Fast quantum limited readout of a superconducting qubit using a slow oscillator
Göran Johansson, Lars Tornberg, Christopher M. Wilson · Physical Review B · 2006
We describe how to perform fast quantum limited readout of a solid state qubit biased at its degeneracy point. The method is based on homodyne detection of the phase of a microwave signal reflected by a slow oscillator coupled to the qubit. Analyzing the whole quantum readout process, we find that the detection is indeed quantum limited and that this limit may be reached even using a resonance circuit with a low quality factor, thus enabling the use of short measurement pulses. As an example, we discuss in detail the readout of a Cooper-pair box capacitively coupled to a lumped element $\mathit{LC}$ oscillator. Furthermore, we give formulas for the backaction while not measuring, and discuss optimal parameters for a realistic design capable of fast $(\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{ns})$ single-shot readout.