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...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
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Nature Research
2018
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| _version_ | 1826288149934899200 |
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| author | Rocchetto, A Grant, E Strelchuk, S Carleo, G Severini, S |
| author_facet | Rocchetto, A Grant, E Strelchuk, S Carleo, G Severini, S |
| author_sort | Rocchetto, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:09:22Z |
| format | Journal article |
| id | oxford-uuid:a0151ada-d9b8-4552-8946-ad0f7c9628fa |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:09:22Z |
| publishDate | 2018 |
| publisher | Nature Research |
| record_format | dspace |
| spelling | oxford-uuid:a0151ada-d9b8-4552-8946-ad0f7c9628fa2022-03-27T02:02:55ZLearning hard quantum distributions with variational autoencodersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a0151ada-d9b8-4552-8946-ad0f7c9628faEnglishSymplectic Elements at OxfordNature Research2018Rocchetto, AGrant, EStrelchuk, SCarleo, GSeverini, SThe 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. |
| spellingShingle | Rocchetto, A Grant, E Strelchuk, S Carleo, G Severini, S Learning hard quantum distributions with variational autoencoders |
| title | Learning hard quantum distributions with variational autoencoders |
| title_full | Learning hard quantum distributions with variational autoencoders |
| title_fullStr | Learning hard quantum distributions with variational autoencoders |
| title_full_unstemmed | Learning hard quantum distributions with variational autoencoders |
| title_short | Learning hard quantum distributions with variational autoencoders |
| title_sort | learning hard quantum distributions with variational autoencoders |
| work_keys_str_mv | AT rocchettoa learninghardquantumdistributionswithvariationalautoencoders AT grante learninghardquantumdistributionswithvariationalautoencoders AT strelchuks learninghardquantumdistributionswithvariationalautoencoders AT carleog learninghardquantumdistributionswithvariationalautoencoders AT severinis learninghardquantumdistributionswithvariationalautoencoders |