The number of measurements necessary to perform the quantum state
reconstruction of a system of qubits grows exponentially with the number of
constituents, creating a major obstacle for the design of scalable tomographic
schemes. We work out a simple and efficient method based on cyclic generation
of mutually unbiased bases. The basic generator requires only Hadamard and
controlled-phase gates, which are available in most practical realizations of
these systems. We show how complete sets of mutually unbiased bases with
different entanglement structures can be realized for three and four qubits. We
also analyze the quantum circuits implementing the various entanglement
classes.Comment: 5 pages, 2 color figures. Comments welcome
