Classical-quantum algorithms for triangle counts in a signed edge stream

We present a classical-quantum framework for analyzing statistics of streaming data through signed graph representations. Using an online correlation computation algorithm, we construct signed graph-structured data from denoised correlation strengths. On this foundation, we develop a classical-quantum streaming algorithm that processes signed edges to efficiently estimate the counts of triangles of diverse signed configurations in the 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 further quantify the lack of balance in the evolving signed graph using the triangular index of balance, and evaluate the framework on time-series stock price data of S&P 500 companies, and. The results demonstrate the capability of the proposed method to uncover structural patterns in financial data streams and highlight its applicability to quantum-enhanced portfolio analysis, particularly for real-time monitoring of portfolio balance and risk.