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Emerging Results, Vision & Reflection Track Paper

DOI: 10.4230/LIPIcs.ESEM.2026.79

Toward Entanglement Dependence Metrics for Quantum Software Complexity

Authors: Haibo Yu and Jianjun Zhao

Published in: LIPIcs, Volume 394, 20th International Symposium on Empirical Software Engineering and Measurement (ESEM 2026)

Abstract

Quantum software is often described using circuit-level metrics, including the number of qubits, the number of gates, circuit depth, the number of two-qubit gates, and the number of measurement operations. These metrics are useful for estimating program size and execution cost, but they do not directly describe whether and to what extent qubits become structurally related through possible entanglement during program execution. This paper argues that entanglement dependence provides a basis for measuring a quantum-specific form of software complexity. The proposed metrics capture possible entanglement-related structural dependence, not physical entanglement observed in a particular execution. Based on this notion, we define a focused set of six metrics that characterize the amount, density, local connectivity, global scope, program span, and modular crossing of entanglement-related dependencies. We also analyze these metrics using Weyuker’s properties for evaluating software complexity measures. The paper presents the metrics as a measurement framework and research direction for empirical quantum software engineering. It discusses how future studies can validate the metrics and examine their usefulness for testing, debugging, maintenance, and program comprehension of quantum software.

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Haibo Yu and Jianjun Zhao. Toward Entanglement Dependence Metrics for Quantum Software Complexity. In 20th International Symposium on Empirical Software Engineering and Measurement (ESEM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 394, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{yu_et_al:LIPIcs.ESEM.2026.79,
  author =	{Yu, Haibo and Zhao, Jianjun},
  title =	{{Toward Entanglement Dependence Metrics for Quantum Software Complexity}},
  booktitle =	{20th International Symposium on Empirical Software Engineering and Measurement (ESEM 2026)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-450-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{394},
  editor =	{Feldt, Robert and Paasivaara, Maria and Mendez, Daniel and Wagner, Stefan and Bar\'{o}n, Marvin Mu\~{n}oz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESEM.2026.79},
  URN =		{urn:nbn:de:0030-drops-280472},
  doi =		{10.4230/LIPIcs.ESEM.2026.79},
  annote =	{Keywords: Quantum software engineering, quantum program analysis, entanglement dependence, software metrics, software complexity}
}

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Toward Entanglement Dependence Metrics for Quantum Software Complexity

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