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: | ; |
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| 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 |
| Summary: | 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. |
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