Quantum Process Tomography of a Controlled-NOT Gate

We demonstrate complete characterization of a two-qubit entangling process—a linear optics controlled-not gate operating with coincident detection—by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.

Figure 1

Process matrix of the cnot gate [37]. (a) Ideal process matrix, in the basis defined by tensor products of Pauli operators (imaginary part is identically zero). (b) Maximum-likelihood experimental process matrix. (c) Histogram of the differences in probability between experimental data and the maximum-likelihood reconstruction for the 256 tomographic measurements. The Gaussian fit $\gamma \exp (-{\Delta }^2/{\sigma }^2)$ has $\sigma =0.021$. (d) Real part of the experimentally determined process matrix, expressed in the cnot operator basis, where the 00 element represents the component of $U_{\mathrm{C}\mathrm{N}\mathrm{O}\mathrm{T}}$ in the process. The elements' imaginary parts are negligible, except for one coherence of magnitude 0.06. In this basis, an ideal cnot has a unit-valued 00 element; all other elements are zero. The abscissaes are the abscissas of (a) and (b), multiplied by ${\widehat{U}}_{\mathrm{C}\mathrm{N}\mathrm{O}\mathrm{T}}.$

Figure 2

(a) State fidelity of our cnot gate outputs (with ideal cnot output states) calculated from $\tilde{\chi }$, plotted against the linear entropy added by the gate. A perfect experimental cnot process would have $F=1$, $S=0$ for all states. (b) Change in tangle between input and output, and linear entropy added, for our cnot gate outputs, calculated from $\tilde{\chi }$. An ideal cnot would have points with $\Delta T$ distributed between $-1$ and 1, and $S=0$.