Typing Quantum Superpositions and Measurement
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-type...
| Authors: | ; |
|---|---|
| Format: | Article |
| Status: | Published version |
| Publication date: | 2017 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/42228 |
| Online Access: | http://hdl.handle.net/11336/42228 |
| Access Level: | Open access |
| Keyword: | QUANTUM COMPUTING LAMBDA CALCULUS ALGEBRAIC LINEARITY LINEAR LOGIC https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| _version_ | 1878403022664499200 |
|---|---|
| author | Díaz Caro, Alejandro |
| author2 | Dowek, Gilles |
| author2_role | author |
| author_browse | Dowek, Gilles Díaz Caro, Alejandro |
| author_facet | Díaz Caro, Alejandro Dowek, Gilles |
| author_role | author |
| collection | CONICET Digital (CONICET) |
| description | We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | AR_2ece6e5fd3cfd125c8bd74bf0af0bd2f |
| identifier_str_mv | Díaz Caro, Alejandro; Dowek, Gilles; Typing Quantum Superpositions and Measurement; Springer; Lecture Notes in Computer Science; 10687; 12-2017; 281-293 978-3-319-71069-3 0302-9743 CONICET Digital CONICET |
| institution | Consejo Nacional de Investigaciones Científicas y Técnicas |
| instname_str | Consejo Nacional de Investigaciones Científicas y Técnicas |
| language | eng |
| network_acronym_str | AR |
| network_name_str | Argentina |
| oai_identifier_str | oai:ri.conicet.gov.ar:11336/42228 |
| publishDate | 2017 |
| publishDateSort | 2017 |
| publisher | Springer |
| publisherStr | Springer |
| reponame_str | CONICET Digital (CONICET) |
| spelling | Typing Quantum Superpositions and Measurement Díaz Caro, Alejandro Dowek, Gilles QUANTUM COMPUTING LAMBDA CALCULUS ALGEBRAIC LINEARITY LINEAR LOGIC https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 We propose a way to unify two approaches of non-cloning in quantum lambda-calculi. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as algebraic-linear functions. We illustrate this idea by defining a quantum extension of first-order simply-typed lambda-calculus, where the type is linear on superposition, while allows cloning base vectors. In addition, we provide an interpretation of the calculus where superposed types are interpreted as vector spaces and non-superposed types as their basis. Fil: Díaz Caro, Alejandro. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Dowek, Gilles. Institut National de Recherche en Informatique et en Automatique; Francia Springer http://hdl.handle.net/11336/42228 Díaz Caro, Alejandro; Dowek, Gilles; Typing Quantum Superpositions and Measurement; Springer; Lecture Notes in Computer Science; 10687; 12-2017; 281-293 978-3-319-71069-3 0302-9743 CONICET Digital CONICET |
| spellingShingle | Typing Quantum Superpositions and Measurement Díaz Caro, Alejandro QUANTUM COMPUTING LAMBDA CALCULUS ALGEBRAIC LINEARITY LINEAR LOGIC https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| status_str | publishedVersion |
| title | Typing Quantum Superpositions and Measurement |
| title_full | Typing Quantum Superpositions and Measurement |
| title_fullStr | Typing Quantum Superpositions and Measurement |
| title_full_unstemmed | Typing Quantum Superpositions and Measurement |
| title_short | Typing Quantum Superpositions and Measurement |
| title_sort | Typing Quantum Superpositions and Measurement |
| topic | QUANTUM COMPUTING LAMBDA CALCULUS ALGEBRAIC LINEARITY LINEAR LOGIC https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| topic_facet | QUANTUM COMPUTING LAMBDA CALCULUS ALGEBRAIC LINEARITY LINEAR LOGIC https://purl.org/becyt/ford/1.2 https://purl.org/becyt/ford/1 |
| url | http://hdl.handle.net/11336/42228 |