A quantum residual neural network using deterministic mixtures of identity and variational unitaries to enable post-selection-free residual learning with 10x fewer gates and reported accuracies of 99% binary and 80% multi-class on image datasets.
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Classification with quantum neural networks on near term processors
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abstract
We introduce a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning. The quantum circuit consists of a sequence of parameter dependent unitary transformations which acts on an input quantum state. For binary classification a single Pauli operator is measured on a designated readout qubit. The measured output is the quantum neural network's predictor of the binary label of the input state. First we look at classifying classical data sets which consist of n-bit strings with binary labels. The input quantum state is an n-bit computational basis state corresponding to a sample string. We show how to design a circuit made from two qubit unitaries that can correctly represent the label of any Boolean function of n bits. For certain label functions the circuit is exponentially long. We introduce parameter dependent unitaries that can be adapted by supervised learning of labeled data. We study an example of real world data consisting of downsampled images of handwritten digits each of which has been labeled as one of two distinct digits. We show through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets. We then discuss presenting the data as quantum superpositions of computational basis states corresponding to different label values. Here we show through simulation that learning is possible. We consider using our QNN to learn the label of a general quantum state. By example we show that this can be done. Our work is exploratory and relies on the classical simulation of small quantum systems. The QNN proposed here was designed with near-term quantum processors in mind. Therefore it will be possible to run this QNN on a near term gate model quantum computer where its power can be explored beyond what can be explored with simulation.
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Quantum neural networks exhibit membership privacy leakage that a proposed quantum machine unlearning framework with three mechanisms can mitigate in simulations and cloud device tests.
QKAN is a quantum algorithmic framework using block-encodings and QSVT to implement wide-and-shallow networks for quantum learning and compositional state preparation.
Classical RNNs trained on small instances provide parameter initializations for QAOA and VQE that reduce total optimization iterations and generalize across problem sizes.
Divide-and-conquer QAOA samples and Hamming-weight-conditioned neural network surrogates accelerate MCMC mixing for constrained Ising problems by average factors of 20.3 and 7.6 over classical pair-flip baselines.
Harmoniq approximates a quantum-harmonic-analysis data augmentation operator as a mixture of at most quadratic-depth n-qubit circuits, enabling modular combination with other quantum subroutines for signal denoising.
Hybrid quantum PINN for hydrology reports 3x faster convergence and 44% fewer parameters than classical PINN on Sri Lankan flood data while using physics constraints for uncertainty quantification.
QAOA for random k-SAT derives efficacy from an adiabatic manifold that supports rigorous performance guarantees at depth Θ(n²) and sublinear parameter optimization via SAMP at depth O(n).
Gate fusion applied to both forward and backward passes in quantum circuit simulation achieves 20-30x throughput gains and supports training large 20-qubit 1000-layer QML models with 60000 parameters using gradient checkpointing.
A dual GNN predictor evaluates hardware-aware quantum circuit graphs to select task-specific kernels that balance expressivity and NISQ constraints, outperforming baselines on classification benchmarks.
Equivariant sp-QCNN encodes general symmetries with group theory, splits circuits at pooling layers to preserve symmetry while enabling parallel measurements, and shows improved efficiency and trainability over standard equivariant QCNNs in noisy quantum data classification.
Optimized QED intervals plus steady-state extraction enable PEC+QED to deliver 2-11x lower error than PEC alone on Iceberg codes for QAOA.
Quantum kernel ridge regression shows double descent in test risk, with the interpolation peak suppressible by regularization, via random matrix theory asymptotics in the high-dimensional limit.
A necessary condition for variational quantum circuits to reach exact ground states requires matching module projection norms between input and solution, enabling classical O(n^5) exact solvers for problems like MaxCut.
Analog quantum kernels with operational noise outperform noiseless versions in benchmarking and non-Markovianity estimation due to increased expressivity and model complexity.
A 4-qubit QCNN classifies entanglement thresholds from fermion density profiles in the Thirring model more effectively than comparable classical CNNs.
PennyLane is a software library extending automatic differentiation to hybrid quantum-classical systems for variational quantum algorithms.
Quantum computers may enable more natural manipulation of Fourier spectra in ML models via the Quantum Fourier Transform, potentially leading to resource-efficient spectral methods.
Increasing the number of local patches in a distributed quantum neural network architecture reduces the largest Hessian eigenvalue at minima and introduces a class-dependent outlier structure in the eigenspectrum.
Selecting a customized Hermitian observable enables training of QNNs up to 10 qubits under noise for global cost functions, outperforming Pauli observables, while PauliZ works best for local cost functions up to 10 qubits.
