Crosstalk suppression of parallel gates for fault-tolerant quantum computation with trapped ions via optical tweezers

The ability to perform entangling operations in parallel with a low error is essential for a large-scale fault-tolerant quantum computer. However, for trapped-ion systems, it is a challenging task due to the crosstalk resulting from the collective motional modes. Here, we develop a highly paralleled quantum circuit demonstrating a logical qubit based on the Steane code and study the impact of the crosstalk error on the performance of the fault-tolerant protocol. We show that the crosstalk indeed greatly destroys the fault-tolerant property of the quantum error correction. To achieve the break-even point with encoded qubits, we identify the suppression requirement of the crosstalk error to be less than ${10}^{\ensuremath{-}6}$ for the Steane code. Furthermore, to mitigate the crosstalk below the fault-tolerant threshold, we propose a highly efficient optimization scheme by utilizing the programmable optical tweezer array. Overall, we make an elegant combination of the pulse-control optimization of parallel gate operations with the fault-tolerant protocol on the error-protected universal quantum computer.