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arXiv:2510.25661 · IEEE/ACM International Symposium on Microarchitecture (MICRO)

Accurate Leakage Speculation for Quantum Error Correction

Chaithanya Naik Mude, Swamit Tannu

Published Oct 17, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum Error Correction (QEC) protects qubits against bit-and phase-flip errors in the |0⟩ /|1⟩ subspace, but physical qubits can also leak into higher energy levels (e.g., |2⟩).Leakage is especially harmful, as it corrupts all subsequent syndrome measurements and can spread to neighboring qubits.Detecting leakage on data qubits is particularly challenging, since they are never measured directly during QEC cycles.Prior work, such as eraser [43], addresses this by inferring leakage from syndrome patterns using a fixed heuristic.However, this approach often misclassifies benign syndromes, triggering excessive leakage-reduction circuits (LRCs).Because LRCs are themselves noisy and slow, these false triggers lengthen QEC cycles and inflate logical error rates.We propose gladiator, a general and adaptable leakage speculation framework that works across surface code, color code, and qLDPC codes.Offline, gladiator builds a code-aware errorpropagation graph calibrated to device data.Online, it classifies each syndrome in a few nanoseconds and schedules LRC only when the observed pattern is provably leakage-dominated.This precise speculation eliminates up to 3× (and on average 2×) unnecessary LRCs, shortens QEC cycles, and suppresses false positives at their source.Evaluated on standard fault-tolerant benchmarks, gladiator delivers 1.7×-3.9×speedups and 16% reduction in logical error rate, advancing the efficiency of fault-tolerant quantum computing.

