A quantum neural network (QNN) built from gates that conserve the Hamming weight keeps its data in one weight sector, so the shots that left the sector can be discarded at readout. This is the qg filter of the qang library [1, 2]. We show that, with equal amplitude damping (T1) on every qubit, the filtered readout of such a network is exactly the noiseless one in any weight sector. The kept fraction of shots is (1 − γ)k d for weight k and depth d, and training under T1 with the filter gives exactly the parameters of noiseless training. We then measure what this is worth on four small classification datasets. Every result is reported with the filter and without it, and every prediction was committed before its run, failures included. Over 60 runs per model, a network trained on a simulator and run under T1 gains +2.5 points from the filter at weight 1 (95% CI [0.8, 4.1]) and +16.5 points at weight 2 ([11.8, 21.2]), recovering its noiseless accuracy exactly. A network trained under the calibrated noise without the filter catches up (diflerences of 0.1 points), and the filter corrects neither dephasing nor unequal T1 across qubits. These models are classically simulable and no quantum advantage is claimed. The filter is a way to make noise—free training valid under relaxation, at a shot cost known in advance. The models are released as qang. qml (version 0.6.0, pip install qang).
A quantum neural network (QNN) built from gates that conserve the Hamming weight keeps its data in one weight sector, so the shots that left the sector can be discarded at readout. This is the qg filter of the qang library [1, 2]. We show that, with equal amplitude damping (T1) on every qubit, the filtered readout of such a network is exactly the noiseless one in any weight sector. The kept fraction of shots is (1 − γ)k d for weight k and depth d, and training under T1 with the filter gives exactly the parameters of noiseless training. We then measure what this is worth on four small classification datasets. Every result is reported with the filter and without it, and every prediction was committed before its run, failures included. Over 60 runs per model, a network trained on a simulator and run under T1 gains +2.5 points from the filter at weight 1 (95% CI [0.8, 4.1]) and +16.5 points at weight 2 ([11.8, 21.2]), recovering its noiseless accuracy exactly. A network trained under the calibrated noise without the filter catches up (diflerences of 0.1 points), and the filter corrects neither dephasing nor unequal T1 across qubits. These models are classically simulable and no quantum advantage is claimed. The filter is a way to make noise—free training valid under relaxation, at a shot cost known in advance. The models are released as qang. qml (version 0.6.0, pip install qang).
A quantum neural network (QNN) built from gates that conserve the Hamming weight keeps its data in one weight sector, so the shots that left the sector can be discarded at readout. This is the qg filter of the qang library [1, 2]. We show that, with equal amplitude damping (T1) on every qubit, the filtered readout of such a network is exactly the noiseless one in any weight sector. The kept fraction of shots is (1 − γ)k d for weight k and depth d, and training under T1 with the filter gives exactly the parameters of noiseless training. We then measure what this is worth on four small classification datasets. Every result is reported with the filter and without it, and every prediction was committed before its run, failures included. Over 60 runs per model, a network trained on a simulator and run under T1 gains +2.5 points from the filter at weight 1 (95% CI [0.8, 4.1]) and +16.5 points at weight 2 ([11.8, 21.2]), recovering its noiseless accuracy exactly. A network trained under the calibrated noise without the filter catches up (diflerences of 0.1 points), and the filter corrects neither dephasing nor unequal T1 across qubits, although alone it loses less than one point up to a ±80% spread of 1/T1. With noise-aware training and a richer readout, the model without the filter was 1.2 points better in one study, but over 60 new runs that gap shrank to +0.5 points and was not significant. The weight-2 deficit comes from the pair-product encoding, not from the readout; with an encoding that fills the whole sector and a full-rank readout, weight 2 reaches the weight-1 accuracy. On noise models of IBM and IonQ devices the filter cuts the error of the measured qgZ by 2.7-3.6×; on the IonQ Forte-1 noise model over 189 inputs of four datasets the filtered model is 1.1 points more accurate than the raw one, and calibrating the errors the filter keeps with five echo circuits per model halves the remaining error of the decision value: decisions that difler from the noiseless model fall from 15 (raw) and 7 (filter) to 3 over 945 readings on five device noise models. With a faithful weight-2 encoding the advantage of the unfiltered model under noise-aware training disappears, and a classifier given both the filtered and the raw features gains nothing over the filter alone. Over 513 readout configurations, including kept fractions down to 2.6×10−7, unequal T1 and dephasing, the filter has the lower readout error whenever about 20 shots are kept, and a closed-form rule predicts the winner. These models are classically simulable and no quantum advantage is claimed. The filter is a way to make noise-free training valid under relaxation, at a shot cost known in advance. The models are released as qang. qml (version 0.6.13, pip install qang).
