Algebraic Effects, Linearity, and Quantum Programming Languages

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 for 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.

• Type: Journal
• Year: 2015
• Where: POPL
• Authors: Sam Staton
• Keywords: POPL 2015, Programming Languages