Block-encodings as programming abstractions: The Eclipse Qrisp BlockEncoding Interface

TL;DR

This paper introduces the BlockEncoding interface in the Eclipse Qrisp framework, making block-encodings accessible as high-level programming abstractions for quantum algorithm implementation.

Contribution

It establishes a practical, high-level programming interface for block-encodings, facilitating implementation and resource estimation of advanced quantum algorithms.

Findings

The interface simplifies the implementation of block-encodings in quantum algorithms.

Code examples demonstrate practical applications like matrix inversion and Hamiltonian simulation.

The framework integrates key concepts such as qubitization and block-encoding construction.

Abstract

Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols like Quantum Singular Value Transformation (QSVT) and Quantum Signal Processing (QSP), the generation of compilable implementations of block-encodings poses a formidable challenge. This work presents the BlockEncoding interface within the Eclipse Qrisp framework, establishing block-encodings as a high-level programming abstraction accessible to a broad scientific audience. Serving as both a technical framework introduction and a hands-on tutorial, this paper explicitly details key underlying concepts abstracted away by the interface, such as block-encoding construction and qubitization, and their practical integration into methods like the Childs-Kothari-Somma (CKS) algorithm. We outline the interface's software architecture, encompassing constructors, core utilities, arithmetic composition, and algorithmic applications such as matrix inversion, polynomial filtering, and Hamiltonian simulation. Through code examples, we demonstrate how this interface simplifies both the practical realization of advanced quantum algorithms and their associated resource estimation.