A quantum neural network (QNN) built from gates that conserve the Hamming weight keeps its data in one weight sector, so the shots that left the sector can be discarded at readout. This is the qg filter of the qang library [1, 2]. We show that, with equal amplitude damping (T1) on every qubit, the filtered readout of such a network is exactly the noiseless one in any weight sector. The kept fraction of shots is (1 − γ)k d for weight k and depth d, and training under T1 with the filter gives exactly the parameters of noiseless training. We then measure what this is worth on four small classification datasets. Every result is reported with the filter and without it, and every prediction was committed before its run, failures included. Over 60 runs per model, a network trained on a simulator and run under T1 gains +2.5 points from the filter at weight 1 (95% CI [0.8, 4.1]) and +16.5 points at weight 2 ([11.8, 21.2]), recovering its noiseless accuracy exactly. A network trained under the calibrated noise without the filter catches up (diflerences of 0.1 points), and the filter alone corrects neither dephasing nor unequal T1 across qubits, although it loses less than one point up to a ±80% spread of 1/T1. Unequal T1 is corrected by training UÏtl the filter under the calibrated decay rates: the kept state depends only on their ratios, so the model lands within 0.5 points of noiseless at a ±100% spread, ignores a 10% calibration error and, at weight 2, loses 0.7 points under a 1.5-fold drift of all T1 that costs the raw noise-aware model 10. With noise-aware training and a richer readout, the model without the filter was 1.2 points better in one study, but over 60 new runs that gap shrank to +0.5 points and was not significant. The weight-2 deficit comes from the pair-product encoding, not from the readout; with an encoding that fills the whole sector and a full-rank readout, weight 2 reaches the weight-1 accuracy. On noise models of IBM and IonQ devices the filter cuts the error of the measured qgZ by 2.7-3.6×; on the IonQ Forte-1 noise model over 189 inputs of four datasets the filtered model is 1.1 points more accurate than the raw one, and calibrating the errors the filter keeps with five echo circuits per model halves the remaining error of the decision value: decisions that difler from the noiseless model fall from 15 (raw) and 7 (filter) to 3 over 945 readings on five device noise models. With a faithful weight-2 encoding the advantage of the unfiltered model under noise-aware training disappears, and a classifier given both the filtered and the raw features gains nothing over the filter alone. Over 513 readout configurations, including kept fractions down to 2.6 ×10−7, unequal T1 and dephasing, the filter has the lower readout error whenever about 20 shots are kept, and a closed-form rule predicts the winner. The same holds beyond the first model: at 8 qubits a weight-2 network keeps its noiseless 0.965 with the filter and drops to 0.705 without it; a five-class classifier (one class per qubit) keeps its noiseless accuracy under T1 with the filter and loses 15-18 points without it on five-class digits; training from 100 or 1000 shots per step with the filter is 1.0-1.5 points ahead of training without it; and the filtered gradient equals the noiseless one, while the raw one is K times smaller at weight 1. On five device noise models the echo calibration turns class confusions back: flipped decisions of the five-class model fall from 51 (raw) and 24 (filter) to 15 over 500 readings. The echo helped only where the filtered error was well above shot noise, and it still removed a third of the filtered error with a 28 × 28 matrix at 8 qubits. These models are classically simulable and no quantum advantage is claimed. The filter is
Circuits built from gates that conserve the Hamming weight keep their state in one weight sector, so the shots that left the sector can be discarded at read-out: the qg filter of the open-source library qang [1], a form of symmetry verification [2, 3]. We make it usable on IBM devices through IBM Runtime and Qiskit, and measure it on the noise models of twenty IBM devices. The library adds a Qiskit transpiler pass that decides whether the filter applies, read-out correction from each device's published per-qubit errors, qg read-outs of IBM Runtime Sampler and Estimator results, zero-noise extrapolation by gate folding that stacks with the filter, a prediction of the filter's kept fraction from the