Quantum abstract machines without circuits: the need for higher algorithmic expressiveness

TL;DR

This paper argues for the development of new quantum computation models that move beyond circuit-based approaches to enable higher-level algorithmic expressiveness and composability, essential for discovering novel quantum algorithms.

Contribution

It proposes the need for higher-level abstract models of quantum computation that facilitate procedural abstractions and better understanding of quantum resource composition.

Findings

Current models limit algorithmic expressiveness

High-level abstractions can reveal quantum resource patterns

New models are essential for future large-scale quantum integration

Abstract

Existing abstract models of quantum computation make reference to circuit elements, much in contrast to their classical counterparts. Circuits, as a model of computation, substantially limit algorithmic expression and obscure high-level connections between problems and quantum resources. It is argued here that new models are needed to achieve high-level algorithmic expressiveness that allow composable procedural abstractions to manifest, leading to the development of instructions in the sense usually understood in high-level programming languages. Doing so appears essential to the discovery of new quantum algorithms, and deeper understanding of how quantum resources compose into useful patterns, or \emph{quantum motifs}. To achieve this, stronger investment in the intersection between higher-algebra, mathematical physics and quantum science is required to cope with future challenges brought forth by \textit{very large quantum scale integration}.