A circular shift operator (or cyclic rotation gate) \({{\,\mathrm{\texttt {ROT}}\,}}_k\) applies a rightward (or leftward) shift to an input register of n qubits o by as many positions as encoded by an additional input \(k \in \mathbb N\) . Specifically, the qubit at position x is moved to position \((x+k) \mod n\) . While it is known that there exists a quantum rotation operator that can be implemented in \({{\,\mathrm{\mathcal {O}}\,}}(\log (n))\) -time, through the repeated parallel application of the elementary \({{\,\mathrm{\texttt {Swap}}\,}}\) operators, there is no systematic procedure that concretely constructs the quantum operator \({{\,\mathrm{\texttt {ROT}}\,}}\) for variable size n of the quantum register and a variable parameter k. We fill the gap, providing a systematic implementation of the cyclic rotation operator (denoted \({{\,\mathrm{\texttt {ROT}}\,}}\) ) in a quantum circuit model of computation whose depth is \({{\,\mathrm{\mathcal {O}}\,}}(\log (n))\) . We show how the circular shift operator can be utilized in quantum approaches to text processing, focusing on the problem of getting all possible cyclic rotations of a string in \({{\,\mathrm{\mathcal {O}}\,}}(\log ^2(n))\) depth.
