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Learning hard quantum distributions with variational autoencoders
The exact description of many-body quantum systems represents one of the major challenges in modern physics, because it requires an amount of computational resources that scales exponentially with the size of the system. Simulating the evolution of a state, or even storing its description, rapidly b...
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| Published in: | npj quantum information 2018-06, Vol.4 (1), p.1-7, Article 28 |
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| Main Authors: | , , , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | The exact description of many-body quantum systems represents one of the major challenges in modern physics, because it requires an amount of computational resources that scales exponentially with the size of the system. Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a practically usable deep architecture for representing and sampling from probability distributions of quantum states. Our representation is based on variational auto-encoders, a type of generative model in the form of a neural network. We show that this model is able to learn efficient representations of states that are easy to simulate classically and can compress states that are not classically tractable. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterizing states of the size expected in first generation quantum hardware.
Quantum state representation: neural networks help encoding quantum many-body states
Artificial neural networks are able to learn how to efficiently represent complex quantum many-body states. An international team lead by Andrea Rocchetto and Edward Grant from University of Oxford and University College London have tested the capabilities of their neural network on quantum states of different complexity and showed that depth influences the representational capability of the model. Their network is able to efficiently represent states for which an efficient classical description is known, and compress the representation of states which can only be generated efficiently by a quantum computer. Increasing the “depth” of the network, i.e. the number of intermediate layers the computation goes through, improves performances in both cases, but not for states which are hard also for quantum computers. This suggests that neural networks are able to learn correlations that arise specifically in quantum processes and are not easily reproducible by a cla |
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| ISSN: | 2056-6387 2056-6387 |
| DOI: | 10.1038/s41534-018-0077-z |