Quantum error correction for long chains of trapped ions

Understand

We propose a model for quantum computing with long chains of trapped ions and we design quantum error correction schemes for this model.

• The main components of a quantum error correction scheme are the quantum code and a quantum circuit called the syndrome extraction circuit, which is executed to perform error correction with this code.
• In this work, we design syndrome extraction circuits tailored to our ion chain model, a syndrome extraction tuning protocol to optimize these circuits, and we construct new quantum codes that outperform the state-of-the-art for chains of about $50$ qubits.
• To establish a baseline under the ion chain model, we simulate the performance of surface codes and bivariate bicycle (BB) codes equipped with our optimized syndrome extraction circuits.