Experimental implementation of a nonthermalizing quantum thermometer

Based on a quantum interferometric circuit, we implement a NMR quantum thermometer, in which a probe qubit measures the temperature of a nuclear spin at thermal equilibrium with a bath. The whole procedure lasts 5.5 ms, a much shorter time than the probe's spin-lattice relaxation time, which is T-i = 7.0 s. The fidelity of the probe final quantum state, in respect to the ideal theoretical prediction, is above 99 %. We show that quantum coherence is essential for the high fidelity of temperature measurement. We discuss the source of errors on the temperature measurement and some possible applications of the thermometer.