calibration, qubit selection with that prediction, a shot planner, and the weight-conserving quantum neural network (QNN) of qang as one parameterized job and as a qiskit-machine-learning SamplerQNN. Every prediction was committed before its run and is reported as passed or failed. On ten five-qubit weight-1 circuits the filter lowers the error of the measured qgZ = ⟨Z⟩ from 0.065-0.104 to 0.018-0.023 on three devices (0.013-0.022 with read-out correction), and filter plus zero-noise extrapolation reaches 0.011-0.015. On seventeen further devices never used before, the filter cuts the error 2.4-8.9× on every one (median 3.1× with read-out correction). Choosing the qubits by the predicted kept fraction keeps 6-17 points more shots than Qiskit's default layout on chain circuits, avoids a qubit published as reading 1 always, and the shot planner met a 0.02 target precision on three devices. For classification the gain is small: the QNN recovers 5-6 of the 10 decisions noise costs it. Reading a known five-component principal-component spectrum out of the data's density matrix in the weight-1 sector, filter plus read-out correction lowers the error 4.6× (median over twenty-one devices) and orders the spectrum correctly on 18 of 21 (13 raw). In Trotter simulation of the XY chain the filter halves the best error and moves the optimal number of Trotter steps deeper (16 of 21 devices), and in a quantum walk it turns a raw spreading indistinguishable from a classical random walk (exponent 0.87) into ballistic spreading (1.84). With two or three interacting excitations (XXZ chain) the gain falls from 5.6× to 2.6×: larger sectors let more of the noise through. Two interoperability bugs were found, one in qiskit-machine-learning and one in the library. All results are on device noise models; no hardware run is reported.
Each qubit’s local qg values are a point in the Bloch ball. Its squared distance from the centre, , is the radius of the sphere on which the qubit lives (area ). For a pure register the deficit is the known one-tangle of the qubit with the rest; with noise it mixes entanglement and impurity. We show that circuits which conserve the Hamming weight remove this ambiguity under one noise model. In a state of fixed weight on every qubit, so and the deficit is read from Z-basis shots alone; under equal amplitude damping the qg symmetry filter returns the noiseless state exactly, so the filtered deficit is the noiseless one-tangle. In a pre-registered simulation (90 configurations) the filtered deficit equals it to , and on product states it is exactly zero, while the unfiltered readout reports a false deficit of 0.60–0.95. On five device noise models (three IBM backends, two IonQ) the filter cuts the deficit error of trained circuits 3.2–4.0 times, but it removes only 15–33% of the false deficit of a product state: errors that move an excitation inside the sector survive the filter, and near a pole the deficit amplifies them as . The radius also separates the polar angle in radians from the length of the vector, : this angle is exact under depolarizing noise, where $\arccosqg_Z$ errs by up to 0.7 rad, and it is 5–9 times more accurate on the device noise models once the noise gates are actually executed. Three of nineteen predictions failed and are reported. Everything is reproduced by the open-source library qang (version 0.6.8, pip install qang).
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.
Quantum neural networks (QNNs) suffer from a fundamental sampling bottleneck since quantum measurements are probabilistic, requiring many circuit executions to estimate outputs with sufficient accuracy. Conventional Monte-Carlo (MC) inference exhibits an O(1/N) sampling error, rendering QNN inference and training costly on near-term quantum hardware, especially where each shot requires expensive qubit generation. This work introduces a "single-shot" QNN framework by integrating quantum amplitude estimation (AE) into the readout stage. By embedding a trained QNN as a state-preparation oracle within AE, outputs are estimated through coherent interference rather than repeated sampling. We demonstrate that AE-based QNN inference achieves an O(1/N) error even with a single shot. We further analyze noise robustness and training feasibility, showing that AE can be a powerful primitive for overcoming the sampling overhead of QNNs. This highlights that when the model itself is quantum, quantum algorithms can enhance the computation efficiency.