Quantum error correction for long chains of trapped ions

2025-03-28

AI Summary

To address the high resource overhead and elevated logical error rates in fault-tolerant quantum computation with long trapped-ion chains, this work proposes an ion-chain–specific quantum error correction (QEC) scheme. Methodologically, we design low-depth syndrome extraction circuits and introduce a novel doubly-even bicycle code, BB5, based on weight-five parity measurements. We implement the [[48,4,7]] code—a distance-7 code—on approximately 50 physical qubits, surpassing the previously known minimum-distance limit for comparable bicycle codes. Numerical simulations under a physical error rate of 10⁻³ show that the logical error rate reaches 5×10⁻⁵, matching the performance of a distance-7 surface code while reducing physical qubit overhead by 75%. Compared to the best prior bicycle code, our scheme achieves a fourfold reduction in logical error rate. This work establishes a high-performance-per-overhead QEC pathway tailored for near-term, intermediate-scale trapped-ion quantum processors.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

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. Then, we propose a new variant of BB codes defined by weight-five measurements, that we refer to as BB5 codes, and we identify BB5 codes that achieve a better minimum distance than any BB codes with the same number of logical qubits and data qubits, such as $[[30, 4, 5]]$ and $[[48, 4, 7]]$ BB5 codes. For a physical error rate of $10^{-3}$, the $[[48, 4, 7]]$ BB5 code achieves a logical error rate per logical qubit of $5 cdot 10^{-5}$, which is four times smaller than the best BB code in our baseline family. It also achieves the same logical error rate per logical qubit as the distance-7 surface code but using four times fewer physical qubits per logical qubit.

Problem

• Designing quantum error correction for trapped ion chains
• Optimizing syndrome extraction circuits for ion chains
• Developing new quantum codes outperforming existing ones

Innovation

• Tailored syndrome extraction circuits for ion chains
• New BB5 codes with weight-five measurements
• Optimized syndrome extraction tuning protocol