Near-term quantum computers are accessed through repeated circuit executions, which produce finite measurement records rather than exact deterministic outputs. In quantum reservoir computing, these records are converted to feature vectors for a classical readout. The standard expectation-value approach averages all shots from one labeled time step into a single feature vector. This reduces finite-shot noise, but it also gives the readout only one training example from many circuit executions. We introduce split-ensemble training: the same shots are split into groups, and each group average is used as a separate, partially denoised feature vector for the same target. The quantum circuit, task, and measurement budget remain unchanged. Across simulated forecasting benchmarks and real hardware experiments, this simple reorganization improves prediction when full averaging leaves the readout with too few training examples, with the strongest gains observed on hardware. Our results establish shot-record organization as a simple, broadly applicable algorithmic lever for improving near-term quantum learning without additional quantum hardware cost.
Near-term quantum computers are accessed through repeated circuit executions, which produce finite measurement records rather than exact deterministic outputs. In quantum reservoir computing, these records are converted to feature vectors for a classical readout. The standard expectation-value approach averages all shots from one labeled time step into a single feature vector. This reduces finite-shot noise, but it also gives the readout only one training example from many circuit executions. We introduce split-ensemble training: the same shots are split into groups, and each group average is used as a separate, partially denoised feature vector for the same target. The quantum circuit, task, and measurement budget remain unchanged. Across simulated forecasting benchmarks and real hardware experiments, this simple reorganization improves prediction when full averaging leaves the readout with too few training examples, with the strongest gains observed on hardware. Our results establish shot-record organization as a simple, broadly applicable algorithmic lever for improving near-term quantum learning without additional quantum hardware cost.
Quantum Machine Learning (QML) has recently emerged as a rapidly growing domain as an intersection of Quantum Computing (QC) and Machine Learning (ML) fields. Hybrid quantum-classical models have demonstrated exponential speedups in various machine learning tasks compared to their classical counterparts. On one hand, training of QML models on real hardware remains a challenge due to long wait queue and the access cost. On the other hand, simulation-based training is not scalable to large QML models due to exponentially growing simulation time. Since the measurement operation converts quantum information to classical binary data, the quantum circuit is executed multiple times (called shots) to obtain the basis state probabilities or qubit expectation values. Higher number of shots worsen the training time of QML models on real hardware and the access cost. Higher number of shots also increase the simulation-based training time. In this paper, we propose shot optimization method for QML models at the expense of minimal impact on model performance. We use classification task as a test case for MNIST and FMNIST datasets using a hybrid quantum-classical QML model. First, we sweep the number of shots for short and full versions of the dataset. We observe that training the full version provides 5-6% higher testing accuracy than short version of dataset with up to 10X higher number of shots for training. Therefore, one can reduce the dataset size to accelerate the training time. Next, we propose adaptive shot allocation on short version dataset to optimize the number of shots over training epochs and evaluate the impact on classification accuracy. We use a (a) linear function where the number of shots reduce linearly with epochs, and (b) step function where the number of shots reduce in step with epochs. We note around 0.01 increase in loss and ~4% (1%) reduction in testing accuracy for reduction in shots by up to 100X (10X) for linear (step) shot function compared to conventional constant shot function for MNIST dataset, and 0.05 increase in loss and ~5-7% (5-7%) reduction in testing accuracy with similar reduction in shots using linear (step) shot function on FMNIST dataset. For comparison, we also use the proposed shot optimization methods to perform ground state energy estimation of different molecules and observe that step function gives the best and most stable ground state energy prediction at 1000X less number of shots.
Quantum machine learning (QML) models hold promise for leveraging quantum computers in data-driven tasks but their performance on today's noisy quantum hardware remains an open question. In this work, we investigate the impact of shot noise, the statistical noise due to finite sampling in quantum measurements, on the training and performance of quantum neural network (QNN) models. Using a dataset of dielectron collision events from CERN, we train QNNs under varying levels of simulated noise. Three ansatz circuit architectures are explored namely BasicEntanglerLayers (Ansatz-1), SimplifiedTwoDesign (Ansatz-2) and StronglyEntanglingLayers (Ansatz-3). Each model is repeatedly trained for multiple runs at noise levels ranging from zero up to significant noise fractions (0.5), with each training run consisting of 20 epochs of parameter optimization. We evaluate the convergence behavior, final error rates and variability across runs for each noise setting. Our results show a clear degradation of QNN performance as shot noise increases with training loss converging more slowly and to higher values and the model's prediction accuracy deteriorates with larger noise. Notably, the ansatz with fewer parametric gates demonstrates relatively better robustness to noise compared to deeper, more strongly entangling circuits which suffer sharper performance drops under noise. We provide detailed comparisons of the three circuit designs, including training loss curves and statistical summaries of performance at each noise level. These findings shed light on the practical limits of QML models in the Noisy Intermediate-Scale Quantum (NISQ) era and highlight the trade-offs between circuit expressiveness and noise resilience. Finally, we discuss implications for designing noise-aware quantum models and possible strategies to mitigate shot noise effects in quantum learning.
