Efficient Iterative Decoding of Quantum Low-Density Parity-Check Codes Under Circuit-Level Noise

Core Concepts

A sliding window decoder based on belief propagation with guided decimation is proposed to efficiently decode quantum low-density parity-check codes in the presence of circuit-level noise.

Abstract

The content introduces a sliding window decoder based on belief propagation (BP) with guided decimation for the purpose of decoding quantum low-density parity-check (QLDPC) codes in the presence of circuit-level noise. Key highlights: Windowed decoding is used to keep the decoding complexity reasonable when repeated rounds of syndrome extraction are required to decode. Within each window, several rounds of BP with decimation of the variable node expected to be most likely to flip in each round are employed. Ensemble decoding is used to keep both decimation options (guesses) open in a small number of chosen rounds, resulting in a guided decimation guessing (GDG) decoder. Applied to bivariate bicycle codes, GDG achieves similar logical error rate as BP with an additional OSD post-processing stage (BP+OSD) and combination-sweep of order 10. For a window size of three syndrome cycles, a multi-threaded CPU implementation of GDG achieves a worst-case decoding latency of 3ms per window for the [[144,12,12]] code.

Stats

The worst-case decoding latency of the GDG decoder is 3ms per window for the [[144,12,12]] code.

Quotes

None

Key Insights Distilled From

Toward Low-latency Iterative Decoding of QLDPC Codes Under Circuit-Level Noise

by Anqi Gong,Se... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2403.18901.pdf

Deeper Inquiries

How can the performance of the GDG decoder be further improved, especially in the error floor region?

To further enhance the performance of the GDG decoder, especially in the error floor region, several strategies can be implemented: Fine-tuning Parameters: Continuously fine-tuning the parameters used in the GDG decoder, such as the decision thresholds, guessing strategies, and depth limits, can help optimize the decoder's performance in different error rate regions. Adaptive Decoding: Implementing adaptive decoding strategies where the decoder dynamically adjusts its parameters based on the error rate observed during decoding can help improve performance across varying error rates. Hybrid Decoding: Combining the GDG decoder with other decoding techniques, such as post-processing methods or advanced error correction algorithms, can potentially mitigate the error floor effect and improve overall performance. Hardware Acceleration: Utilizing specialized hardware accelerators like GPUs or TPUs to parallelize the decoding process can significantly speed up the decoding process and potentially improve performance in the error floor region. Error Analysis: Conducting thorough error analysis to understand the specific error patterns and characteristics that lead to error floors can help in devising targeted strategies to address these issues within the GDG decoder.

How can the GDG decoder be adapted for codeword decoding instead of just syndrome decoding?

Adapting the GDG decoder for codeword decoding involves modifying the decoder's functionality to not only correct errors based on syndrome information but also to decode the entire codeword. Here are some steps to adapt the GDG decoder for codeword decoding: Expand Decision Criteria: Modify the VN selection criteria to consider the entire codeword rather than just syndrome information. This may involve incorporating additional error correction strategies that focus on correcting the entire codeword. Integrate Codeword Information: Enhance the decoder to utilize information about the entire codeword structure, including parity checks and logical operators, to make more informed decoding decisions. Iterative Decoding: Implement iterative decoding processes that iteratively refine the estimated codeword based on feedback from the entire decoding process, not just syndrome bits. Optimize Path Selection: Develop algorithms that optimize the path selection process to ensure that the decoder explores all possible error patterns within the codeword space efficiently. Error Correction Capability: Enhance the decoder's error correction capability to handle complex error patterns and efficiently correct errors across the entire codeword, considering the interdependencies between different qubits. By incorporating these modifications and enhancements, the GDG decoder can be effectively adapted for codeword decoding, enabling it to decode quantum codes more accurately and efficiently.

What are the potential challenges in implementing the GDG decoder in specialized hardware like FPGAs or ASICs?

Implementing the GDG decoder in specialized hardware like FPGAs or ASICs presents several challenges: Resource Utilization: Optimizing the GDG decoder for hardware implementation requires efficient resource utilization to ensure that the decoder can run within the constraints of the FPGA or ASIC, such as limited memory and processing capabilities. Parallelization: Effectively parallelizing the decoding process to leverage the parallel processing capabilities of FPGAs or ASICs while maintaining synchronization and minimizing latency can be challenging. Algorithm Mapping: Mapping the GDG decoding algorithm onto the hardware architecture in a way that maximizes performance and minimizes power consumption requires careful design and optimization. Clock Speed: Ensuring that the GDG decoder can operate at the required clock speeds on FPGA or ASIC hardware without compromising accuracy or efficiency is crucial but can be challenging. Testing and Verification: Verifying the correctness and functionality of the GDG decoder in a hardware implementation, especially in the presence of potential hardware-related issues like timing violations or signal integrity problems, can be complex. Scalability: Ensuring that the GDG decoder can scale effectively on FPGA or ASIC platforms to handle larger quantum codes or more complex decoding scenarios without sacrificing performance or accuracy is a significant challenge. Addressing these challenges requires a deep understanding of both the GDG decoder algorithm and the intricacies of FPGA or ASIC design, as well as careful optimization and testing to ensure successful hardware implementation.