Cyclic Hypergraph Product Codes Achieve Surface Code Error Rates with Reduced Qubit Overhead Via Exhaustive Search

Hypergraph product codes represent a promising approach to quantum error correction, offering the potential to reduce the number of qubits needed to protect quantum information, and recent work by Arda Aydin from the University of Maryland, College Park, and Nicolas Delfosse and Edwin Tham from IonQ Inc, significantly advances this field. The team systematically explores a specific class of hypergraph product codes, termed CxC codes, built from the product of cyclic and repetition codes, and discovers designs that dramatically outperform existing codes. Results demonstrate a reduction in logical error rates of up to three orders of magnitude per logical qubit, surpassing the performance of established codes like bivariate bicycle codes in some instances. Crucially, the researchers also leverage the inherent symmetry of these new codes to develop a streamlined architecture for implementation on trapped ion quantum computers, paving the way for practical, efficient syndrome extraction circuits.

Hypergraph Product Codes Correct Quantum Errors

Scientists are making significant progress in protecting quantum information from errors with a new focus on hypergraph product (HGP) codes. These codes offer a promising route to reliable quantum computation by encoding information in a way that tolerates the inherent fragility of quantum states. Researchers are now demonstrating that carefully designed HGP codes can substantially improve the stability of quantum calculations by optimizing the structure of these codes, specifically how errors are detected without disturbing the quantum information itself. Researchers are achieving improvements in both the code rate, which determines how much logical quantum information can be stored per physical qubit, and the error threshold, which indicates how much error the code can tolerate before failing. By increasing both of these parameters, scientists are moving closer to building practical, scalable quantum computers.

Cyclic Hypergraph Codes for Quantum Error Correction

Scientists have pioneered a new approach to quantum error correction by constructing hypergraph product (HGP) codes from cyclic codes. Rather than relying on complex machine learning techniques, researchers imposed global symmetries, specifically cyclicity, to drastically simplify the search for optimal code configurations. This systematic approach involved exhaustively exploring combinations of cyclic and repetition codes, leading to the discovery of high-performing codes suitable for practical implementation. Detailed simulations reveal that these cyclic HGP codes significantly outperform previously optimized codes.

A specific code, with parameters [[882, 50, 10]], achieved a logical error rate substantially lower than a comparable code optimized using machine learning. Another code, [[450, 32, 8]], achieved the same error-correcting capability with fewer qubits, while maintaining a low error rate. Remarkably, the performance of these cyclic HGP codes is comparable to that of bivariate bicycle (BB) codes, with some instances simultaneously achieving lower error rates and smaller qubit overhead. Researchers also designed a planar layout for these codes, compatible with architectures utilizing flying qubits, paving the way for practical implementation on quantum computing platforms.

Cyclic Hypergraph Codes Correct Errors Dramatically

Scientists have achieved a significant breakthrough in quantum error correction by developing cyclic hypergraph product (CxC) codes that substantially outperform previously optimized codes. This work focuses on constructing codes from cyclic codes, specifically C2 codes and CxR codes. Through an exhaustive search leveraging these symmetries, researchers discovered codes with parameters and performance exceeding those of existing methods. Experiments reveal that these cyclic HGP codes deliver a logical error rate per logical qubit up to three orders of magnitude better than previous designs. Notably, a [[882, 50, 10]] C2 code achieved a logical error rate below 2×10⁻⁸, a dramatic improvement over a comparable code.

Another C2 code, [[450, 32, 8]], reached the same minimum distance as earlier designs but with a shorter block length and more logical qubits. Even the simpler CxR codes demonstrated significantly improved performance. These CxC codes achieve comparable performance to state-of-the-art bivariate bicycle (BB) codes in terms of both logical error rate and qubit overhead. The team designed an efficient planar layout for these codes, compatible with a quantum charge-coupled device (QCCD) architecture, enabling constant-depth syndrome extraction for LDPC codes. This layout utilizes a 2×n array of qubits with a cyclic shift, simplifying qubit interactions and making the codes practically relevant for platforms employing flying qubits, such as photonic qubits, spin qubits, or trapped ions. These results demonstrate a substantial advancement in quantum error correction, offering a pathway to more robust and efficient quantum computation.

Cyclic Hypergraph Codes Lower Logical Error Rates

Scientists are presenting a new approach to designing high-performance quantum error-correcting codes, specifically within the family of hypergraph product codes. Researchers achieved significant improvements by focusing on codes constructed from cyclic codes, termed CxC codes, and exhaustively searching for optimal configurations based on inherent symmetries. The resulting C2 and CxR codes demonstrably outperform previously optimized hypergraph product codes, achieving logical error rates per logical qubit up to three orders of magnitude lower. Notably, some of these newly discovered codes simultaneously offer reduced logical error rates and smaller qubit overhead compared to established codes like bivariate bicycle codes.

Furthermore, the team designed an efficient planar layout for these codes, compatible with trapped ion quantum computing architectures, enabling constant-depth syndrome extraction circuits. This efficient layout is particularly advantageous for practical hardware implementation. While acknowledging that their work concentrates on code design and fault-tolerant memory, leaving the development of logical gates for future research, this work establishes hypergraph product codes as a continuing viable candidate for long-term fault tolerance in quantum computation.