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Algebraic Effects, Linearity, and Quantum Programming Languages

Published:14 January 2015Publication History
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Abstract

We develop a new framework of algebraic theories with linear parameters, and use it to analyze the equational reasoning principles of quantum computing and quantum programming languages. We use the framework as follows:

  • we present a new elementary algebraic theory of quantum computation, built from unitary gates and measurement;

  • we provide a completeness theorem or the elementary algebraic theory by relating it with a model from operator algebra;

  • we extract an equational theory for a quantum programming language from the algebraic theory;

  • we compare quantum computation with other local notions of computation by investigating variations on the algebraic theory.

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        • Published in

          cover image ACM SIGPLAN Notices
          ACM SIGPLAN Notices  Volume 50, Issue 1
          POPL '15
          January 2015
          682 pages
          ISSN:0362-1340
          EISSN:1558-1160
          DOI:10.1145/2775051
          • Editor:
          • Andy Gill
          Issue’s Table of Contents
          • cover image ACM Conferences
            POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
            January 2015
            716 pages
            ISBN:9781450333009
            DOI:10.1145/2676726

          Copyright © 2015 ACM

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          Association for Computing Machinery

          New York, NY, United States

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          • Published: 14 January 2015

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