DOI
10.1145/3725843.3756053

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Quantum Error Correction (QEC) protects qubits against bit-and phase-flip errors in the |0⟩ /|1⟩ subspace, but physical qubits can also leak into higher energy levels (e.g., |2⟩).Leakage is especially harmful, as it corrupts all subsequent syndrome measurements and can spread to neighboring qubits.Detecting leakage on data qubits is particularly challenging, since they are never measured directly during QEC cycles.Prior work, such as eraser [43], addresses this by inferring leakage from syndrome patterns using a fixed heuristic.However, this approach often misclassifies benign syndromes, triggering excessive leakage-reduction circuits (LRCs).Because LRCs are themselves noisy and slow, these false triggers lengthen QEC cycles and inflate logical error rates.We propose gladiator, a general and adaptable leakage speculation framework that works across surface code, color code, and qLDPC codes.Offline, gladiator builds a code-aware errorpropagation graph calibrated to device data.Online, it classifies each syndrome in a few nanoseconds and schedules LRC only when the observed pattern is provably leakage-dominated.This precise speculation eliminates up to 3× (and on average 2×) unnecessary LRCs, shortens QEC cycles, and suppresses false positives at their source.Evaluated on standard fault-tolerant benchmarks, gladiator delivers 1.7×-3.9×speedups and 16% reduction in logical error rate, advancing the efficiency of fault-tolerant quantum computing.
Quantum error correction (QEC) codes can tolerate hardware errors by encoding fault-tolerant logical qubits using redundant physical qubits and detecting errors using parity checks. Leakage errors occur in quantum systems when a qubit leaves its computational basis and enters higher energy states. These errors severely limit the performance of QEC due to two reasons. First, they lead to erroneous parity checks that obfuscate the accurate detection of errors. Second, the leakage spreads to other qubits and creates a pathway for more errors over time. Prior works tolerate leakage errors by using leakage reduction circuits (LRCs) that modify the parity check circuitry of QEC codes. Unfortunately, naively using LRCs always throughout a program is sub-optimal because LRCs incur additional two-qubit operations that (1) facilitate leakage transport, and (2) serve as new sources of errors.
Abstract The leakage of quantum information out of the two computational states of a qubit into other energy states represents a major challenge for quantum error correction. During the operation of an error-corrected algorithm, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of the logical error with scale, thus challenging the feasibility of quantum error correction as a path towards fault-tolerant quantum computation. Here, we demonstrate a distance-3 surface code and distance-21 bit-flip code on a quantum processor for which leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a tenfold reduction in the steady-state leakage population of the data qubits encoding the logical state and an average leakage population of less than 1 × 10 −3 throughout the entire device. Our leakage removal process efficiently returns the system back to the computational basis. Adding it to a code circuit would prevent leakage from inducing correlated error across cycles. With this demonstration that leakage can be contained, we have resolved a key challenge for practical quantum error correction at scale.
Quantum error correction (QEC) is indispensable for scalable fault-tolerant quantum computing. However, discovering QEC codes that remain effective is challenging, as logical performance depends on the interplay between code structure, hardware, syndrome extraction, and decoding, which often impose competing requirements. Here we introduce OmniQEC, an efficient AI scientist for discovering QEC codes suited to deployment on modern quantum processors. OmniQEC formulates QEC design as an iterative discovery process in which an orchestrator, implemented by advanced large language models (LLMs), coordinates code generation, code-level screening, syndrome-extraction synthesis, and decoder-based circuit evaluation. At its core, OmniQEC combines a self-evolving reasoning mechanism with a slow--fast synergistic workflow: a fast loop explores candidates using inexpensive code-level proxies, whereas a slow loop performs physically grounded circuit-level evaluation and feeds the resulting evidence back into the search. We evaluate OmniQEC across four qLDPC construction families, three LLM backends, and 141414 total-physical-qubit budgets per backend. The discovered codes show steadily improving logical-error suppression with increasing physical-qubit budgets and outperform the BB codes with [ ⁣[72,12,6] ⁣][\![72,12,6]\!][[72,12,6]] and [ ⁣[144,12,12] ⁣][\![144,12,12]\!][[144,12,12]] under complete-implementation budgets of 98 and 240 physical qubits, respectively. The discovered codes are hardware-friendly and may be of independent interest for practical QEC implementation. These findings pave the way towards LLM-assisted QEC discovery grounded in physically informed code--circuit--decoder co-design.
Quantum Error Correction (QEC) codes store information reliably in logical qubits by encoding them in a larger number of less reliable qubits.The surface code, known for its high resilience to physical errors, is a leading candidate for fault-tolerant quantum computing (FTQC).Logical qubits encoded with the surface code can be in different phases of their syndrome generation cycle, thereby introducing desynchronization in the system.This can occur due to the production of non-Clifford states, dropouts due to fabrication defects, and the use of other QEC codes with the surface code to reduce resource requirements.Logical operations require the syndrome generation cycles of the logical qubits involved to be synchronized.This requires the leading qubit to pause or slow down its cycle, allowing more errors to accumulate before the next cycle, thereby increasing the risk of uncorrectable errors.To synchronize the syndrome generation cycles of logical qubits, we define three policies -Passive, Active, and Hybrid.The Passive policy is the baseline, and the simplest, wherein the leading logical qubits idle until they are synchronized with the remaining logical qubits.On the other hand, the Active policy aims to slow the leading logical qubits down gradually, by inserting short idle periods before multiple code cycles.This approach reduces the logical error rate (LER) by up to 2.4× compared to the Passive policy.The Hybrid policy further reduces the LER by up to 3.4× by reducing the synchronization slack and running a few additional rounds of error correction.Furthermore, the reduction in the logical error rate with the proposed synchronization policies enables a speedup in decoding latency of up to 2.2× with a circuit-level noise model.
Quantum error correction protects logical information only when every physical operation remains below the fault-tolerance threshold, a condition that must be maintained continuously rather than only at the initial calibration. In practice, however, analog control parameters inevitably drift because of environmental fluctuations. As future fault-tolerant quantum computations are expected to run for days or even months, interrupting computation for repeated recalibration becomes fundamentally impractical. A promising alternative is to integrate calibration directly into computation by repurposing syndrome measurements as a calibration signal (Sivak et al, Nature 2026), but whether such self-calibration can be achieved with provable efficiency remains an open question. Here we establish a theoretical framework for such self-calibrating quantum fault tolerance. We prove that, for a broad class of control-induced errors, the detection rate defines a locally strongly convex surrogate objective for analog calibration with high probability. This geometric property enables a simple and efficient online optimization algorithm using only syndrome measurements collected during normal error correction. We prove convergence to an ε\varepsilonε detection rate within O(1/ε2)O(1/\varepsilon^2)O(1/ε2) epochs for time-independent drifts and also establish guarantees for time-dependent drifts. We further show that the convergence rate is independent of the code distance for quantum low-density parity-check (LDPC) codes. Pulse-level simulations of neutral-atom arrays and large-scale circuit-level Clifford simulations confirm these theoretical predictions. Our results establish self-calibrating fault tolerance as a provably efficient paradigm in which the same syndrome measurements simultaneously protect logical information and stabilize the underlying hardware.
Quantum codes excel at correcting local noise but fail to correct leakage faults that excite qubits to states outside the computational space. Aliferis and Terhal \cite{aliferis07} have shown that an accuracy threshold exists for leakage faults using gadgets called leakage reduction units (LRUs). However, these gadgets reduce the accuracy threshold and increase overhead and experimental complexity, and these costs have not been thoroughly understood. We explore a variety of techniques for leakage-resilient, fault-tolerant error correction in topological codes. Our contributions are threefold. First, we develop a leakage model that is physically motivated and efficient to simulate. Second, we use Monte-Carlo simulations to survey several syndrome extraction circuits. Third, given the capability to perform 3-outcome measurements, we present a dramatically improved syndrome processing algorithm. Our simulations show that simple circuits with one extra CNOT per check operator and no additional ancillas reduce the accuracy threshold by less than a factor of 444 when leakage and depolarizing noise rates are comparable. This becomes a factor of 222 when the decoder uses 3-outcome measurements. Finally, when the physical error rate is less than 2×10−42\times 10^{-4}2×10−4, placing LRUs after every gate may achieve the lowest logical error rates of all of the circuits we considered. We anticipate that the closely related planar codes might exhibit the same accuracy thresholds and that the ideas may generalize naturally to other topological codes.