GPU-Accelerated Decoder Enables Low-Latency Decoding of Quantum Low-Density Parity-Check Codes

Quantum error correction represents a critical hurdle in building practical quantum computers, and researchers continually seek codes that balance performance with computational demands. Oscar Ferraz, Bruno Coutinho, and Gabriel Falcao, from the University of Coimbra alongside colleagues, demonstrate a new approach to decoding quantum low-density parity-check (QLDPC) codes that significantly reduces processing time. Their work achieves decoding speeds below the crucial 63 microsecond latency threshold, a benchmark previously met by surface code decoders on advanced quantum hardware, but with the added benefit of maintaining constant encoding rates. By harnessing the power of readily available graphics processing units (GPUs), the team unlocks real-time decoding for these promising codes, paving the way for scalable and efficient fault-tolerant quantum computation beyond the limitations of current surface code technology. This advancement suggests that powerful quantum error correction is becoming increasingly attainable using existing, widely accessible hardware.

GPU Decoding Meets Quantum Error Correction

This research explores implementing and optimizing a decoder for Quantum Low-Density Parity-Check (LDPC) codes on Graphics Processing Units (GPUs) to achieve low-latency decoding, specifically below 63 microseconds, relevant to current quantum computing hardware. The team addressed a significant challenge in building practical quantum computers: efficiently correcting errors that inevitably occur during computation. The researchers implemented a syndrome-based iterative decoder on GPUs, focusing on maximizing speed to keep pace with quantum gate operations.

The results demonstrate sub-threshold latency for all tested codes on high-end RTX 3090 and 4090 GPUs, with the [[784, 24, 24]] code reaching 62. 9 μs and 43. 7 μs respectively. Performance on lower-end Jetson platforms was significantly slower, exceeding the 63 μs threshold due to limited computational power. Profiling revealed the decoding kernel as the primary bottleneck, with data transfer contributing to latency for smaller codes, but becoming less significant for larger ones.

Several optimization strategies are outlined, including utilizing lower-precision arithmetic, tuning parallel processing, leveraging faster on-chip memory, and overlapping data transfers with kernel execution. This research demonstrates the feasibility of achieving low-latency decoding for quantum LDPC codes on GPUs, bringing practical real-time quantum error correction closer to reality. The identified optimization strategies provide a roadmap for further improving performance and scalability. The work also highlights the importance of hardware acceleration for quantum error correction and the need to consider platform limitations.

QLDPC Decoding with Accelerated Belief Propagation

Researchers addressed the challenge of decoding quantum information by developing a highly efficient decoder for quantum low-density parity-check (QLDPC) codes, moving beyond the limitations of more established surface codes. While surface codes offer a pathway to fault-tolerant quantum computation, their encoding rates diminish as code size increases, hindering scalability. QLDPC codes offer a potential solution with constant encoding rates but demand significant computational resources for decoding. To overcome this hurdle, the team implemented a decoding algorithm based on belief propagation and accelerated it using the parallel processing capabilities of modern graphics processing units (GPUs).

This dramatically reduced the time required for decoding, achieving speeds fast enough to meet the stringent demands of real-time quantum error correction. The core of the methodology lies in leveraging the inherent parallelism of the belief propagation algorithm, which involves iteratively updating probabilities related to potential errors in the quantum information. Instead of processing these updates sequentially, the researchers distributed the calculations across the many cores of a GPU, enabling numerous updates to occur simultaneously, significantly speeding up the decoding process. This parallelization was carefully optimized to maximize performance within the constraints of the target latency, ensuring that the decoding could keep pace with the rapid operations of a quantum processor.

This innovative use of GPU acceleration represents a departure from traditional decoding methods, which often rely on central processing units and struggle to meet the speed requirements for practical quantum error correction. By adapting a well-established classical algorithm and harnessing the power of readily available hardware, the researchers have created a scalable and efficient decoding solution. The results demonstrate that real-time decoding of these advanced quantum codes is achievable, paving the way for more robust and scalable fault-tolerant quantum computers.

Real-time Quantum Error Correction with GPUs

Researchers have developed a new decoder for quantum low-density parity-check (QLDPC) codes that achieves a significant milestone in fault-tolerant quantum computing: real-time performance. This decoder, implemented on widely available graphics processing units (GPUs), can process information fast enough, in under 63 microseconds, to keep pace with the demands of current quantum processors, surpassing a critical threshold. The breakthrough addresses a key limitation of QLDPC codes, which, while offering advantages over other error correction methods, traditionally require substantial computational resources for decoding. Current quantum computers are susceptible to errors, necessitating complex error correction schemes.

Surface codes, a leading approach, are effective but suffer from a significant drawback: as the code size increases to protect more quantum information, the rate at which logical qubits can be encoded drops towards zero, creating substantial overhead. QLDPC codes offer a promising alternative, maintaining a constant encoding rate and potentially scaling more efficiently for large-scale quantum computation. However, decoding these codes has been computationally intensive, hindering their practical implementation. This new decoder overcomes this challenge by leveraging the parallel processing capabilities of GPUs.

Unlike traditional decoding methods, which require sequential processing, the GPU-based approach simultaneously analyzes multiple parts of the error correction code, dramatically reducing the decoding time. The team achieved this by carefully mapping the decoding process to the GPU architecture, optimizing memory access and maximizing processing throughput. For codes with 784 qubits, the decoder operates in under 50 microseconds, and even smaller codes are decoded in as little as 23. 3 microseconds, comfortably meeting the stringent timing requirements of advanced quantum processors. The significance of this achievement lies in its potential to move beyond the limitations of surface codes.

By enabling real-time decoding of asymptotically good QLDPC codes, this research paves the way for more efficient and scalable quantum computers, bringing the promise of fault-tolerant quantum computation closer to reality. The decoder’s reliance on readily available GPU hardware also makes it a practical and accessible solution for researchers and developers in the field. This advancement represents a crucial step towards building quantum computers capable of tackling complex problems beyond the reach of classical computers.

Real-time QLDPC Decoding on GPUs Demonstrated

This work demonstrates a GPU-accelerated decoder for quantum low-density parity-check (QLDPC) codes that achieves sub-63 microsecond latency, meeting the real-time threshold established by Google’s Willow quantum processor. The decoder leverages parallel processing of syndrome information on standard GPU hardware to overcome the decoding complexity typically associated with these codes, which offer constant encoding rates and good asymptotic performance.