Quantum Accelerated Causal Tomography: Circuit Considerations Towards Applications

In this research we study quantum computing algorithms for accelerating causal inference. Specifically, we investigate the formulation of causal hypothesis testing presented in [\textit{Nat Commun} 10, 1472 (2019)]. The theoretical description is constructed as a scalable quantum gate-based algorithm on qiskit. We present the circuit construction of the oracle embedding the causal hypothesis and assess the associated gate complexities. Our experiments on a simulator platform validates the predicted speedup. We discuss applications of this framework for causal inference use cases in bioinformatics and artificial general intelligence.Comment: 9 pages, 5 figure

Visualizing Quantum Circuit Probability -- estimating computational action for quantum program synthesis

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.Comment: 17 page

Visualizing Quantum Circuit Probability: Estimating Quantum State Complexity for Quantum Program Synthesis

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