Researchers Develop Lightweight Error-correcting Codes for Superconducting Circuits

Data transmission between superconducting circuits and conventional electronics faces a critical challenge, as signals are vulnerable to errors caused by factors like manufacturing imperfections and variations in operating conditions. Yerzhan Mustafa from the University of Rochester, Berker Peköz from Embry-Riddle Aeronautical University, and Selçuk Köse from the University of Rochester, address this issue by developing compact error-correction codes specifically designed for these systems. The team proposes three lightweight encoders, based on established Hamming and Reed-Muller codes, and implements them using superconducting logic. This research is significant because it demonstrates how to protect data integrity within the tight size and power constraints of superconducting electronics, paving the way for more reliable and efficient quantum and cryogenic computing systems.

Data transmission from superconducting electronic circuits, such as those employing single flux quantum (SFQ) logic, is susceptible to bit errors. These errors stem from factors including flux trapping, manufacturing defects, and variations during the fabrication process. Limited cooling power and chip area constrain the complexity of error-correction code encoders. This research introduces three lightweight error-correction code encoders, Hamming(7,4), Hamming(8,4), and Reed-Muller(1,3), all implemented using SFQ logic. The team meticulously analysed the performance of these encoders, specifically considering the impact of variations that occur during manufacturing.

SFQ Logic Enables Lightweight Error Correction

Researchers have developed three lightweight error-correction code encoders, Hamming(7,4), Hamming(8,4), and Reed-Muller(1,3), designed for use with superconducting electronic circuits. These encoders address the critical issue of bit errors that arise during data transmission from superconducting circuits to room-temperature electronics, a problem caused by factors like flux trapping and variations during the manufacturing process. The team implemented these codes using SFQ logic, a technology well-suited for high-speed digital circuits, and meticulously analysed their performance under realistic conditions. The designs prioritize minimizing circuit complexity while maximizing error correction capabilities.

Error Correction Boosts Superconducting Circuit Reliability

This work demonstrates the feasibility of employing lightweight error-correction codes, specifically Hamming(7,4), Hamming(8,4), and Reed-Muller(1,3), within superconducting electronic circuits to improve data transmission reliability. The research focuses on mitigating bit errors that arise when transmitting signals from cryogenic temperatures to room temperature, a challenge stemming from factors like flux trapping and fabrication imperfections. By implementing these codes using single flux quantum (SFQ) logic, the team analysed their performance in the presence of variations that occur during manufacturing, identifying trade-offs between code complexity and physical size.

The team evaluated each encoder’s performance through detailed simulations, incorporating process parameter variations (PPV) of up to ±20% to mimic the imperfections inherent in fabrication. Results demonstrate that the Hamming(8,4) code encoder achieves the highest level of error correction, providing a 92. 7% probability of receiving 100 messages with no errors. This represents a significant improvement over a system without any error correction, which only achieves an 80. 0% probability.

Further analysis revealed a trade-off between theoretical code complexity and physical circuit size. While the Reed-Muller(1,3) code initially appeared promising, its implementation required a larger number of Josephson junctions, the fundamental building blocks of SFQ circuits, increasing the likelihood of circuit failure due to manufacturing variations. The Hamming(8,4) encoder, despite a moderate level of complexity, offered the best balance between error correction capability and circuit robustness. These findings are crucial for advancing superconducting digital electronics, enabling more reliable data transmission and paving the way for more complex and powerful computing systems.

The results show that all three codes can detect and correct single-bit errors, with the extended Hamming(8,4) code offering improved detection of multi-bit errors. The study acknowledges limitations inherent in the chosen 8-bit interface and 4-bit message length, representing a practical compromise given constraints on chip area and cooling power. Future work could explore these codes with larger data sizes or investigate other lightweight error-correction techniques tailored for superconducting systems, potentially enhancing the robustness of cryogenic digital links.