We introduce Mechanistic Error Reduction with Abstention (MERA), a principled framework for steering language models (LMs) to mitigate errors through selective, adaptive interventions. Unlike existing methods that rely on fixed, manually tuned steering strengths, often resulting in under or oversteering, MERA addresses these limitations by (i) optimising the intervention direction, and (ii) calibrating when, and how much to steer, thereby provably improving performance or abstaining when no confident correction is possible. Experiments across diverse datasets, and LM families demonstrate safe, effective, non-degrading error correction, and that MERA outperforms existing baselines. Moreover, MERA can be applied on top of existing steering techniques to further enhance their performance, establishing it as a general-purpose, and efficient approach to mechanistic activation steering.

Note that this is defined up to an absolute phase, i.e. Learning models In this section we first describe the learning models we will be concerned with in this paper. Such quantum examples have been investigated in prior works [6, 8, 9]. A natural way to extend the learning model is to allow the algorithm quantum statistical queries . QSQ model allows a quantum advantage in learning in this framework.

This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of existing high-performance computing power with quantum-enabled exponential speedups. The proposed approximate quantum Fourier transform (AQFT) for quantum algorithm optimization improves the circuit execution on top of an exponential speed-ups the quantum Fourier transform has provided.

The concepts behind quantum computing have existed since the 1980's, but in the past few years, the field has experienced significant, rapid progress. In October 2019, Google demonstrated quantum supremacy for the first time, showing that a quantum computer took less time to complete a calculation than a classical computer would. In classical computers, information is stored as zeroes and ones in bits. In quantum computers, information is stored as a superposition (a digital mix) of zeroes and ones in qubits. A quantum computer manipulates the probabilities associated with superpositions to perform operations and maximize the probability of the correct answer being measured at the end. A sufficiently developed quantum computer would be capable of performing computations that classical computers cannot do by leveraging quantum principles. However, quantum computing is currently in the NISQ (Noisy Intermediate-Scale Quantum) era, meaning that quantum computers contain too much noise and not enough qubits. Noise, such as decoherence, introduces error to computations performed.

Quantum computers have the potential to outperform classical computers for some complex computational problems. However, current quantum computers (e.g., from IBM and Google) have inherent noise that results in errors in the outputs of quantum software executing on the quantum computers, affecting the reliability of quantum software development. The industry is increasingly interested in machine learning (ML)--based error mitigation techniques, given their scalability and practicality. However, existing ML-based techniques have limitations, such as only targeting specific noise types or specific quantum circuits. This paper proposes a practical ML-based approach, called Q-LEAR, with a novel feature set, to mitigate noise errors in quantum software outputs. We evaluated Q-LEAR on eight quantum computers and their corresponding noisy simulators, all from IBM, and compared Q-LEAR with a state-of-the-art ML-based approach taken as baseline. Results show that, compared to the baseline, Q-LEAR achieved a 25% average improvement in error mitigation on both real quantum computers and simulators. We also discuss the implications and practicality of Q-LEAR, which, we believe, is valuable for practitioners.

Indoor positioning systems based on Ultra-wideband (UWB) technology are gaining recognition for their ability to provide cm-level localization accuracy. However, these systems often encounter challenges caused by dense multi-path fading, leading to positioning errors. To address this issue, in this letter, we propose a novel methodology for unsupervised anchor node selection using deep embedded clustering (DEC). Our approach uses an Auto Encoder (AE) before clustering, thereby better separating UWB features into separable clusters of UWB input signals. We furthermore investigate how to rank these clusters based on their cluster quality, allowing us to remove untrustworthy signals. Experimental results show the efficiency of our proposed method, demonstrating a significant 23.1% reduction in mean absolute error (MAE) compared to without anchor exclusion. Especially in the dense multi-path area, our algorithm achieves even more significant enhancements, reducing the MAE by 26.6% and the 95th percentile error by 49.3% compared to without anchor exclusion.

Variational Quantum Algorithms (VQAs) are often viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of VQAs. In this work, we first show that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategies includes as special cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression. Second, we perform analytical and numerical analysis of these EM protocols, and we find that some of them (e.g., Virtual Distillation) can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.

Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANN) and the Yang-Baxter equation (YBE). Unlike traditional error correction methods, which are computationally intensive, we investigate artificial error mitigation. The manuscript introduces the basics of quantum error sources and explores the potential of using classical computation for error mitigation. The Yang-Baxter equation plays a crucial role, allowing us to compress time dynamics simulations into constant-depth circuits. By introducing controlled noise through the YBE, we enhance the dataset for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in correcting errors in time-evolving quantum states.

In this work we make progress in understanding the relationship between learning models with access to entangled, separable and statistical measurements in the quantum statistical query (QSQ) model. To this end, we show the following results. $\textbf{Entangled versus separable measurements.}$ The goal here is to learn an unknown $f$ from the concept class $C\subseteq \{f:\{0,1\}^n\rightarrow [k]\}$ given copies of $\frac{1}{\sqrt{2^n}}\sum_x \vert x,f(x)\rangle$. We show that, if $T$ copies suffice to learn $f$ using entangled measurements, then $O(nT^2)$ copies suffice to learn $f$ using just separable measurements. $\textbf{Entangled versus statistical measurements}$ The goal here is to learn a function $f \in C$ given access to separable measurements and statistical measurements. We exhibit a class $C$ that gives an exponential separation between QSQ learning and quantum learning with entangled measurements (even in the presence of noise). This proves the "quantum analogue" of the seminal result of Blum et al. [BKW'03]. that separates classical SQ and PAC learning with classification noise. $\textbf{QSQ lower bounds for learning states.}$ We introduce a quantum statistical query dimension (QSD), which we use to give lower bounds on the QSQ learning. With this we prove superpolynomial QSQ lower bounds for testing purity, shadow tomography, Abelian hidden subgroup problem, degree-$2$ functions, planted bi-clique states and output states of Clifford circuits of depth $\textsf{polylog}(n)$. $\textbf{Further applications.}$ We give and $\textit{unconditional}$ separation between weak and strong error mitigation and prove lower bounds for learning distributions in the QSQ model. Prior works by Quek et al. [QFK+'22], Hinsche et al. [HIN+'22], and Nietner et al. [NIS+'23] proved the analogous results $\textit{assuming}$ diagonal measurements and our work removes this assumption.