Quantifying the magic of quantum channels
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ o...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab451d |
| _version_ | 1827873096496840704 |
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| author | Xin Wang Mark M Wilde Yuan Su |
| author_facet | Xin Wang Mark M Wilde Yuan Su |
| author_sort | Xin Wang |
| collection | DOAJ |
| description | To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d , it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise. |
| first_indexed | 2024-03-12T16:33:42Z |
| format | Article |
| id | doaj.art-a7d467f370dd49798a5c5383f844060c |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:33:42Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a7d467f370dd49798a5c5383f844060c2023-08-08T15:23:54ZengIOP PublishingNew Journal of Physics1367-26302019-01-01211010300210.1088/1367-2630/ab451dQuantifying the magic of quantum channelsXin Wang0https://orcid.org/0000-0002-0641-3186Mark M Wilde1https://orcid.org/0000-0002-3916-4462Yuan Su2https://orcid.org/0000-0003-1144-3563Joint Center for Quantum Information and Computer Science, University of Maryland , College Park, MD 20742, United States of America; Institute for Quantum Computing, Baidu Research, Beijing 100193, People’s Republic of ChinaHearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University , Baton Rouge, LA 70803, United States of AmericaJoint Center for Quantum Information and Computer Science, University of Maryland , College Park, MD 20742, United States of America; Department of Computer Science, Institute for Advanced Computer Studies, University of Maryland , College Park, United States of AmericaTo achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d , it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.https://doi.org/10.1088/1367-2630/ab451dresource theory of magic quantum channelscompletely positive-Wigner-preserving quantum operationsthauma of a quantum channeldistillable magicclassical simulation of noisy quantum circuits |
| spellingShingle | Xin Wang Mark M Wilde Yuan Su Quantifying the magic of quantum channels New Journal of Physics resource theory of magic quantum channels completely positive-Wigner-preserving quantum operations thauma of a quantum channel distillable magic classical simulation of noisy quantum circuits |
| title | Quantifying the magic of quantum channels |
| title_full | Quantifying the magic of quantum channels |
| title_fullStr | Quantifying the magic of quantum channels |
| title_full_unstemmed | Quantifying the magic of quantum channels |
| title_short | Quantifying the magic of quantum channels |
| title_sort | quantifying the magic of quantum channels |
| topic | resource theory of magic quantum channels completely positive-Wigner-preserving quantum operations thauma of a quantum channel distillable magic classical simulation of noisy quantum circuits |
| url | https://doi.org/10.1088/1367-2630/ab451d |
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