01164nas a2200121   4500000000100000000000100001008004100002260001100043245011100054856004400165490000700209520082600216       2023                            d  c5/202300aVisualizing quantum circuit probability: estimating quantum state complexity for quantum program synthesis  uhttps://www.mdpi.com/1099-4300/25/5/7630 v253 a<p>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.</p>