In this work, a scalable quantum gate-based algorithm for accelerating causal inference is introduced. Specifically, the formalism of causal hypothesis testing presented in [Nat Commun 10, 1472 (2019)] is considered. Through the algorithm, the existing definition of error probability is generalized, which is a metric to distinguish between two competing causal hypotheses, to a practical scenario. The results on the Qiskit validate the predicted speedup and show that in the realistic scenario, the error probability depends on the distance between the competing hypotheses. To achieve this, the causal hypotheses are embedded as a circuit construction of the oracle. Furthermore, by assessing the complexity involved in implementing the algorithm's subcomponents, a numerical estimation of the resources required for the algorithm is offered. Finally, applications of this framework for causal inference use cases in bioinformatics and artificial general intelligence are discussed.

This work applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. The relations among the statistical, algorithmic, computational, and circuit complexities of states are reviewed. Thereafter, the probability of states in the circuit model of computation is defined. Classical and quantum gate sets are compared to select some characteristic sets. The reachability and expressibility in a space-time-bounded setting for these gate sets are enumerated and visualized. These results are studied in terms of computational resources, universality, and quantum behavior. The article suggests how applications like geometric quantum machine learning, novel quantum algorithm synthesis, and quantum artificial general intelligence can benefit by studying circuit probabilities.