Quantum entanglement analysis based on abstract interpretation

TL;DR

This paper introduces an abstract interpretation framework for approximating quantum entanglement analysis, enabling more efficient understanding of entanglement evolution in quantum programs.

Contribution

It develops a novel abstract semantics for quantum entanglement using partitions of memory, providing a sound approximation method for entanglement analysis.

Findings

Abstract semantics for quantum entanglement is sound.

Partition-based representation effectively captures entanglement.

Framework enables approximate analysis of entanglement evolution.

Abstract

Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum algorithm which does not create entanglement can be efficiently simulated on a classical computer. The exact role of the entanglement is nevertheless not well understood. Since an exact analysis of entanglement evolution induces an exponential slowdown, we consider approximative analysis based on the framework of abstract interpretation. In this paper, a concrete quantum semantics based on superoperators is associated with a simple quantum programming language. The representation of entanglement, i.e. the design of the abstract domain is a key issue. A representation of entanglement as a partition of the memory is chosen. An abstract semantics is introduced, and the soundness of the approximation is proven.