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We present a construction method for complete sets of cyclic mutuallyunbiased bases (MUBs) in Hilbert spaces of even prime power dimensions. Incomparison to usual complete sets of MUBs, complete cyclic sets possess theadditional property of being generated by a single unitary operator. Theconstruction method is based on the idea of obtaining a partition ofmulti-qubit Pauli operators into maximal commuting sets of orthogonal operatorswith the help of a suitable element of the Clifford group. As a consequence, weexplicitly obtain complete sets of cyclic MUBs generated by a single element ofthe Clifford group in dimensions $2^m$ for $m=1,2,...,24$.

Complete sets of cyclic mutually unbiased bases in even prime power dimensions