A Unified Approach to Quantum Computation and Classical Reversible Computation

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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