Quantum machine learning (QML) models conventionally rely on repeated measurements (shots) of observables to obtain reliable predictions. This dependence on large shot budgets leads to high inference cost and time overhead, which is particularly problematic as quantum hardware access is typically priced proportionally to the number of shots. In this work we propose Y ou Only Measure Once (Y omo), a simple yet effective design that achieves accurate inference with dramatically fewer measurements, down to the single-shot regime. Y omo replaces Pauli expectation-value outputs with a probability aggregation mechanism and introduces loss functions that encourage sharp predictions. Our theoretical analysis shows that Y omo avoids the shot-scaling limitations inherent to expectation-based models, and our experiments on MNIST and CIFAR-10 confirm that Y omo consistently outperforms baselines across different shot budgets and under simulations with depolarizing channels. By enabling accurate single-shot inference, Y omo substantially reduces the financial and computational costs of deploying QML, thereby lowering the barrier to practical adoption of QML. Quantum computing (Nielsen & Chuang, 2010) has emerged as a promising paradigm for advancing computational capabilities beyond the classical regime. Unlike classical machine learning, however, QML inherently involves probabilistic measurement outcomes. To obtain reliable outputs, QML models typically require repeated circuit executions, aggregating many measurement shots to estimate expectation values of observables. This reliance on repeated measurements constitutes one of the fundamental distinctions between classical and quantum machine learning.

Parameter shift rules (PSRs) are key techniques for efficient gradient estimation in variational quantum eigensolvers (VQEs). In this paper, we propose its Bayesian variant, where Gaussian processes with appropriate kernels are used to estimate the gradient of the VQE objective. Our Bayesian PSR offers flexible gradient estimation from observations at arbitrary locations with uncertainty information and reduces to the generalized PSR in special cases. In stochastic gradient descent (SGD), the flexibility of Bayesian PSR allows the reuse of observations in previous steps, which accelerates the optimization process. Furthermore, the accessibility to the posterior uncertainty, along with our proposed notion of gradient confident region (GradCoRe), enables us to minimize the observation costs in each SGD step. Our numerical experiments show that the VQE optimization with Bayesian PSR and GradCoRe significantly accelerates SGD and outperforms the state-of-the-art methods, including sequential minimal optimization.

The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise -- one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. The adaptive cost control is performed by first setting the required accuracy according to the progress of the optimization, and then choosing the minimum number of measurement shots and their distribution such that the required accuracy is satisfied. We demonstrate that SubsCoRe significantly improves the efficiency of SMO, and outperforms the state-of-the-art methods.

The ability to extract general laws from a few known examples depends on the complexity of the problem and on the amount of training data. In the quantum setting, the learner's generalization performance is further challenged by the destructive nature of quantum measurements that, together with the no-cloning theorem, limits the amount of information that can be extracted from each training sample. In this paper we focus on hybrid quantum learning techniques where classical machine-learning methods are paired with quantum algorithms and show that, in some settings, the uncertainty coming from a few measurement shots can be the dominant source of errors. We identify an instance of this possibly general issue by focusing on the classification of maximally entangled vs. separable states, showing that this toy problem becomes challenging for learners unaware of entanglement theory. Finally, we introduce an estimator based on classical shadows that performs better in the big data, few copy regime. Our results show that the naive application of classical machine-learning methods to the quantum setting is problematic, and that a better theoretical foundation of quantum learning is required.

Equivariant quantum neural networks (QNNs) are promising quantum machine learning models that exploit symmetries to provide potential quantum advantages. Despite theoretical developments in equivariant QNNs, their implementation on near-term quantum devices remains challenging due to limited computational resources. This study proposes a resource-efficient model of equivariant quantum convolutional neural networks (QCNNs) called equivariant split-parallelizing QCNN (sp-QCNN). Using a group-theoretical approach, we encode general symmetries into our model beyond the translational symmetry addressed by previous sp-QCNNs. We achieve this by splitting the circuit at the pooling layer while preserving symmetry. This splitting structure effectively parallelizes QCNNs to improve measurement efficiency in estimating the expectation value of an observable and its gradient by order of the number of qubits. Our model also exhibits high trainability and generalization performance, including the absence of barren plateaus. Numerical experiments demonstrate that the equivariant sp-QCNN can be trained and generalized with fewer measurement resources than a conventional equivariant QCNN in a noisy quantum data classification task. Our results contribute to the advancement of practical quantum machine learning algorithms.

