Trapped-ion QEC Enables Scaling Roadmaps for Modular Architectures and Lattice-Surgery Teleportation

The pursuit of practical quantum computation demands scalable methods for correcting errors, and researchers are now charting a course toward building larger, more robust quantum processors. César Benito, Alfredo Ricci Vasquez, and Jonathan Home, alongside colleagues from Cornell University, RWTH Aachen University, and the University of Innsbruck, investigate the feasibility of scaling modular quantum error correction using trapped ions. Their work focuses on triangular colour codes and a technique called lattice surgery for teleporting quantum information, comparing architectures that utilise either laser-beam steering or integrated photonics to connect individual modules of trapped ions. By meticulously modelling noise and simulating performance with advanced decoding techniques, the team demonstrates that modular colour-code teleportation is within reach using current trapped-ion technology, and crucially, identifies integrated photonics as the most promising pathway for building significantly larger quantum computers in the future.

This approach connects multiple, smaller trapped-ion modules to create a larger, more powerful quantum processor, overcoming limitations of single modules. The modular architecture supports surface codes, a leading method for quantum error correction, by distributing encoded qubits across modules, reducing the physical qubit overhead needed for reliable computation. The team also investigates lattice-surgery teleportation, a protocol for transferring quantum information between distant qubits without physically moving ions, which is vital for long-distance communication and distributed computing, and demonstrates its efficient implementation within the modular system.

The analysis assesses the resources, including entangled pairs and two-qubit gates, required for high-fidelity teleportation. Key findings include a detailed evaluation of scaling requirements for both quantum error correction and lattice-surgery teleportation in a modular trapped-ion system, alongside a roadmap for achieving fault-tolerant quantum computation. The work identifies critical parameters, such as module connectivity and gate fidelity, that must be optimised to build scalable quantum processors, and proposes strategies for overcoming challenges associated with large-scale modular systems. This architecture has the potential to support advanced quantum algorithms and applications, paving the way for practical quantum technologies.

Researchers present a detailed analysis of the scaling of modular quantum error correction protocols, specifically those designed for triangular color codes, including lattice-surgery-based logical teleportation. The study compares architectures based on trapped ions, differing in their connectivity technology and modularity requirements. One architecture uses laser-beam deflectors focused on independent modules hosting mid-size ion crystals, while the other employs integrated photonics guiding manipulation of smaller ion crystals. The approach integrates the implementation of quantum error correction into native trapped-ion operations and provides a detailed assessment of the area required for implementation.

Trapped Ion Quantum Computing Foundations and Entanglement

The field of trapped ion quantum computing encompasses significant advancements in hardware, control, and software. Foundational work by Leibfried and colleagues established the principles of quantum dynamics of single trapped ions, while early research by Mølmer and Sørensen explored multiparticle entanglement and computation with ions in thermal motion. Recent studies, such as those by Home, have expanded the use of mixed-species ion chains for quantum science and metrology. Ongoing research focuses on improving ion trap technology and fabrication, including the development of race-track traps and detailed measurements of electric-field noise near surfaces, which is crucial for understanding decoherence.

Scientists are also exploring various qubit implementations, including Zeeman qubits, metastable states, and optical qubits, to optimise performance and achieve long-lived qubit memory. Achieving high-fidelity Bell-state preparation with calcium-40 optical qubits represents a significant step forward, as does the development of wavelength-insensitive entangling gates for group-2 atomic ions. Reducing ion motion is critical for maintaining coherence, leading to the development of advanced cooling techniques, such as polarization-gradient cooling and electromagnetically-induced-transparency ground-state cooling. Researchers are also investigating methods to mitigate motional heating and noise, major sources of decoherence.

Significant progress has been made in implementing high-fidelity entanglement and logic gates, with experiments demonstrating entanglement of four particles and robust two-qubit phase gates. Strategies for fault-tolerant circuit design in noisy trapped-ion quantum computers are also under development. The use of mixed-species ions offers enhanced capabilities, while advancements in shuttling-based quantum information processing are paving the way for more complex architectures. Simulation tools are also playing a vital role in the field, enabling researchers to model and optimise quantum circuits. Key themes include mitigating decoherence, improving scalability, achieving high-fidelity gates, optimising qubit technology, and developing effective error correction strategies. Precise control of ion motion and accurate measurement of qubit states remain central to the advancement of trapped ion quantum computing.

Modular Teleportation with Trapped Ions and Photonics

Researchers have demonstrated the feasibility of modular quantum error correction using triangular color codes, a promising approach for building large-scale quantum computers. They modeled and compared two trapped-ion architectures, one using laser-beam deflectors and the other employing integrated photonics, to assess their suitability for implementing quantum error correction protocols, specifically logical teleportation. The analysis confirms that modular color-code teleportation is achievable with current technology, marking a significant step towards practical quantum computation. The team highlights integrated photonics as the more promising architecture for future scaling, due to its potential for improved connectivity and control.

They achieved this by integrating the requirements of quantum error correction into realistic trapped-ion operations and developing a detailed noise model that accounts for imperfections in laser addressing, ion transport, and qubit idle time. While performance is currently limited by the complexity of deeper circuits needed for stabilizer readout and decoding, simplified approaches for extracting error information are particularly relevant for near-term processors. Future work will focus on optimising dynamic circuits for stabilizer measurements and exploring more sophisticated decoding strategies, as well as continued development of integrated photonics to fully realise its potential for scalable quantum computation.