Abstract
We build on the series of work by Dal Lago and coauthors and identify proof nets (of linear logic) as higher-order quantum circuits. By accommodating quantum measurement using additive slices, we obtain a comprehensive framework for programming and interpreting quantum computation. Specifically, we introduce a quantum lambda calculus MLLqm and define its geometry of interaction (GoI) semantics—in the style of token machines—via the translation of terms into proof nets. Its soundness, i.e. invariance under reduction of proof nets, is established. The calculus MLLqm attains a pleasant balance between expressivity (it is higher-order and accommodates all quantum operations) and concreteness of models (given as token machines, i.e. in the form of automata).
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Yoshimizu, A., Hasuo, I., Faggian, C., Dal Lago, U.: Measurements in proof nets as higher-order quantum circuits. Extended version with proofs (2014), www-mmm.is.s.u-tokyo.ac.jp/~ayoshimizu
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Yoshimizu, A., Hasuo, I., Faggian, C., Dal Lago, U. (2014). Measurements in Proof Nets as Higher-Order Quantum Circuits. In: Shao, Z. (eds) Programming Languages and Systems. ESOP 2014. Lecture Notes in Computer Science, vol 8410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54833-8_20
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DOI: https://doi.org/10.1007/978-3-642-54833-8_20
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