# Estimating Algorithmic Information Using Quantum Computing for Genomics Applications
## 6 Conclusions  
In this research, we presented a framework for empirically evaluating algorithmic metrics on a quantum accelerator. The estimation of the universal prior distribution and thereby the algorithmic complexity and algorithmic probability of finite sequences is theoretically the most optimal technique for inferring algorithmic structure in data for discovering causal generative models. These metrics are uncomputable but can be approximated in practice by restricting the time and memory resources available to the computational model. Nevertheless, due to the exponential scaling of the number of possible automata that need to be enumerated they are intractable except for the simplest of the cases on classical computation. Moreover, owing to the unstructured output and computational irreducibility, it is not possible to dequantized or approximate the computation using heuristics. In this work, we propose a quantum circuit framework to estimate the universal distribution by simulating a superposition of programs (or transition functions) for a resource-bounded automata. The quantum resource complexity scales linearly in qubits and gates with respect to the data or automata size, thus achieving a polynomial speedup over classical exhaustive enumeration. Thus, exploring the space of program-output relations is one of the most promising problems for demonstrating speedup using quantum search on the quantum supremacy roadmap. Specific properties of the program or output data can be inferred from the universal distribution represented as a quantum superposition.  
The algorithmic information theoretic approach of causal generative mechanism discovery is more theoretically sound than data-driven approaches such as deep learning, lossless compression and Shannon entropy-based correlation, allowing it to find causal insights missed by these approaches. As a use case, we presented a full experimental framework for using this approach on DNA sequences for meta-biology and genome analysis. This is the first time a quantum computation approach is implemented for approximating algorithmic information. We implemented our copy-left design on the Qiskit programming language and tested it using the quantum computing simulator. The availability of better quantum processors would allow this algorithm to be readily ported on a quantum accelerator with our quantum computing stack. With quantum-accelerated genome analysis, a better understanding of the algorithmic structures in DNA sequences would greatly advance domains such as personalized medication and artificial life.  
Conceptualization, A.S. and Z.A.-A.; methodology, A.S. and Z.A.-A.; software, A.S.; validation, A.S. and Z.A.-A.; formal analysis, A.S. and Z.A.-A.; investigation, A.S. and Z.A.-A.; writing--original draft preparation, A.S.; writing--review and editing, A.S., Z.A.-A. and K.B.; visualization, A.S. and Z.A.-A.; supervision, Z.A.-A. and K.B.; project administration, Z.A.-A. and K.B. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are openly available on GitHub at DOI:10.5281/zenodo.4607476.  
The authors declare no conflict of interest.