On Circuit Description Languages, Indexed Monads, and Resource Analysis

TL;DR

This paper introduces a monad-based denotational model for circuit description languages, enabling precise reasoning about circuit size and effects, which supports advanced type systems for resource control in quantum programming languages.

Contribution

It presents a novel semantic framework using circuit algebra that allows effect typing to guarantee quantitative circuit properties, even with optimizations.

Findings

Adequate monad-based model for Proto-Quipper calculi

Separation of value and circuit side effects in semantics

Effect typing guarantees circuit size properties

Abstract

In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to separate the value to which a term reduces from the circuit that the term itself produces as a side effect. In turn, this enables the denotational interpretation and validation of rich type systems in which the size of the produced circuit can be controlled. Notably, the proposed semantic framework, through the novel concept of circuit algebra, suggests forms of effect typing guaranteeing quantitative properties about the resulting circuit, even in presence of optimizations.