# Tierkreis: A Dataflow Framework for Hybrid Quantum-Classical Computing

arXiv: https://arxiv.org/abs/2211.02350 · HTML: https://mlsanity.com/paper/2211.02350/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [Function+Data Flow: A Framework to Specify Machine Learning Pipelines for Digital Twinning](https://mlsanity.com/paper/2406.19670/) (2024)
- [Building real-time digital twin instances with Function+Data Flow: user evaluation and extension for iterative pipelines](https://mlsanity.com/paper/2608.18480/) (2026)

## Abstract (arXiv)

We present Tierkreis, a higher-order dataflow graph program representation and runtime designed for compositional, quantum-classical hybrid algorithms. The design of the system is motivated by the remote nature of quantum computers, the need for hybrid algorithms to involve cloud and distributed computing, and the long-running nature of these algorithms. The graph-based representation reflects how designers reason about and visualise algorithms, and allows automatic parallelism and asynchronicity. A strong, static type system and higher-order semantics allow for high expressivity and compositionality in the program. The flexible runtime protocol enables third-party developers to add functionality using any language or environment. With Tierkreis, quantum software developers can easily build, visualise, verify, test, and debug complex hybrid workflows, and immediately deploy them to the cloud or a custom distributed environment.