Fig. 3: Experimental results for testing the error-tradeoff relations in superconducting quantum processor “ScQ-P136” accessed through the Quafu cloud quantum computation platform.
a Scheme diagram to evaluate the mean squared error of each Xj using the “3-state method''. b Error-tradeoff relations for the simultaneous measurement of three spin operators, \(\{\frac{1}{2}{\sigma }_{x},\frac{1}{2}{\sigma }_{y},\frac{1}{2}{\sigma }_{z}\}\), on a pure state \(\left\vert \psi \right\rangle ={R}_{z}(\frac{\pi }{2}){R}_{y}(\theta )\left\vert 0\right\rangle\). c Error-tradeoff relations for the simultaneous measurement of three spin operators, \(\{\frac{1}{2}{\sigma }_{x},\frac{1}{2}{\sigma }_{y},\frac{1}{2}{\sigma }_{z}\}\), on a mixed state \(\rho =p\left\vert 0\right\rangle \left\langle 0\right\vert +(1-p)\left\vert 1\right\rangle \left\langle 1\right\vert\). For both cases, the statistics of each measurement was obtained through 2000 shots and the error bars represent the standard deviations obtained by repeating the experiment 20 times.
