Kavli Affiliate: Eliska Greplova
| First 5 Authors: Thomas Spriggs, Arash Ahmadi, Bokai Chen, Eliska Greplova,
| Summary:
Variational techniques have long been at the heart of atomic, solid-state,
and many-body physics. They have recently extended to quantum and classical
machine learning, providing a basis for representing quantum states via neural
networks. These methods generally aim to minimize the energy of a given
ans"atz, though open questions remain about the expressivity of quantum and
classical variational ans"atze. The connection between variational techniques
and quantum computing, through variational quantum algorithms, offers
opportunities to explore the quantum complexity of classical methods. We
demonstrate how the concept of non-stabilizerness, or magic, can create a
bridge between quantum information and variational techniques and we show that
energy accuracy is a necessary but not always sufficient condition for accuracy
in non-stabilizerness. Through systematic benchmarking of neural network
quantum states, matrix product states, and variational quantum methods, we show
that while classical techniques are more accurate in non-stabilizerness, not
accounting for the symmetries of the system can have a severe impact on this
accuracy. Our findings form a basis for a universal expressivity
characterization of both quantum and classical variational methods.
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