Visualizing Quantum Circuit Probability
Estimating Quantum State Complexity for Quantum Program Synthesis
Bao Gia Bach (Ho Chi Minh City University of Technology (HCMUT))
Akash Kundu (Silesian University of Technology, Polish Academy of Sciences, Student TU Delft)
Tamal Acharya (Student TU Delft)
A. Sarkar (TU Delft - QuTech Advanced Research Centre, TU Delft - QCD/Feld Group)
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Abstract
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.
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