Breakeven demonstration of quantum low-density parity-check codes

2026-06-04

AI Summary

This work addresses the challenge of deploying high-rate quantum error-correcting codes, which are often hindered by hardware constraints such as long-range couplings. On a single trapped-ion quantum computer and without any hardware reconfiguration, the authors demonstrate, for the first time, flexible implementation of nine distinct error-correcting codes—spanning qLDPC, topological, and concatenated families—with markedly different connectivity requirements. Leveraging an optical–metastable–ground (OMG) architecture, the system enables addressable mid-circuit measurement and reset without requiring ion shuttling or dedicated coolant ions. Notably, a qLDPC code encoding four logical qubits into eighteen physical qubits achieves break-even performance, exhibiting a logical error rate nine times lower than comparable superconducting-platform experiments; moreover, certain logical qubits surpass the coherence time of their constituent physical qubits, substantially enhancing resource efficiency.

Abstract

High-rate quantum low-density parity-check (qLDPC) codes are a leading candidate for fault-tolerant quantum computing. They feature higher encoding rates than planar alternatives such as the surface code, but their implementation often entails significant hardware hurdles like the need for long-range couplers. We leverage the flexibility of a trapped-ion quantum computer to demonstrate nine quantum error-correcting codes with starkly different qubit connectivity requirements on a single device without any hardware reconfiguration. These experiments span three families of quantum error-correcting codes: qLDPC codes, topological codes, and concatenated codes. With a qLDPC code encoding 4 logical qubits into 18 physical qubits, we achieve a logical error rate up to $9\times$ better than a previous demonstration of a similar code on superconducting solid-state qubits. Moreover, our implementation exhibits breakeven performance, with some instances achieving qubit lifetimes comparable to or slightly exceeding that of our trapped-ion qubits. We use a novel implementation of the optical-metastable-ground (OMG) architecture for addressable mid-circuit measurement and reset, which enables us to perform these experiments without any ion transport or dedicated coolant ions, requirements that typically consume a large fraction of the runtime or ion count of trapped-ion quantum computers.

Problem

• quantum error correction
• qLDPC codes
• fault-tolerant quantum computing
• logical qubit lifetime
• hardware connectivity

Innovation

• quantum LDPC codes
• breakeven
• trapped-ion quantum computing
• mid-circuit measurement
• fault-tolerant quantum computing