Abstract Single-qubit data re-uploading classifiers map every input to a point on the Bloch sphere and are routinely evaluated by thresholding an expectation value estimated from many repetitions of the circuit (shots). A single measurement, however, can deliver at most the Helstrom accuracy of the two class-conditional mixtures, which for one qubit reduces to the length of the difference between the class-mean Bloch vectors. We call the difference between thresholded accuracy and single-shot accuracy the shot gap and measure it in a computational experiment with known ground truth: four synthetic tasks with exact Bayes accuracy, five circuit depths, three training losses, two label-noise levels and ten seeds (1,200 runs), simulated exactly and validated against a state-vector simulation, finite-difference gradients and a brute-force search over measurements. The Helstrom bound held in every run. For circuits of depth two or more, models whose thresholded accuracy averaged 0.857 delivered 0.696 per single measurement, a mean shot gap of 0.161; at depth six, models with 0.93–0.98 thresholded accuracy on the linear, circle and XOR tasks delivered 0.67–0.86 per shot. The embedding, not the choice of measurement, accounted for 96.3% of the single-shot shortfall. Training with the single-shot log-likelihood narrowed the shot gap relative to a smoothed hinge loss in 89% of paired configurations (median reduction 0.085) at a median cost of 0.011 in thresholded accuracy, and eleven shots recovered 74% of the gap against 41% under the hinge loss. Two preregistered hypotheses were not supported: the gap did not grow with boundary nonlinearity, and training loss predicted it better than class-mean Bloch-vector length. Accuracy reports for quantum classifiers should state the number of shots per prediction, as they state training data and compute.
On near-term quantum hardware, estimating a Born probability requires repeated circuit executions. A quantum learning experiment with a fixed measurement budget B must therefore decide how many distinct training states n to use and how many shots S to allocate to each state. We study this tradeoff for binary quantum classifiers with fixed or independently selected measurement operators M, where the ideal score is Tr(Mρ). We prove a distribution-free generalization bound that separates the finite-sample and finite-shot contributions. The sample term scales as d/n, while the shot term scales as (logn)/S; under the constraint B=nS, these two terms move in opposite directions. Minimising a conservative closed-form surrogate of the bound gives the allocation rule n∗=22dB/log(2B/δ) and S∗=B/nstar. This surrogate has the same asymptotic scaling as the exact minimizer and yields a worst-case rate of B−1/4. The guarantee is intentionally conservative, since it applies to the full class of binary quantum measurements. We complement the theory with PennyLane simulations using 2-qubit and 4-qubit variational quantum circuits on nine synthetic binary classification benchmarks. In all tested configurations, the one-sided empirical generalization gap remains below the theoretical bound. The result provides a conservative statistical guideline for allocating measurement budgets in finite-shot evaluation and pre-experimental planning for near-term quantum learning systems, complementing hardware-level scheduling and circuit-design considerations. Extending the guarantee to fully adaptive shot-noisy training remains an open problem.
Symmetry reduces the capacity of a quantum learning model, but the imposed group must match both the measured information and the label transformation. We establish a finite-measurement theory for inferring this group from candidate transformations. The central structural result identifies observable-invisible transformations with the stabilizer of a projected state whenever the probe span is invariant. It turns recovered generators into a valid subgroup and identifies the continuous invisible space with its Lie algebra. For finite dictionaries, an unbiased shadow statistic distinguishes zero from positive squared expectation discrepancies with an inverse-gap measurement rate, improving the inverse-square-gap rate of uniform discrepancy estimation. A commuting qubit lower bound proves the gap dependence optimal at fixed snapshot scale, and simultaneous intervals support data-dependent tolerances. Task validation then tests either the joint distribution through a characteristic kernel or its encoded mean through a classical--quantum discrepancy. An exact group-average identity relates the latter to joint-state asymmetry and specifies its conversion to binary task breaking mass. Projection bias quantifies the cost of excessive symmetry, while an ℓ1 readout bound quantifies the capacity gained by relaxing it. At an invariant pure-state backbone, retained and nontrivial breaking sectors are Fisher-orthogonal. Ising-chain calculations connect finite-shot recovery, label-dependent symmetry, and physical sector drift. These results determine which symmetry the measurements support and provide the statistical and geometric basis for a subsequent release decision.
Quantum Machine Learning (QML) is an exciting frontier applying the philosophy of quantum computation to classical machine learning for improved learning performance of complicated tasks. However, QML is greatly challenged by realistic issues like noisy quantum measurements and limited labeled quantum data caused by the high cost and technological limitations. This paper explores the novel transfer-learning mechanisms to tackle these issues, which allow the reuse of the knowledge from related quantum tasks for improving model performance and generalization in resource-limited scenarios. Transfer learning, one of the great and successful concepts of classical machine learning, is to transfer the learned parameters or features from the source domain (or task) to the target domain (or task). We further develop and investigate, in quantum, a methodology where parameterized quantum circuits (PQCs) learnt on a source quantum data set have certain parts partially re-used or fine-tuned for a target task, given limited amount of target data. This strategy also avoids large quantum training runs that are not scalable on state-of-the-art noisy intermediate-scale quantum (NISQ) processors. The suggested methods are layerwise quantum adaptation, quantum kernel reuse and hybrid quantum-classical feature transfer. We investigate the robustness of these mechanisms in presence of noise by simulating quantum circuits using depolarizing and readout noise models. Moreover, we show that pretraining of quantum models on synthetic (or simulated) data sets (which are generated using larger, less noisy systems) can be instrumental in learning on real, small-sized quantum devices. Experiment results in quantum classification tasks demonstrate the effectiveness of transfer learning in boosting the accuracy, accelerating the convergence, and lowering the quantum circuit depth of successfully trained model. It is interesting to mention that transfer using layer-wise models became very resistant to quantum noise, as its performance did not degrade significantly for noisy inputs. These results demonstrate that transfer learning can overcome the scarce quantum data and suppress the harmful impact of measurement noise. This work presents a potential venue for enhancing the applicability of QML in the NISQ era. By transferring knowledge from theoretical quantum learning models to actual quantum hardware constraints, transfer learning allows quantum algorithms to learn faster and generalize better across tasks.