Variational quantum algorithms, a popular heuristic for near-term computers, utilize parameterized circuits which naturally express Lie groups. It has been postulated that many properties of variational algorithms can be understood by studying their corresponding groups, chief among them the presence vanishing gradients or barren plateaus, but theoretical derivation lacking. Using tools from representation theory compact we formulate plateaus whose observables lie in dynamical algebra,...

Exploiting the power of quantum computation to realize superior machine learning algorithms has been a major research focus recent years, but prospects (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes—large regions where cost function gradients vanish exponentially number qubits employed, rendering large effectively untrainable. leading strategy for...

We introduce several probabilistic quantum algorithms that overcome the normal unitary restrictions in machine learning by leveraging linear combination of unitaries (LCU) method. cover three distinct topics, beginning with native implementations residual networks (ResNets). demonstrate while connections between layers a variational can prevent barren plateaus models, this approach is accompanied trade-off success probability. Second, we implement analogue average-pooling from convolutional...

Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver advantage, but its realization for practical applications remains impeded by challenges. Among these, a key barrier computationally expensive task encoding classical data into state, which could erase any prospective speedups over algorithms. In this study, we implement methods efficient preparation states representing encoded image using variational, genetic, and matrix product...

Abstract Quantum computers have the potential to speed up certain computational tasks. A possibility this opens within field of machine learning is use quantum techniques that may be inefficient simulate classically but could provide superior performance in some Machine algorithms are ubiquitous particle physics and as advances made technology there a similar adoption these techniques. In work support vector (QSVM) implemented for signal-background classification. We investigate effect...

Using tools from the representation theory of compact Lie groups, we formulate a Barren Plateaus (BPs) for parameterized quantum circuits whose observables lie in their dynamical algebra (DLA), setting that term Supported Ansatz (LASA). A large variety commonly used ans\"atze such as Hamiltonian Variational Ansatz, Quantum Alternating Operator and many equivariant neural networks are LASAs. In particular, our provides, first time, ability to compute variance gradient cost function compound...

Ensuring data privacy in machine learning models is critical, particularly distributed settings where model gradients are typically shared among multiple parties to allow collaborative learning. Motivated by the increasing success of recovering input from classical models, this study addresses a central question: How hard it recover quantum models? Focusing on variational circuits (VQC) as we uncover crucial role played dynamical Lie algebra (DLA) VQC ansatz determining vulnerabilities....

Federated learning has emerged as a viable distributed solution to train machine models without the actual need share data with central aggregator. However, standard neural network-based federated have been shown be susceptible leakage from gradients shared server. In this work, we introduce variational quantum circuit model built using expressive encoding maps coupled overparameterized ans\"atze. We show that lead inherent privacy against gradient inversion attacks, while...

We introduce several novel probabilistic quantum algorithms that overcome the normal unitary restrictions in machine learning by leveraging Linear Combination of Unitaries (LCU) method. Among our contributions are native implementations Residual Networks (ResNet); demonstrating a path to avoiding barren plateaus while maintaining complexity models hard simulate classically. Furthermore, generalising allow control strength residual connections, we show lower bound LCU success probability can...

Quantum Computing offers a potentially powerful new method for performing Machine Learning. However, several Learning techniques have been shown to exhibit poor generalisation as the number of qubits increases. We address this issue by demonstrating permutation invariant quantum encoding method, which exhibits superior performance, and apply it point cloud data (three-dimensional images composed points). Point clouds naturally contain symmetry with respect ordering their points, making them...

Quantum machine learning (QML) is emerging as an application of quantum computing with the potential to deliver advantage, but its realisation for practical applications remains impeded by challenges. Amongst those, a key barrier computationally expensive task encoding classical data into state, which could erase any prospective speed-ups over algorithms. In this work, we implement methods efficient preparation states representing encoded image using variational, genetic and matrix product...

Exploiting the power of quantum computation to realise superior machine learning algorithmshas been a major research focus recent years, but prospects (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes -- large regions where cost function gradients vanish exponentially number qubits employed, rendering effectively untrainable. leading strategy for combating...

The data encoding circuits used in quantum support vector machine (QSVM) kernels play a crucial role their classification accuracy. However, manually designing these poses significant challenges terms of time and performance. To address this, we leverage the GASP (Genetic Algorithm for State Preparation) framework gate sequence selection QSVM kernel circuits. We explore supervised unsupervised loss functions' impact on circuit optimisation evaluate them diverse datasets binary multiple-class...

Quantum computers have the potential to speed up certain computational tasks. A possibility this opens within field of machine learning is use quantum techniques that may be inefficient simulate classically but could provide superior performance in some Machine algorithms are ubiquitous particle physics and as advances made technology there a similar adoption these techniques. In work support vector (QSVM) implemented for signal-background classification. We investigate effect different...