This article brings together critical International Relations (IR) and quantum social science to understand the power of algorithms over human activity. It argues that a critical quantum theory can accommodate both algorithmic authority and resistance against it. By placing the early Frankfurt School of critical theory in direct dialogue with quantum IR, the article demonstrates how algorithms and big data reinforce relations of power and domination, while leaving avenues for contestation and disruption. The proposed critical quantum framework contributes to contemporary debates about the relationship between humans and algorithms through three interrelated lines of inquiry. It highlights a shared commitment to relationality within critical and quantum social theories. It corrects for technological determinism characteristic of the early Frankfurt School. Finally, it cautions against a flattened quantum ontology which glosses over inequalities and injustices of the algorithmic condition. The article suggests that future research on algorithmic governance would benefit from positioning itself at the intersection of quantum and critical social science.