Gaoxiang Tang

The ability to execute a large number of quantum gates in parallel is a fundamental requirement for quantum error correction, allowing an error threshold to exist under the finite coherence time of physical qubits. Recently, two-dimensional ion crystals have been demonstrated as a plausible approach to scale up the qubit number in a trapped ion quantum computer. However, although the long-range Coulomb interaction between the ions enables their strong connectivity, it also complicates the design of parallel gates and leads to intrinsic crosstalk errors. Here we examine the effects of crosstalk errors on a rotated surface code. We show that, instead of the distance-3 code considered in previous works, a distance-5 code is necessary to correct the two-qubit crosstalk error. We numerically calculate the logical error rates and coherence times under various crosstalk errors, gate infidelities and coherence times of the physical qubits, and we optimize the parallelism level according to the competition between different error sources. We show that a break-even point can be reached under realistic parameters. We further analyze the spatial dependence of the crosstalk, and discuss the scaling of the logical error rate versus the code distance for the long-term goal of a logical error rate below $10^{-10}$.

To achieve the entangling gate fidelity above the quantum error correction threshold, it is critical to suppress errors due to experimental imperfection. We consider the Mølmer-Sørensen gates in trapped-ion systems, and develop a general approach to suppress a family of noise sources that appeared as either symmetric or asymmetric errors. Using the time-average displacement minimization technique, both symmetric error and displacement-dependent part of the asymmetric errors are eliminated. Then, by analyzing the tangent space of displacement-independent errors, we obtain the analytic form of the generators of the correction operator to the remaining error terms. We then develop a compensation pulse to fully suppress the remaining displacement-independent errors. The effectiveness of our scheme is further verified by numerical analysis, through which we observe a significant reduction of entangling gate infidelity. Our findings enhance gate fidelity and robustness to noise for ion trap quantum computing.