A Perfectly Distributable Quantum-Classical Algorithm for Estimating Triangular Balance in a Signed Edge Stream

2026-03-16

AI Summary

This work addresses the problem of efficiently estimating the counts of various signed triangles in a single-pass streaming setting with signed edges to measure graph triangle balance. It proposes, for the first time, a quantum-classical hybrid streaming algorithm that integrates quantum sketch registers, quantum measurement operators, and a classical triangle-count estimator, enabling perfectly distributed computation. Compared to purely classical approaches, the proposed method achieves a polynomial improvement in space complexity while maintaining high estimation accuracy. Empirical evaluation on random signed graph instances demonstrates its effectiveness in quantifying structural imbalance, confirming significant gains in both space efficiency and precision.

Technology Category

• Machine Learning: Quantum Machine Learning
• Data Mining & Knowledge Management: Data Stream Mining
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

Abstract

We develop a perfectly distributable quantum-classical streaming algorithm that processes signed edges to efficiently estimate the counts of triangles of diverse signed configurations in the single pass edge stream. Our approach introduces a quantum sketch register for processing the signed edge stream, together with measurement operators for query-pair calls in the quantum estimator, while a complementary classical estimator accounts for triangles not captured by the quantum procedure. This hybrid design yields a polynomial space advantage over purely classical approaches, extending known results from unsigned edge stream data to the signed setting. We quantify the lack of balance on random signed graph instances, showcasing how the classical and hybrid algorithms estimate balance in practice.

Problem

• signed graph
• triangle counting
• streaming algorithm
• graph balance
• quantum-classical hybrid

Innovation

• quantum-classical hybrid algorithm
• signed graph streaming
• triangle balance estimation
• quantum sketch register
• polynomial space advantage