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Decompositions of average probability uninitialized sequential quantum machines

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Abstract

Sequential quantum machines (SQMs) are the quantum version of probabilistic transition systems. As important quantum automata, SQM has strong computing power. Uninitialized sequential quantum machines (USQMs) are sequential quantum machines which have no initialized states, and average probability USQMs are special USQMs. The main purpose of this paper is to study homomorphic relations between products of USQMs and investigate decompositions of average probability USQMs. We firstly discuss some homomorphic relations between products of USQMs. We then give definitions of probability homomorphism and probability decomposition of USQMs, and give definitions of general probability homomorphism and general probability decomposition of USQMs. Furthermore, we prove two decomposition theorems of average probability uninitialized sequential quantum machines. Finally, we give some examples to illustrate these two decomposition theorems.

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Acknowledgements

This work is supported by National Social Science Foundation (No.20XZX017), and Growth Project of Young Scientific and Technological Talents in Universities of Guizhou Province (No. KY[2019]157 and No. KY[2020]144).

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  1. Department of Mathematics, Guizhou University of Engineering Science, Bijie, China

    Feidan Huang

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  1. Feidan Huang
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Correspondence to Feidan Huang.

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Huang, F. Decompositions of average probability uninitialized sequential quantum machines. Soft Comput 26, 5965–5974 (2022). https://doi.org/10.1007/s00500-022-07063-2

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