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Spatially parallel decoding for multi-qubit lattice surgery (2403.01353v2)

Published 3 Mar 2024 in quant-ph, cs.AR, and cs.ET

Abstract: Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are generated. Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for surface code, quantum programs of utility will require multi-qubit interactions performed via lattice surgery. A large merged patch can arise during lattice surgery -- possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this work, we demonstrate how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput -- a decision that should be influenced by the device's physical noise.

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Citations (2)
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Summary

  • The paper introduces spatially parallel decoding through overlapping windows to efficiently manage large merged patches in lattice surgery.
  • It demonstrates that an optimal buffer width, balanced against hardware constraints, boosts both decoding accuracy and throughput.
  • Scalability improvements enable real-time error correction, paving the way for fault-tolerant quantum computing advancements.

Enhancing Quantum Error Correction with Spatially Parallel Decoding for Lattice Surgery

Introduction to Quantum Error Correction and Lattice Surgery

Quantum error correction (QEC) is pivotal for the realization of large-scale quantum computing. It preserves quantum information against imperfections and noise inherent in quantum processors by encoding logical qubits across multiple physical qubits. A prominent QEC technique is the surface code, known for its fault tolerance and compatibility with 2D nearest-neighbor architectures. To perform logical operations on qubits encoded in the surface code, lattice surgery—a method that merges and splits patches of codes—is extensively used due to its efficiency.

Scalability Challenges in Real Time Decoding

Real time decoding, essential for the dynamic correction of errors during quantum operations, encounters scalability issues when applied to large patches arising during lattice surgery. These issues include maintaining decoding throughput to avoid data backlog and ensuring high fidelity of logical qubits post-operations. Previous strategies, primarily designed for isolated qubits or small patches, fall short in addressing the unique demands posed by multi-qubit operations through lattice surgery.

Introducing Spatially Parallel Windows

This paper introduces a novel approach—spatially parallel decoding through overlapping windows, each with a dedicated decoder module, to effectively manage the decoding of large merged patches in lattice surgery. This setup ensures compatibility with hardware accelerators like FPGAs and ASICs, supports general lattice surgery operations, sustains logical qubit fidelity, and meets real time decoding requirements. It's a pioneering paper that practically addresses system-specific considerations and hardware constraints which were previously unexplored.

Configuration and Performance Analysis

The configuration of spatially parallel windows is carefully analyzed to ensure that it adheres to practical constraints such as fixed positions for hardware accelerators and window sizes no smaller than individual code patches. Numerical simulations highlight the critical balance between buffer width (the overlapping area between windows) against accuracy and throughput, revealing that an optimal buffer width depends significantly on the device's physical noise level.

Throughput Assessment and Implications

The throughput analysis confirms that inter-window communication—critical for information transfer between windows—does not become a throughput bottleneck, even for large window sizes. However, the scalability of the inner decoder modules, necessary for processing within individual windows, ultimately limits the maximum feasible window size. For FPGAs and ASICs, the trade-off between increasing window size (and thus, computational resources) and decoder throughput presents a crucial design consideration.

Conclusions and Future Directions

The paper conclusively shows that spatially parallel windows can significantly enhance the scalability of real time decoding for quantum error correction, especially for the large patches encountered during lattice surgery. It opens avenues for future research into optimizing hardware decoder designs and exploring the potential of ASICs for supporting larger code distances and more complex lattice surgery operations. The investigation sets a foundation for developing more efficient, real time decoding strategies that can keep pace with the evolving requirements of fault-tolerant quantum computing.

In essence, this work marks a significant step towards practical, large-scale quantum computations by addressing one of the critical challenges in quantum error correction and decoding. Its implications for the design and operation of future quantum computers are profound, paving the way for more sophisticated and fault-tolerant quantum information processing techniques.

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