Classical learning of the expectation values of observables for quantum states is a natural variant of learning quantum states or channels. While learning-theoretic frameworks establish the sample complexity and the number of measurement shots per sample required for learning such statistical quantities, the interplay between these two variables has not been adequately quantified before. In this work, we take the probabilistic nature of quantum measurements into account in classical modelling and discuss these quantities under a single unified learning framework. We provide provable guarantees for learning parameterized quantum models that also quantify the asymmetrical effects and interplay of the two variables on the performance of learning algorithms. These results show that while increasing the sample size enhances the learning performance of classical machines, even with single-shot estimates, the improvements from increasing measurements become asymptotically trivial beyond a constant factor. We further apply our framework and theoretical guarantees to study the impact of measurement noise on the classical surrogation of parameterized quantum circuit models. Our work provides new tools to analyse the operational influence of finite measurement noise in the classical learning of quantum systems.

Finding practically relevant problems where quantum computation offers a speedup compared to the best known classical algorithms is one of the central challenges in the field. Quantifying a speedup requires a provable convergence rate of the quantum algorithms, which restricts us to studying algorithms that can be analyzed rigorously. The impressive recent progress on building quantum computers gives us a new possibility: We can use heuristic quantum algorithms that can be run on current devices to demonstrate the speedup empirically. This however requires a hardware friendly implementation, i.e., a moderate number of qubits and shallow circuits. In recent years, more and more evidence has been found supporting machine learning tasks as good candidates for demonstrating quantum advantage [1-4]. In particular, the so-called supervised learning setting, where in the simplest case the goal is to learn a binary classifier of classical data, received much attention. The reasons are manifold: (i) The algorithms only require classical access to data.

Factorization Machine (FM) is the most commonly used model to build a recommendation system since it can incorporate side information to improve performance. However, producing item suggestions for a given user with a trained FM is time-consuming. It requires a run-time of $O((N_m \log N_m)^2)$, where $N_m$ is the number of items in the dataset. To address this problem, we propose a quadratic unconstrained binary optimization (QUBO) scheme to combine with FM and apply quantum annealing (QA) computation. Compared to classical methods, this hybrid algorithm provides a faster than quadratic speedup in finding good user suggestions. We then demonstrate the aforementioned computational advantage on current NISQ hardware by experimenting with a real example on a D-Wave annealer.

Optimization of parameterized quantum circuits is indispensable for applications of near-term quantum devices to computational tasks with variational quantum algorithms (VQAs). However, the existing optimization algorithms for VQAs require an excessive number of quantum-measurement shots in estimating expectation values of observables or iterating updates of circuit parameters, whose cost has been a crucial obstacle for practical use. To address this problem, we develop an efficient framework, \textit{stochastic gradient line Bayesian optimization} (SGLBO), for the circuit optimization with fewer measurement shots. The SGLBO reduces the cost of measurement shots by estimating an appropriate direction of updating the parameters based on stochastic gradient descent (SGD) and further by utilizing Bayesian optimization (BO) to estimate the optimal step size in each iteration of the SGD. We formulate an adaptive measurement-shot strategy to achieve the optimization feasibly without relying on precise expectation-value estimation and many iterations; moreover, we show that a technique of suffix averaging can significantly reduce the effect of statistical and hardware noise in the optimization for the VQAs. Our numerical simulation demonstrates that the SGLBO augmented with these techniques can drastically reduce the required number of measurement shots, improve the accuracy in the optimization, and enhance the robustness against the noise compared to other state-of-art optimizers in representative tasks for the VQAs. These results establish a framework of quantum-circuit optimizers integrating two different optimization approaches, SGD and BO, to reduce the cost of measurement shots significantly.