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Niveau: Supérieur, Doctorat, Bac+8

Quantum Implicit Computational Complexity Ugo Dal Lago a Andrea Masini b Margherita Zorzi b aDipartimento di Scienze dell'Informazione, Universita di Bologna bDipartimento di Informatica, Universita di Verona Abstract We introduce a quantum lambda calculus inspired by Lafont's Soft Linear Logic and capturing the polynomial quantum complexity classes EQP, BQP and ZQP. The calculus is based on the “classical control and quantum data” paradigm. This is the first example of a formal system capturing quantum complexity classes in the spirit of implicit computational complexity — it is machine-free and no explicit bound (e.g., polynomials) appears in its syntax. 1 Introduction This paper is about quantum computation and implicit computational com- plexity. More precisely, a lambda calculus is defined and proved to capture some (polynomial time) quantum complexity classes. The language under con- sideration is not built up from any notion of polynomials or from any concrete machine. To the authors' knowledge, this is the first example of an implicit characterization of some classes of problems coming from quantum complexity theory. A brief introduction to these two research areas is now in order. Quantum Computation. Quantum Computation (QC) [6,9–11,17,13,22] is nowadays one of the most promising computation paradigms between those going beyond classical computation (e.g. biological computation, nanocom- puting, etc.).

Quantum Implicit Computational Complexity Ugo Dal Lago a Andrea Masini b Margherita Zorzi b aDipartimento di Scienze dell'Informazione, Universita di Bologna bDipartimento di Informatica, Universita di Verona Abstract We introduce a quantum lambda calculus inspired by Lafont's Soft Linear Logic and capturing the polynomial quantum complexity classes EQP, BQP and ZQP. The calculus is based on the “classical control and quantum data” paradigm. This is the first example of a formal system capturing quantum complexity classes in the spirit of implicit computational complexity — it is machine-free and no explicit bound (e.g., polynomials) appears in its syntax. 1 Introduction This paper is about quantum computation and implicit computational com- plexity. More precisely, a lambda calculus is defined and proved to capture some (polynomial time) quantum complexity classes. The language under con- sideration is not built up from any notion of polynomials or from any concrete machine. To the authors' knowledge, this is the first example of an implicit characterization of some classes of problems coming from quantum complexity theory. A brief introduction to these two research areas is now in order. Quantum Computation. Quantum Computation (QC) [6,9–11,17,13,22] is nowadays one of the most promising computation paradigms between those going beyond classical computation (e.g. biological computation, nanocom- puting, etc.).

- linear logic
- based
- quantum complexity
- logic-based characterizations
- affect quantum
- language can
- both quantum
- proof strictly
- quantum computation

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Published by | mijec |

Reads | 10 |

Language | English |

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