Josephson Junction Comparator as a Quantum-Limited Detector for Flux Qubit Readout

We have applied the Langevin-Heisenberg-Lax formalism for dissipative quantum systems to a balanced Josephson junction comparator operating as a fast, single-shot detector of state of a flux (rf-SQUID) qubit. Earlier experiments and theoretical analysis have shown that such a detector may reach quantum- limited resolution when it measures signal from a high-impedance (current) source. In this work, we have calculated the flux resolution of a detector for a signal source with finite inductive impedance (e.g., a flux qubit) for both an instant switching of the comparator, and for its switching with a realistic SFQ driver. The results show that the flux resolution may be quite high: for typical experimental parameters, the signal-to-noise ratio may be on the order of 10, at 10-ps-scale measurement time. Moreover, the natural energy measure of the resolution, E_out, may be made (within a narrow range of parameters) smaller than planck/2. This situation is similar to the case of continuous flux measurements using SQUIDs. In both cases, a more adequate sensitivity measure requires an account of the fluctuation back-action of the detector on the signal source. In this work we have shown that in the case of single-shot measurements, the back-action effects as characterized by the "information/dephasing" measure, may be brought down to their fundamental limit by at least two methods: coupling quenching and feedback compensation.