- Quantum superpositions and projective measurement in the lambda calculus. Research Report 1601.04294, Computing Research Repository, January 2016. 22 pages. ( Web page | PDF ) .

- Abstract:
- We propose an extension of simply typed lambda-calculus to handle some properties of quantum computing. The equiprobable quantum superposition is taken as a commutative pair and the quantum measurement as a non-deterministic projection over it. Destructive interferences are achieved by introducing an inverse symbol with respect to pairs. The no-cloning property is ensured by using a combination of syntactic linearity with linear logic. Indeed, the syntactic linearity is enough for unitary gates, while a function measuring its argument needs to enforce that the argument is used only once.

@techreport{DD-arxiv16, | ||

author = |
{D{\'i}az{-}Caro, Alejandro and Dowek, Gilles}, | |

institution = |
{Computing Research Repository}, | |

month = | jan,
| |

note = |
{22~pages}, | |

number = |
{1601.04294}, | |

type = |
{Research Report}, | |

title = |
{Quantum superpositions and projective measurement in the lambda calculus},
| |

url = |
{http://arxiv.org/abs/1601.04294}, | |

year = |
{2016}, | |

} |

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