Crosstalk Insensitive Trapped-Ion Entanglement through Coupling Matrix Engineering

Optical crosstalk due to imperfect addressing in trapped-ion entangling gates generates unwanted nonlocal entanglement between target ions and their combined set of neighbors that is difficult to mitigate using standard quantum error correction. We present a method to design entangling operations that are inherently insensitive to crosstalk by engineering the effective qubit-qubit coupling matrix. By controlling the geometric phases generated in the motional modes of the ion string, we engineer a coupling matrix that selectively excludes coupling between target and neighbor ions from the entangling operation. This approach requires no knowledge of the amount of crosstalk present and avoids the need for additional gate operations or modifications to the optical setup. We numerically demonstrate the construction of crosstalk-insensitive entangling pulses for target ion pairs within an equispaced 20-ion string and provide experimental validation of coupling matrix engineering for crosstalk-insensitive entanglement in a 3-ion string.