Error statistics and scalability of quantum error mitigation formulas
Abstract Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit re...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-04-01
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| Series: | npj Quantum Information |
| Online Access: | https://doi.org/10.1038/s41534-023-00707-7 |
| _version_ | 1797845845038596096 |
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| author | Dayue Qin Yanzhu Chen Ying Li |
| author_facet | Dayue Qin Yanzhu Chen Ying Li |
| author_sort | Dayue Qin |
| collection | DOAJ |
| description | Abstract Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(ϵ N) with the gate number N before mitigation and sublinearly $$O({\epsilon }^{{\prime} }{N}^{\gamma })$$ O ( ϵ ′ N γ ) after mitigation, where γ ≈ 0.5, ϵ is the error rate of a quantum gate, and $${\epsilon }^{{\prime} }$$ ϵ ′ is a protocol-dependent factor. The $$\sqrt{N}$$ N scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result. |
| first_indexed | 2024-04-09T17:46:38Z |
| format | Article |
| id | doaj.art-ee210d9e548340528231834a96a478b5 |
| institution | Directory Open Access Journal |
| issn | 2056-6387 |
| language | English |
| last_indexed | 2024-04-09T17:46:38Z |
| publishDate | 2023-04-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | npj Quantum Information |
| spelling | doaj.art-ee210d9e548340528231834a96a478b52023-04-16T11:21:09ZengNature Portfolionpj Quantum Information2056-63872023-04-019111410.1038/s41534-023-00707-7Error statistics and scalability of quantum error mitigation formulasDayue Qin0Yanzhu Chen1Ying Li2Graduate School of China Academy of Engineering PhysicsDepartment of Physics, Virginia TechGraduate School of China Academy of Engineering PhysicsAbstract Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources. While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly O(ϵ N) with the gate number N before mitigation and sublinearly $$O({\epsilon }^{{\prime} }{N}^{\gamma })$$ O ( ϵ ′ N γ ) after mitigation, where γ ≈ 0.5, ϵ is the error rate of a quantum gate, and $${\epsilon }^{{\prime} }$$ ϵ ′ is a protocol-dependent factor. The $$\sqrt{N}$$ N scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.https://doi.org/10.1038/s41534-023-00707-7 |
| spellingShingle | Dayue Qin Yanzhu Chen Ying Li Error statistics and scalability of quantum error mitigation formulas npj Quantum Information |
| title | Error statistics and scalability of quantum error mitigation formulas |
| title_full | Error statistics and scalability of quantum error mitigation formulas |
| title_fullStr | Error statistics and scalability of quantum error mitigation formulas |
| title_full_unstemmed | Error statistics and scalability of quantum error mitigation formulas |
| title_short | Error statistics and scalability of quantum error mitigation formulas |
| title_sort | error statistics and scalability of quantum error mitigation formulas |
| url | https://doi.org/10.1038/s41534-023-00707-7 |
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