Adaptive Aborting Schemes for Quantum Error Correction Decoding

TL;DR

The first adaptive abort schemes considered for QEC, which dynamically adjust the number of syndrome measurement rounds per shot using real-time syndrome information, are considered and highlight the potential importance of abort rules for increasing efficiency as the authors scale to large, resource-intensive quantum architectures.

Abstract

Quantum error correction (QEC) is essential for realizing fault-tolerant quantum computation. Current QEC controllers execute all scheduled syndrome (parity-bit) measurement rounds before decoding, even when early syndrome data indicates that the run will result in an error. The resulting excess measurements increase the decoder's workload and system latency. To address this, we introduce an adaptive abort module that simultaneously reduces decoder overhead and suppresses logical error rates in surface codes and color codes under an existing QEC controller. The key idea is that initial syndrome information allows the controller to terminate risky shots early before additional resources are spent. An effective scheme balances the cost of further measurement against the restart cost and thus increases decoder efficiency. Adaptive abort schemes dynamically adjust the number of syndrome measurement rounds per shot using real-time syndrome information. We consider three schemes: fixed-depth (FD) decoding (the standard non-adaptive approach used in current state-of-the-art QEC controllers), and two adaptive schemes, AdAbort and One-Step Lookahead (OSLA) decoding. For surface and color codes under a realistic circuit-level depolarizing noise model, AdAbort substantially outperforms both OSLA and FD, yielding higher decoder efficiency across a broad range of code distances. Numerically, as the code distance increases from 5 to 15, AdAbort yields an improvement that increases from 5% to 35% for surface codes and from 7% to 60% for color codes. To our knowledge, these are the first adaptive abort schemes considered for QEC. Our results highlight the potential importance of abort rules for increasing efficiency as we scale to large, resource-intensive quantum architectures.

Figures (11)

• Figure 1: a) Current state‑of‑the‑art QEC stack architecture, b) QEC controller architecture augmented with an adaptive abort module. The adaptive-abort module sits within the shot orchestration layer, between the QEC decoder and the physical qubits, continuously evaluating decoding confidence and issuing early aborts.
• Figure 2: Sub-figures (a) and (b) illustrate how adaptive schemes alter the number of measurement rounds compared to the FD scheme for the $[9,1,3]$ surface code. In both cases, $\mathbf{s}_i = [s_{i,1}, s_{i,2}, \dots, s_{i,8}]$ denotes the eight syndrome bits obtained from the $i$-th measurement round, with bits highlighted in red indicating detected errors. In (a), under the FD scheme, the circuit executes all three predetermined syndrome measurement rounds regardless of the observed syndromes. In (b), the adaptive scheme terminates the measurement process early, after the second round, based on the observed syndrome pattern, avoiding unnecessary additional measurements.
• Figure 3: (a) Layout of the $[9,1,3]$ rotated‑surface code patch: red circles are data qubits, black circles are ancilla qubits; grey plaquettes indicate $X$‑type checks and blue plaquettes indicate $Z$‑type checks. A pink chain of $X$ operators between the two rough boundaries implements the logical $X_L$ operator, while a green chain of $Z$ operators between the smooth boundaries implements the logical $Z_L$ operator. (b) Quantum circuit used to measure an $X$‑stabilizer in the rotated surface code.
• Figure 4: The $[7,1,3]$ triangular color code. Data qubits (red circles) reside on the vertices, with each of the three triangular faces shaded with red, green, and blue colors. An example $X$-type stabilizer $S_f^X$ on the top (red) face. The logical $Z$ operator $Z_L$ is realized by the product of $Z$'s on the three qubits along any one colored boundary in this illustration, the bottom red edge.
• Figure 5: Decoder efficiency as a function of code distance $d$ for the surface code. Each data point runs for $2\times 10^5$ shots.

Theorems & Definitions (2)

• Remark 1
• Remark 2