. In conclusion, our message is a somewhat sobering one: we conjecture that quantum machine learning models can offer speedups only if we manage to encode knowledge about the problem at hand into quantum circuits, while encoding the same bias into a classical model would be hard. These situations may plausibly occur when learning on data generated by a quantum process, however, they appear to be harder to come by for classical datasets.
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