Gerrits, L., & Verweij, S. (2013). Critical realism as a meta-framework for understanding the relationships between complexity and qualitative comparative analysis. Journal of Critical Realism, 12(2), 166-182.
It seems to me that couching the logic of QCA in terms of critical realism as a "meta-framework" is a case of putting (very) old wine into new bottles, which doesn't necessarily improve the quality of the wine.
The methodological foundations of QCA go back to John Stuart Mill (1882) and two of his canons: that on the Method of Agreement and that on the Method of Difference (A System of Logic, Book III, Chapter VIII). These two methods essentially underlie all the technical machinery that is used in QCA today, formalized in Boolean-algebraic principles and operations.
Also, almost everything of the theory of causation behind QCA is already contained in Mill's System of Logic, Book III, chapter X, "Of Plurality of Causes; and of the Intermixture of Effects". Current studies that emphasize configurational causal complexity for the most part rephrase what had already been said in a much clearer way about 150 years ago.
Most importantly from the perspective of the epistemological foundations of QCA, in the 1960s and 1970s, John L. Mackie (1965, 1974) took Mill's ideas and some later developments up to propose his more elaborate INUS theory of causation, which is now, with very few refinements, at the heart of QCA and related configurational methods. Surprisingly, many proponents of QCA do not even know Mackie or have read his relevant works.
Thus, if you really want to understand the theoretical basis of QCA, you need to read at least Mackie (1965).
For a concise introduction to and tutorial on QCA that explains these historical roots while also incorporating the latest methodological advances, see entry 21 on my website at http://www.alrik-thiem.net/about/, whose link will take you directly to the corresponding article website of the American Journal of Evaluation (just drop me a line if you have no access; I can send you the article).
Best wishes,
Alrik
References
Mackie, John L. 1965. "Causes and Conditions." American Philosophical Quarterly 2 (4):245-64.
Mackie, John L. 1974. The Cement of the Universe: A Study of Causation. Oxford: Oxford University Press.
Mill, John Stuart. 1882. A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation. 8th ed. New York: Harper & Brothers.
In addition to the article of Lasse Gerrits and myself that was suggested in one of the previous comments, as well as the other suggestions, you may also want to have a look at the work of Barbara Befani, e.g., her article in Evaluation with the title Realistic Evaluation and QCA: Conceptual Parallels and an Empirical Application. She introduce QCA within the framework of Realistic Evaluation, which in turn is based on ideas from critical realism. She proposes then that QCA can be used to study CMO-configurations.
Another interesting author is David S. Byrne. He considers QCA as a method to model complex systems. His ideas on complex systems have a critical realist basis. There are multiple works of him on the topic, see e.g. here: https://www.dur.ac.uk/sass/staff/profile/?id=645.