This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. 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.

翻译：本研究将算法概率的概念应用于布尔和量子组合逻辑电路。文中首先以教程形式介绍了状态及其复杂性的多种概念。随后，定义了计算模型电路中状态的概率。通过比较经典与量子门集合，选取了若干特征集。在时空有界设定下，枚举并可视化了这些门集合的可达性与可表达性。研究从计算资源、普适性和量子行为的角度分析了这些结果。本文指出，通过研究电路概率，几何量子机器学习、新型量子算法合成以及量子通用人工智能等应用领域将从中受益。