Quantum error correction represents a crucial step towards building practical quantum computers, and researchers continually seek ways to simplify the complex circuitry required to protect quantum information. Runshi Zhou from Tsinghua University, alongside Fang Zhang, Hui-Hai Zhao, and colleagues at Zhongguancun Laboratory, present a new framework called Louvre that significantly relaxes the hardware demands of a promising class of quantum codes known as generalized bicycle codes. Louvre achieves this by intelligently routing information within the quantum processor, effectively reducing the number of connections needed between quantum bits. This innovation lowers the complexity of the required hardware, making these codes more feasible to implement, and simulations demonstrate that Louvre maintains, or only slightly increases, the accuracy of error correction, even with fewer connections. By minimising long-range connections, Louvre offers a distinct advantage over previous approaches and broadens the potential for practical quantum error correction architectures.
Connectivity represents a crucial challenge in realising large-scale quantum computation. A subclass of graph-based (GB) codes, known as bivariate bicycle codes (BB codes), has attracted considerable interest due to its compatibility with two-layer connectivity architectures on superconducting quantum processors. Building on recent progress in implementing multiple two-qubit gates on a single chip, this work introduces Louvre, a routing-based framework designed to reduce qubit connectivity requirements in GB codes.
Superconducting Qubit Implementation of Quantum Error Correction
This research details advancements in quantum error correction (QEC) and the practical implementation of these codes on superconducting qubit hardware. It explores various code designs, routing techniques, and hardware considerations to improve the feasibility of building fault-tolerant quantum computers. The work moves beyond theoretical QEC codes, focusing on how to actually implement them on real hardware. This involves addressing challenges related to qubit connectivity, routing, and minimizing overhead, emphasizing the need for codes that are not just theoretically good, but also hardware-efficient.
The research investigates and optimizes Generalized Bicycle codes, aiming to reduce the required connectivity and overhead. Quantum Low-Density Parity-Check (LDPC) codes are also explored, particularly for long-range connected qubit architectures. The team delves into geometric codes, including planar codes, and their potential for efficient implementation, alongside quantum two-block group algebra codes. A technique called tangling schedules is explored to ease hardware connectivity requirements. Efficient routing of quantum information is a major bottleneck in implementing QEC.
The use of 3D integrated superconducting qubits is explored as a way to increase connectivity and reduce routing distances. The research investigates and adapts classical wire routing algorithms, like those used in VLSI design, considering algorithms by Bastert and Fekete, Pach and Wenger, and Schaefer. Algorithms for placing and routing non-local QEC codes on multi-layer superconducting qubit hardware are developed, alongside a routing-based technique called Halma for defect mitigation. Improving qubit connectivity is a recurring theme, explored through increasing connectivity via hardware (3D integration) and reducing the need for connectivity through code design and routing.
The use of Through-Silicon Vias (TSVs) is investigated to create more complex and efficient qubit connections, alongside multi-layer qubit architectures to increase density and connectivity. Techniques for mitigating the impact of defects in qubit hardware are also explored. The paper emphasizes the need to balance the theoretical performance of a QEC code with the practical challenges of implementing it on real hardware. Efficient routing algorithms are crucial for minimizing overhead and maximizing the performance of QEC. 3D integrated qubit architectures offer a promising path towards increasing connectivity and reducing routing distances.
Classical wire routing algorithms can be adapted and applied to the quantum domain to solve routing problems. The work reports on demonstrations of low-overhead QEC codes, showcasing progress towards building fault-tolerant quantum computers. In essence, this research represents a significant step towards bridging the gap between theoretical quantum error correction and practical implementation.
Louvre Framework Reduces Qubit Connectivity in Codes
Researchers have developed a new framework, Louvre, to significantly reduce the connectivity requirements of generalized bicycle (GB) codes, a promising family of quantum error correction codes. Louvre addresses this challenge by strategically routing connections within the code, minimizing the number of direct links required between qubits while preserving the efficiency of error correction. The team introduced two primary schemes, Louvre-7 and Louvre-8, both designed to reduce the degree of the GB codes. Louvre-7 achieves this reduction without increasing the complexity of the syndrome extraction circuit, while Louvre-8 further minimizes connectivity, accepting a slight increase in circuit depth as a trade-off.
When applied to bivariate bicycle (BB) codes, these schemes successfully reduce the average qubit connection requirement to 4. 5 with Louvre-7 and 4 with Louvre-8, representing a substantial improvement over previous designs. Crucially, Louvre eliminates long-range connections, which are particularly vulnerable to errors. Numerical simulations demonstrate that Louvre-7 performs indistinguishably from standard GB code syndrome extraction circuits in terms of logical error rate, while Louvre-8 incurs only a minor penalty. Furthermore, by intelligently reordering the sequence of operations, researchers were able to shorten the physical distance between connected qubits without compromising performance. These advancements extend beyond specific code configurations, as Louvre is adaptable to various grid layouts, including those with open boundaries or defects. This work paves the way for building more robust and scalable quantum computers by simplifying the physical connections required for error correction, bringing the realization of fault-tolerant quantum computation closer to reality.
Louvre Framework Simplifies Quantum Error Correction
This research introduces Louvre, a routing-based framework designed to simplify the connectivity requirements of generalized bicycle codes. Louvre achieves a reduction in the number of connections needed while maintaining, or only slightly increasing, the complexity of the error-correction process. Specifically, two versions of the framework, Louvre-7 and Louvre-8, reduce the average connection degree to 4. 5 and 4 respectively, when applied to bivariate bicycle codes. The key innovation lies in strategically re-routing connections within the code, eliminating some of the longer-range, error-prone links that characterize previous approaches.
Numerical simulations demonstrate that Louvre-7 performs comparably to standard error-correction circuits, while Louvre-8 exhibits a small increase in error rate. Furthermore, the researchers show that by reordering the sequence of operations, they can shorten the physical distance between connected qubits without compromising performance. The adaptability of Louvre to different grid layouts suggests its potential for practical implementation in various quantum computing architectures. This work represents a significant step towards building more robust and scalable quantum error correction systems.
👉 More information
🗞 Louvre: Relaxing Hardware Requirements of Quantum LDPC Codes by Routing with Expanded Quantum Instruction Set
🧠ArXiv: https://arxiv.org/abs/2508.20858