Measurements in Proof Nets as Higher-Order Quantum Circuits

  • Akira Yoshimizu
  • Ichiro Hasuo
  • Claudia Faggian
  • Ugo Dal Lago
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8410)


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).


Quantum Computation Monoidal Category Quantum Circuit Linear Logic Reduction Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Akira Yoshimizu
    • 1
  • Ichiro Hasuo
    • 1
  • Claudia Faggian
    • 2
  • Ugo Dal Lago
    • 3
  1. 1.University of TokyoJapan
  2. 2.CNRSUniversité Paris DiderotParis 7France
  3. 3.Università di BolognaItaly

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