Distributed QNNs with partitioned feature encoding achieve >96% accuracy on MNIST 10-class classification using ensembles of small circuits.
Quantum reservoir computing with distributed architectures reduces time-series forecasting errors by up to 78.8% MAE and 72.3% RMSE in NISQ simulations compared to classical methods.
Brickwall quantum circuits with Haar-random, dual-unitary, and solvable two-qubit gates serve as effective reservoirs for temporal processing tasks, with performance correlated to circuit dynamics and validated on synthetic prediction benchmarks.
Quantum-inspired deep neural networks extract Compton form factors from JLab data with higher predictive accuracy and tighter uncertainties than classical DNNs on pseudodata benchmarks, then applied to real measurements.
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Harmoniq: Efficient Data Augmentation on a Quantum Computer Inspired by Harmonic Analysis
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Variational Quantum Physics-Informed Neural Networks for Hydrological PDE-Constrained Learning with Inherent Uncertainty Quantification
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Mechanism of Efficacy in QAOA for Random k-SAT: From Adiabatic Manifold to Sublinear Parameter Optimization
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Fast and memory-efficient classical simulation of quantum machine learning via forward and backward gate fusion
Gate fusion applied to both forward and backward passes in quantum circuit simulation achieves 20-30x throughput gains and supports training large 20-qubit 1000-layer QML models with 60000 parameters using gradient checkpointing.
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Hardware-Aware Quantum Kernel Design Based on Graph Neural Networks
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Resource-efficient equivariant quantum convolutional neural networks
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Co-Designing Error Mitigation and Error Detection for Logical Qubits
Optimized QED intervals plus steady-state extraction enable PEC+QED to deliver 2-11x lower error than PEC alone on Iceberg codes for QAOA.
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Double Descent in Quantum Kernel Ridge Regression
Quantum kernel ridge regression shows double descent in test risk, with the interpolation peak suppressible by regularization, via random matrix theory asymptotics in the high-dimensional limit.
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Reachability Constraints in Variational Quantum Circuits: Optimization within Polynomial Group Module
A necessary condition for variational quantum circuits to reach exact ground states requires matching module projection norms between input and solution, enabling classical O(n^5) exact solvers for problems like MaxCut.
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Noise-enhanced quantum kernels on analog quantum computers
Analog quantum kernels with operational noise outperform noiseless versions in benchmarking and non-Markovianity estimation due to increased expressivity and model complexity.
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Quantum Machine Learning for particle scattering entanglement classification
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PennyLane: Automatic differentiation of hybrid quantum-classical computations
PennyLane is a software library extending automatic differentiation to hybrid quantum-classical systems for variational quantum algorithms.
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Spectral methods: crucial for machine learning, natural for quantum computers?
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The effect of the number of parameters and the number of local feature patches on loss landscapes in distributed quantum neural networks
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HQNET: Harnessing Quantum Noise for Effective Training of Quantum Neural Networks in NISQ Era
Selecting a customized Hermitian observable enables training of QNNs up to 10 qubits under noise for global cost functions, outperforming Pauli observables, while PauliZ works best for local cost functions up to 10 qubits.
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Distributed Quantum Neural Networks via Partitioned Features Encoding
Distributed QNNs with partitioned feature encoding achieve >96% accuracy on MNIST 10-class classification using ensembles of small circuits.
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Scalable Quantum Reservoir Computing over Distributed Quantum Architectures
Quantum reservoir computing with distributed architectures reduces time-series forecasting errors by up to 78.8% MAE and 72.3% RMSE in NISQ simulations compared to classical methods.
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Evaluating quantum circuits in the reservoir computing paradigm
Brickwall quantum circuits with Haar-random, dual-unitary, and solvable two-qubit gates serve as effective reservoirs for temporal processing tasks, with performance correlated to circuit dynamics and validated on synthetic prediction benchmarks.
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Compton Form Factor Extraction using Quantum Deep Neural Networks
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Magnitude Is All You Need? Rethinking Phase in Quantum Encoding of Complex SAR Data
Magnitude-only encoding reaches 99.57% accuracy on 3-class and 71.19% on 8-class SAR tasks in hybrid models, beating phase-inclusive alternatives, while phase boosts pure quantum models by up to 21.65 points.
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A Comprehensive Analysis of Accuracy and Robustness in Quantum Neural Networks
QCNN, QRNN, and QViT perform well on low-feature data but degrade on high-feature datasets, with QViT most robust to quantum noise and classical-style models better against adversarial noise.
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Hybrid Quantum Neural Networks for Enhanced Breast Cancer Thermographic Classification: A Novel Quantum-Classical Integration Approach
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A Review of Variational Quantum Algorithms: Insights into Fault-Tolerant Quantum Computing
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