Abstract
The design of a quantum computer and the design of a classical computer can be based on quite similar circuit designs. The former is based on the subgroup structure of the infinite group of unitary matrices, whereas the latter is based on the subgroup structure of the finite group of permutation matrices. Because these two groups display similarities as well as differences, the corresponding circuit designs are comparable but not identical.
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Acknowledgements
The authors thank the European COST Action IC 1405 ‘Reversible computation’ for its valuable support.
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De Vos, A., De Baerdemacker, S. (2018). A Unified Approach to Quantum Computation and Classical Reversible Computation. In: Kari, J., Ulidowski, I. (eds) Reversible Computation. RC 2018. Lecture Notes in Computer Science(), vol 11106. Springer, Cham. https://doi.org/10.1007/978-3-319-99498-7_9
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