Do Not Let CNOTs Overwhelm the Decoder: Scheduling Transversal Gates for Fast FTQC

2026-08-12

AI Summary

This work addresses the challenge that dense transversal CNOT scheduling, while accelerating fault-tolerant quantum computation, imposes substantial latency and memory overhead on classical decoders and impedes precompilation of detector error models (DEMs). To overcome these limitations, the authors propose the PACE framework—the first decoder-aware transversal CNOT scheduler—which integrates dynamic DEM generation, hybrid-window decoding, and graph coloring–driven subwindow parallel decoding. This approach significantly reduces decoding overhead while preserving quantum acceleration. By explicitly accounting for classical processing bottlenecks traditionally overlooked in circuit scheduling, PACE reveals the performance boundaries of decoding systems under transversal CNOT architectures.

Abstract

Transversal CNOT (TCNOT) gates can accelerate fault-tolerant quantum computation (FTQC) in the surface code by reducing the number of syndrome extraction rounds required between logical operations from $O(d)$ to $O(1)$. This is particularly attractive for quantum platforms with long-range connectivity, such as neutral atoms. However, dense TCNOT schedules substantially increase the classical decoding workload. TCNOTs propagate errors across multiple surface-code patches, enlarging the spatiotemporal region that must be decoded jointly. Consequently, denser TCNOT schedules increase decoding latency and memory requirements and potentially exceed available decoder capacity. Moreover, because the detector error model (DEM) of each decoding window depends on the TCNOT schedule, exhaustively precomputing all possible window-level DEMs is infeasible, requiring just-in-time (JIT) DEM compilation. Thus, the practical benefit of TCNOT gates is limited not only by quantum hardware performance but also by classical decoding and DEM-compilation capacity. We introduce PACE, a decoder-aware scheduling framework for TCNOT-based FTQC. PACE first mitigates the decoder-side costs of aggressive TCNOT scheduling through three complementary techniques. Hybrid Window Decoding assigns different decoders for each decoding window according to its DEM structure. DEM Stitch generates schedule-specific window-level DEMs just in time by assembling reusable precompiled fragments. Sub-window Parallel Decoding decomposes large windows into smaller sub-windows with graph-coloring formulation. Building on these techniques, PACE then performs decoder-aware scheduling to maximize TCNOT concurrency within the available decoder resources. Our evaluation shows the trade-off between quantum acceleration and classical decoding cost, revealing the limitations of current decoding systems for TCNOT-based FTQC.

Problem

• Transversal CNOT
• fault-tolerant quantum computation
• decoding workload
• detector error model
• decoder capacity

Innovation

• transversal CNOT
• decoder-aware scheduling
• detector error model
• hybrid window decoding
• just-in-time compilation