Approximating Entanglement Based on Abstract Interpretation

TL;DR

This paper introduces a static analysis method that approximates quantum entanglement efficiently, aiding quantum program optimization and correctness verification without exponential complexity.

Contribution

It extends existing abstract interpretation techniques to approximate entanglement, ensuring soundness and linear-time scalability in analysis.

Findings

The method is sound for approximating entanglement.

Implementation achieves linear-time analysis.

Applicable to quantum circuit optimization.

Abstract

Entanglement is a fundamental property of quantum systems, essential for non-trivial quantum programs. Identifying when qubits become entangled is critical for circuit optimization, and for arguing for the correctness of quantum algorithms. This paper presents a static analysis method for approximating entanglement by extending an already existing abstract interpretation, thus avoiding the exponential slowdown of an exact analysis. The approach is shown to be sound and an implementation is provided in Standard ML with linear-time scalability.