Decoder Switching: Breaking the Speed-Accuracy Tradeoff in Real-Time Quantum Error Correction

TL;DR

The paper tackles the speed-accuracy tension in real-time quantum error correction by introducing decoder switching, which combines a fast, soft-output 'weak' decoder with a slower, high-accuracy 'strong' decoder. A key contribution is the double window online decoding scheme that stabilizes backlog and relaxes latency requirements, enabling the strong decoder to operate only when necessary based on soft information $g$. The authors provide a theoretical framework for optimizing the soft-threshold $g_{\text{th}}$ via a thresholded logical error rate and demonstrate, through numerical simulations on rotated surface codes, that decoder switching can attain strong-decoder-like accuracy with weak-decoder-like average latency, with the switching rate decaying exponentially as code distance grows. This work paves the way for scalable, real-time decoding devices by decoupling decoder design, supporting a broader range of codes and hardware implementations.

Abstract

The realization of fault-tolerant quantum computers hinges on the construction of high-speed, high-accuracy, real-time decoding systems. The persistent challenge lies in the fundamental trade-off between speed and accuracy: efforts to improve the decoder's accuracy often lead to unacceptable increases in decoding time and hardware complexity, while attempts to accelerate decoding result in a significant degradation in logical error rate. To overcome this challenge, we propose a novel framework, decoder switching, which balances these competing demands by combining a faster, soft-output decoder ("weak decoder") with a slower, high-accuracy decoder ("strong decoder"). In usual rounds, the weak decoder processes error syndromes and simultaneously evaluates its reliability via soft information. Only when encountering a decoding window with low reliability do we switch to the strong decoder to achieve more accurate decoding. Numerical simulations suggest that this framework can achieve accuracy comparable to, or even surpassing, that of the strong decoder, while maintaining an average decoding time on par with the weak decoder. We also develop an online decoding scheme tailored to our framework, named double window decoding, and elucidate the criteria for preventing an exponential slowdown of quantum computation. These findings break the long-standing speed-accuracy trade-off, paving the way for scalable real-time decoding devices.

Figures (21)

• Figure 1: A possible device configuration for real-time decoding systems based on decoder switching. In this example, the weak decoder is implemented with FPGA or ASIC chips to realize a low response time, based on a fast algorithm like the UF decoder. This decoder also outputs a kind of soft information $g$, for example, by using the method proposed in Ref. Meister2024. On the other hand, the strong decoder is implemented with CPU or GPU-based devices to perform highly accurate decoding schemes like a transformer-based neural network decoder Bausch2024alphaqubit. In decoder switching, only when we obtain a smaller value of the soft information than a given threshold $g_{\text{th}}$, we wait for the outcome from the strong decoder. Otherwise, we use the decoding result from the weak decoder to maintain the average decoding speed sufficiently low.
• Figure 2: A gate-teleportation circuit to execute a $T$ gate by utilizing a magic state denoted as $\ket{T}:=T\ket{+}$. This circuit incorporates a classically controlled $S$ gate, whose operation is contingent on the measurement outcome. In fault-tolerant implementations based on QEC codes, it is necessary to decode the logical $Z$ measurement outcome prior to the adaptive application of the $S$ correction. The response time is predominantly determined by the decoding time, but is also affected by communication and control latency.
• Figure 3: Schematic diagrams to describe how to calculate two types of soft outputs. ( a,b) Complementary gapBombin2024Gidney2025yoked: First, we find the minimum-weight perfect matching (black solid lines) by using some matching-based decoder, given a syndrome configuration (yellow stars). By flipping the boundary conditions (red stars), we then find the so-called complementary matching (red dotted lines), which has a minimum weight conditioned on the new boundary conditions Hutter2014. The complementary gap is defined as the difference between the weights of these two matchings. ( c,d) Cluster gapMeister2024: First, we find a perfect matching (black solid lines) by using some clustering-based decoder, such as the Sparse-Blossom decoder or the UF decoder. Then we find the shortest path (red solid lines) between boundary nodes on the quotient graph $G/C$, where $G$ is the decoding graph (background lattice) and $C$ is the set of clusters formed by the decoder (blue circles). The cluster gap is defined as the weights of the shortest path.
• Figure 4: Histograms of (signed) complementary gaps $\tilde{g}_{\text{comp}}$ for rotated surface code, sampled from $10d$-rounds memory experiments with perfect terminal time boundaries. which is reproduced based on the approach in Ref. Gidney2025yoked. This data was gathered with $N=10^7$ shots under the uniform circuit-level noise model at a physical error rate of $p_{\text{ph}}=10^{-3}$. Here we denote the value of complementary gaps in the unit of dB.
• Figure 5: Gap-conditional logical error rate $P_{\text{weak}}(e|g_{\text{comp}})$ for MWPM decoder, which is produced from the histogram data in Fig. \ref{['fig:histogram']}. As demonstrated in Ref. Gidney2025yoked, each plot is fitted well with an empirical function $f(g_{\text{comp}})=(1+10^{0.09g_{\text{comp}}})^{-1}$ (gray solid line), where the complementary gap $g_{\text{comp}}$ is also denoted in the unit of dB.

Theorems & Definitions (1)

• Theorem 1: Sufficient conditions for avoiding the backlog problem in the double window decoding scheme