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Flux states of an RF SQUID are promising candidates for the implementation of quantum bits (qubits) for quantum computing. Accurate measurements of the flux states, especially in the time domain, require a controllable coupling between a qubit and a readout circuit (e.g., a dc SQUID magnetometer). Since the readout circuit can also be a source of decoherence, such a controllable coupling also allows one to control (minimize) the back action of the magnetometer. For this purpose we suggest a balanced, tunable transformer. This has a gradiometer configuration such that each arm is broken by a small loop containing two Josephson junctions. As a result the inductance of each arm can be adjusted by an applied bias flux. In the symmetrical case there is no coupling between the qubit and the magnetometer while a desired coupling can be achieved by changing the asymmetry of the arms. Similar transformers may be be useful for achieving controllable, lossless coupling that is required between qubits. Theoretical analysis of the noise back action of the transformer as well as preliminary experimental results are presented.