Approximate Relational Reasoning for Quantum Programs Article Swipe
Peng Yan
,
Hanru Jiang
,
Nengkun Yu
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/978-3-031-65633-0_22
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/978-3-031-65633-0_22
Quantum computation is inevitably subject to imperfections in its implementation. These imperfections arise from various sources, including environmental noise at the hardware level and the introduction of approximate implementations by quantum algorithm designers, such as lower-depth computations. Given the significant advantage of relational logic in program reasoning and the importance of assessing the robustness of quantum programs between their ideal specifications and imperfect implementations, we design a proof system to verify the approximate relational properties of quantum programs. We demonstrate the effectiveness of our approach by providing the first formal verification of the renowned low-depth approximation of the quantum Fourier transform. Furthermore, we validate the approximate correctness of the repeat-until-success algorithm. From the technical point of view, we develop approximate quantum coupling as a fundamental tool to study approximate relational reasoning for quantum programs, a novel generalization of the widely used approximate probabilistic coupling in probabilistic programs, answering a previously posed open question for projective predicates.
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Metadata
- Type
- book-chapter
- Language
- en
- Landing Page
- https://doi.org/10.1007/978-3-031-65633-0_22
- https://link.springer.com/content/pdf/10.1007/978-3-031-65633-0_22.pdf
- OA Status
- hybrid
- Cited By
- 1
- References
- 70
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4400995151
All OpenAlex metadata
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https://doi.org/10.1007/978-3-031-65633-0_22Digital Object Identifier
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Approximate Relational Reasoning for Quantum ProgramsWork title
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book-chapterOpenAlex work type
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enPrimary language
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2024Year of publication
- Publication date
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2024-01-01Full publication date if available
- Authors
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Peng Yan, Hanru Jiang, Nengkun YuList of authors in order
- Landing page
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https://doi.org/10.1007/978-3-031-65633-0_22Publisher landing page
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https://link.springer.com/content/pdf/10.1007/978-3-031-65633-0_22.pdfDirect link to full text PDF
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hybridOpen access status per OpenAlex
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https://link.springer.com/content/pdf/10.1007/978-3-031-65633-0_22.pdfDirect OA link when available
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Computer science, Correctness, Probabilistic logic, Quantum computer, Theoretical computer science, Quantum, Quantum algorithm, Algorithm, Artificial intelligence, Quantum mechanics, PhysicsTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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70Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.verify | 71 |
| abstract_inverted_index.widely | 140 |
| abstract_inverted_index.Fourier | 100 |
| abstract_inverted_index.Quantum | 1 |
| abstract_inverted_index.between | 58 |
| abstract_inverted_index.develop | 119 |
| abstract_inverted_index.program | 46 |
| abstract_inverted_index.quantum | 31, 56, 77, 99, 121, 133 |
| abstract_inverted_index.subject | 5 |
| abstract_inverted_index.various | 15 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.approach | 85 |
| abstract_inverted_index.coupling | 122, 144 |
| abstract_inverted_index.hardware | 22 |
| abstract_inverted_index.programs | 57 |
| abstract_inverted_index.question | 153 |
| abstract_inverted_index.renowned | 94 |
| abstract_inverted_index.sources, | 16 |
| abstract_inverted_index.validate | 104 |
| abstract_inverted_index.advantage | 41 |
| abstract_inverted_index.algorithm | 32 |
| abstract_inverted_index.answering | 148 |
| abstract_inverted_index.assessing | 52 |
| abstract_inverted_index.imperfect | 63 |
| abstract_inverted_index.including | 17 |
| abstract_inverted_index.low-depth | 95 |
| abstract_inverted_index.programs, | 134, 147 |
| abstract_inverted_index.programs. | 78 |
| abstract_inverted_index.providing | 87 |
| abstract_inverted_index.reasoning | 47, 131 |
| abstract_inverted_index.technical | 114 |
| abstract_inverted_index.algorithm. | 111 |
| abstract_inverted_index.designers, | 33 |
| abstract_inverted_index.importance | 50 |
| abstract_inverted_index.inevitably | 4 |
| abstract_inverted_index.previously | 150 |
| abstract_inverted_index.projective | 155 |
| abstract_inverted_index.properties | 75 |
| abstract_inverted_index.relational | 43, 74, 130 |
| abstract_inverted_index.robustness | 54 |
| abstract_inverted_index.transform. | 101 |
| abstract_inverted_index.approximate | 28, 73, 106, 120, 129, 142 |
| abstract_inverted_index.computation | 2 |
| abstract_inverted_index.correctness | 107 |
| abstract_inverted_index.demonstrate | 80 |
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| abstract_inverted_index.lower-depth | 36 |
| abstract_inverted_index.predicates. | 156 |
| abstract_inverted_index.significant | 40 |
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| abstract_inverted_index.introduction | 26 |
| abstract_inverted_index.verification | 91 |
| abstract_inverted_index.approximation | 96 |
| abstract_inverted_index.computations. | 37 |
| abstract_inverted_index.effectiveness | 82 |
| abstract_inverted_index.environmental | 18 |
| abstract_inverted_index.imperfections | 7, 12 |
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| abstract_inverted_index.implementations, | 64 |
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| cited_by_percentile_year.max | 95 |
| cited_by_percentile_year.min | 91 |
| corresponding_author_ids | https://openalex.org/A5088217238 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 3 |
| corresponding_institution_ids | https://openalex.org/I59553526 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/15 |
| sustainable_development_goals[0].score | 0.7200000286102295 |
| sustainable_development_goals[0].display_name | Life in Land |
| citation_normalized_percentile.value | 0.74245338 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |