Quantum error correction uses the measurement of syndromes and classical decoding algorithms to estimate the location and type of errors while protecting the encoded quantum bits. Here we consider how prior information and Bayesian updates can play a critical role in improving the performance of QEC in the scenario of a particularly noisy qubit. This allows for leveraging even distance codes, which typically are less valued in QEC, to handle the noisy qubit, changing the power-law scaling of the logical error rate with the baseline physical error rate. A crucial component of this is updating the prior by real time feeding of decoder outputs into a approximate Kalman filter. Thus our approach provides a bootstrap to the actual error rates. We show this via simulation of the full closed-loop system: starting from uniform priors, the update procedure gradually learns site-specific error rates, enabling the decoder to outperform a fixed-prior baseline. In turn, we show that this enables in situ calibration of unitary operations via injection of gate set tomography operations with only moderate overhead in the more typical scenario of low noise qubits.
Quantum error correction uses the measurement of syndromes and classical decoding algorithms to estimate the location and type of errors while protecting the encoded quantum bits. Here we consider how prior information and Bayesian updates can play a critical role in improving the performance of QEC in the scenario of a particularly noisy qubit. This allows for leveraging even distance codes, which typically are less valued in QEC, to handle the noisy qubit, changing the power-law scaling of the logical error rate with the baseline physical error rate. A crucial component of this is updating the prior by real time feeding of decoder outputs into a approximate Kalman filter. Thus our approach provides a bootstrap to the actual error rates. We show this via simulation of the full closed-loop system: starting from uniform priors, the update procedure gradually learns site-specific error rates, enabling the decoder to outperform a fixed-prior baseline. In turn, we show that this enables in situ calibration of unitary operations via injection of gate set tomography operations with only moderate overhead in the more typical scenario of low noise qubits.
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses these measurements to infer which error most likely occurred, so that the system can correct it. The decoder's accuracy-how rarely it makes the wrong guess-directly determines the scale of quantum computation that can be reliably executed. With a wealth of competing decoding algorithms, a QEC system designer needs reliable methods to evaluate them. Today, the dominant approach is to evaluate decoders using Monte Carlo simulation. However, simulation has several drawbacks such as requiring many samples to produce low variance estimates.
In this work, we develop a new systematic analysis for evaluating decoders. We introduce a novel formal semantics of a core language for QEC programs that captures the de facto standard Stim circuit format, providing a principled theoretical foundation for the emerging space of fault-tolerant quantum systems design. Given a QEC program and a decoder, our verifier can quantify both the decoder accuracy and the decoder robustness to drift in physical error rate. Our approach has two key components: (i) a structured search over the space of possible errors; and (ii) a constrained polynomial optimization kernel. A thorough empirical evaluation of our approach suggests that it can outperform simulation, especially in low error rate regimes, and that it can be deployed to quantify decoder robustness over an interval of physical error rates.
Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this information as a prior to the decoder. We introduce a reinforcement learning inspired method for calibrating these priors that aims to minimize the logical error rate. Our method significantly improves the decoding accuracy in repetition and surface code memory experiments executed on Google's Sycamore processor, outperforming the leading decoder-agnostic method by 16% and 3.3%, respectively. This calibration approach will serve as an important tool for maximizing the performance of both near-term and future error-corrected quantum devices.
This paper investigates adaptive optimization techniques for quantum error correction (QEC) codes. The core claim is that dynamic adjustment of QEC parameters, guided by estimates of decoherence probabilities, can significantly enhance the efficiency of quantum information transmission. The proposed mechanism utilizes real-time adjustments to the code's redundancy, encoding scheme, and error correction protocols, adapting to varying noise environments and qubit states. Traditional QEC approaches typically employ fixed parameters, lacking the crucial element of adaptability. This research addresses this limitation by introducing a framework for continuous optimization based on accurate decoherence probability assessment. The framework involves estimating the decoherence probability (Pd) of individual qubits, which is then used to dynamically modify key parameters of the QEC code. Specifically, we explore adjusting the code rate (R), the minimum distance (d) of the code, and the choice of error correction scheme. The optimization algorithm aims to minimize the overall error rate while maintaining a desired level of performance. This work presents a novel approach to QEC, promising improved robustness and efficiency in quantum communication and computation. The key mathematical components of this work are presented below.
Error rates in current noisy quantum hardware are not static; they vary over time and across qubits. This temporal and spatial variation challenges the effectiveness of fixed-distance quantum error correction (QEC) codes. In this paper, we analyze 12 days of calibration data from IBM’s 127qubit device (ibm_kyiv), showing the fluctuation of Pauli-X and CNOT gate error rates. We demonstrate that fixed-distance QEC can either underperform or lead to excessive overhead, depending on the selected qubit and the error rate of the day. We then propose a simple adaptive QEC approach that selects an appropriate code distance per qubit, based on daily error rates. Using logical error rate modeling, we identify qubits that cannot be used and qubits that can be recovered with minimal resources. Our method avoids unnecessary resource overhead by excluding outlier qubits and tailoring code distances. Across 12 calibration days on ibm_kyiv, our adaptive strategy reduces physical qubit overhead by over 50% per logical qubit while maintaining access to 85−100% of usable physical qubits. To further validate the method, we repeat the experiment on two additional 127qubit devices, ibm_brisbane and ibm_sherbrooke, where the overhead savings reach up to 71% while still preserving over 80% physical qubit usability. This approach offers a practical and efficient path forward for Noisy Intermediate-Scale Quantum (NISQ)-era QEC strategies.
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across redundant physical qubits, such that errors can be detected and corrected. In this work, we efficiently train novel end-to-end deep quantum error decoders. We resolve the quantum measurement collapse by augmenting syndrome decoding to predict an initial estimate of the system noise, which is then refined iteratively through a deep neural network. The logical error rates calculated over finite fields are directly optimized via a differentiable objective, enabling efficient decoding under the constraints imposed by the code. Finally, our architecture is extended to support faulty syndrome measurement, by efficient decoding of repeated syndrome sampling. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy, outperforming for small distance topological codes, the existing end-to-end neural and classical decoders, which are often computationally prohibitive.
Quantum computation has the promise to solve problems that are not efficiently solvable by classical means. Yet, due to the fragile nature of quantum states, it is unavoidable that quantum systems are subject to decoherence, gate imperfections, and measurement errors. These problems stand as a major roadblock to the construction of large-scale fault-tolerant quantum computers. Conventional quantum error correction (QEC) codes, such as the surface code or Shor code, need to use an extensive amount of redundancy and classical control, which can be both computationally expensive and challenging to scale. In this context, we propose to investigate the use of machine learning (ML) techniques by realizing on-line identification, localization and correction of these quantum errors for fault-tolerant quantum computation by means of fault-tolerant quantum computing processes. Our model introduces a hybrids ML-QEC architecture that combines classical neural networks and decision-tree classifiers with quantum syndrome decoding. These models are trained on error syndromes produced using the approximation of common noise models (for example, depolarizing noise, dephasing and amplitude damping), simulated under different QEC schemes. The machine learning methods are trained with quantum error patterns and have a capability to rapidly infer where errors are likely to occur, as well as recommend correction operations with high confidence. As a result, the system reduces dramatically the delay and computational costs when compared to conventional decoding methods. There is also a self-adaptive learning module in the work, which recommences training on fresh quantum error distributions, meaning the system can adapt to changes in the environment (and also the decay of the hardware) as time progresses. The study further carries out ML predictions inside a real-time loop and cross-checks them with quantum state tomography and entanglement fidelity such as indicators. Experimental characterization on dedicated devices as well as noise models show that our ML-enhanced decoders reach higher fidelity and lower logical error rates compared to baseline decoders, especially in non-uniform or time-dependent noise. This work is a significant stride towards realizing practical fault-tolerant quantum computation by combining quantum error correction with the versatility and scalability of machine learning. With intelligent models to dictate learning, our proposed framework is able to eliminate a lot of trial-and-error manual processes in the conventional heuristic-based approach, and points to a potential path to achieve scalable quantum information processing platforms.