Performance Analysis for Crosstalk Errors between Parallel Entangling Gates in Trapped Ion Quantum Error Correction

TL;DR

This paper investigates how crosstalk errors affect parallel entangling gates in trapped ion quantum computers, demonstrating the need for larger codes and optimizing parallelism to achieve low logical error rates.

Contribution

It shows that a distance-5 surface code is required to correct crosstalk errors and provides a numerical analysis of error rates, guiding the design of scalable quantum error correction.

Findings

A distance-5 code corrects crosstalk errors effectively.

Logical error rates can reach break-even under realistic parameters.

Crosstalk spatial dependence impacts scaling of logical error rates.

Abstract

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 $10^{-10}$.