Process Tomography of Ion Trap Quantum Gates

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this Letter, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single-gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude-shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.

Figure 1

Process matrix obtained by process tomography of a gate operation implemented by pulse sequence ($B$) in Table . The absolute value, real part, and imaginary part of ${\chi }_{\mathrm{CNOT}}$ are shown in (a), (b), and (c), respectively. The matrix is expressed in terms of the products of the identity $\widehat{I}$ and the Pauli operators $\widehat{X}$, $\widehat{Y}$, and $\widehat{Z}$. In order to compensate for the rotation ${\widehat{U}}_Z$ the phase of all tomography pulses was shifted appropriately.

Figure 2

Absolute value of the measured process matrix resulting from two gate operations successively applied to a pair of ion qubits. Ideally the process matrix should only contain the $II$, $II$ element. The height of the $II$, $II$ element in the measured process matrix of 79.3% directly gives the process fidelity.