Crosstalk Insensitive Trapped-Ion Entanglement through Coupling Matrix Engineering

Abstract

Optical crosstalk due to imperfect addressing in trapped-ion entangling gates generates unwanted non-local entanglement between target ions and their 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 coupling matrix. By controlling the geometric phases generated in the motional modes of the ion string, we construct a coupling matrix that selectively excludes crosstalk-affected 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 crosstalk-insensitive entanglement in a three-ion string.

Figures (3)

• Figure 1: Crosstalk-insensitive qubit couplings. (a) A target gate (solid line) between two ions is driven using a laser (purple) incident on the two target ions. Spillover of the laser light onto ions neighboring the target ions results in crosstalk interactions (dashed lines). (b) The $\boldsymbol{J}^{(m)}$ single-mode coupling matrices of the radial modes of an equispaced $8$-ion string. The relative strengths of the target coupling (solid outline) and target-neighbor couplings (dashed outlines) depend on the mode. (c) A linear combination $\boldsymbol{J}$ of the single mode couplings matrices in (a) chosen such that the coupling of the target ions is nonzero but couplings between target and neighbor ions are zero.
• Figure 2: (a) The independence of the crosstalk and target gates, as indicated by the parameter $a_{t_1,t_2} = \lvert\lvert \text{proj}_{R^\perp}(\boldsymbol{g}^{(t_1,t_2)}) \rvert\rvert/\lvert\lvert \boldsymbol{g}^{(t_1,t_2)} \rvert\rvert$. (b) The infidelity $\mathcal{I}_\text{cross}$ due to target-neighbor crosstalk in a 20-ion equispaced string for multitone driving pulses optimized to eliminate target-neighbor crosstalk. Infidelity is calculated using Eq. \ref{['eq:infidelity_approximation']} using crosstalk $\epsilon=0.02$ and target gate angle $\Theta=\pi/4$. Higher target-crosstalk independence correlates with lower crosstalk infidelity from the optimized pulse.
• Figure 3: a) Parity between the target and center ion for single mode excitation (black, blue, and red) and composite gate (purple) as a function of crosstalk. The inset shows the single-mode coupling matrices $\boldsymbol{J}^{(m)}$ for the three modes and the composite coupling matrix $\boldsymbol{J}$. b) The parity between the two target ions (pale) and target-center ions (dark) for each gate at $\epsilon=0.25$.