Quantum Computation, Categorical Semantics and Linear Logic Export

@article{citeulike:216776, abstract = {We develop a type theory and provide a denotational semantics for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic. In our semantics, terms inhabit certain Hilbert bundles, and computations are interpreted as the appropriate inner product preserving maps between Hilbert bundles. These bundles and maps form a symmetric monoidal closed category, as expected for a calculus based on linear logic.}, archivePrefix = {arXiv}, author = {van Tonder, Andr\'{e} and Dorca, Miquel}, citeulike-article-id = {216776}, citeulike-linkout-0 = {http://arxiv.org/abs/quant-ph/0312174}, citeulike-linkout-1 = {http://arxiv.org/pdf/quant-ph/0312174}, day = {17}, eprint = {quant-ph/0312174}, keywords = {category-theory, lambda-calculus, quantum, semantics}, month = {Feb}, posted-at = {2009-08-10 15:46:52}, priority = {2}, title = {Quantum Computation, Categorical Semantics and Linear Logic}, url = {http://arxiv.org/abs/quant-ph/0312174}, year = {2007} }

TY - JOUR ID - citeulike:216776 L3 - citeulike-article-id:216776 N2 - We develop a type theory and provide a denotational semantics for a simple fragment of the quantum lambda calculus, a formal language for quantum computation based on linear logic. In our semantics, terms inhabit certain Hilbert bundles, and computations are interpreted as the appropriate inner product preserving maps between Hilbert bundles. These bundles and maps form a symmetric monoidal closed category, as expected for a calculus based on linear logic. TI - Quantum Computation, Categorical Semantics and Linear Logic KW - category-theory KW - lambda-calculus KW - quantum KW - semantics AU - van Tonder, André AU - Dorca, Miquel PY - 2007/Feb/17/ UR - http://arxiv.org/abs/quant-ph/0312174 ER -