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In the process of research leading up to my previous question, I found out about matrix, vector & logical clocks.

The citation in the aforementioned question mentions clock and shift matrices. Wikipedia states:

These two matrices are also the cornerstone of quantum mechanical dynamics in finite-dimensional vector spaces as formulated by Hermann Weyl, and find routine applications in numerous areas of mathematical physics. The clock matrix amounts to the exponential of position in a "clock" of d hours, and the shift matrix is just the translation operator in that cyclic vector space, so the exponential of the momentum. They are (finite-dimensional) representations of the corresponding elements of the Weyl-Heisenberg on a d-dimensional Hilbert space.

I am curious to find out

  • if there is any usage of matrix, vector or logical clocks in quantum computing
  • how clock matrices and matrix clocks compare & contrast
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