Maria Schuld

Quantum Computing’s Spectral Advantage in Machine Learning

Quantum computers may offer a novel approach to machine learning by leveraging spectral methods. These methods, which involve manipulating the Fourier spectrum of machine learning models, are inherently suited to quantum computing due to the efficiency of the Quantum Fourier Transform. This could enable unprecedented manipulation of model properties, potentially leading to more resource-efficient and fundamentally different machine learning designs.

2026-04-14 - NITheCS Public Talk & launch of the Quantum Africa Society - Presented by Maria Schuld

mariaschuld starred PennyLaneAI/pennylane-rigetti: This PennyLane plugin allows the Rigetti Forest QPUs, QVM, and wavefunction simulator to optimize quantum circuits.

This PennyLane plugin allows the Rigetti Forest QPUs, QVM, and wavefunction simulator to optimize quantum circuits.. Stars: 45

mariaschuld starred ysig/GraKeL: A scikit-learn compatible library for graph kernels

A scikit-learn compatible library for graph kernels. Stars: 639

mariaschuld starred XanaduAI/thewalrus: A library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling.

A library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling.. Stars: 108

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Expert Perspectives on the Trajectory and Challenges of Quantum Machine Learning

Experts in quantum machine learning (QML) discuss the field's current state, emphasizing the need for critical evaluation beyond "speedups." Key areas of focus include the potential for QML algorithms to process quantum data directly, the importance of rigorous theoretical foundations, and the necessity of interdisciplinary collaboration. The discussion highlights the uncertainty surrounding immediate commercial applications, instead pointing to scientific discovery and tool development as more immediate and attainable goals.

Quantum Computers Excel at Spectral Methods Fundamental to Machine Learning

Spectral methods, which manipulate the Fourier spectrum of ML models for learning and regularization, align naturally with quantum computing capabilities like the Quantum Fourier Transform. Representing generative models as quantum states enables efficient spectrum manipulation unavailable classically. These methods underpin ML successes, including spectral bias in deep learning, SVM Fourier regularization, and CNN Fourier filters, suggesting quantum approaches could yield more direct, resource-efficient model design.

Quantum Fourier Transform Enables Exact Probabilistic Modeling of Permutations

Quantum computers exploit super-exponential speedup in the Quantum Fourier Transform (QFT) over the symmetric group to encode exact non-Abelian harmonic analysis models for permutation-structured data. These models, intractable classically, capture permutation correlations via group Fourier spectra, powering Markov chains with diffusion and Bayesian conditioning steps. The approach targets applications like multi-object tracking and recommendation systems, marking an initial step toward practical non-Abelian QFT utility.

Quantum Heuristics Detect Weak Entanglement via Approximate Hidden Subgroup Algorithms

The paper extends the hidden cut algorithm, which detects fully unentangled qubit partitions using Shor's hidden subgroup method, to identify weakly entangled registers through approximate symmetries. It establishes a rigorous link between the hidden cut algorithm's output distribution and a reward function quantifying cut quality. Reducing input state copies yields measurement samples revealing weak entanglement patterns, broadening hidden subgroup applications beyond cryptography.

Stratonovich-Weyl Quantum Phase Spaces Act as Tunable Group Fourier Filters for Quantum Resources

Group Fourier analysis decomposes quantum states into irreducible representations (irreps) of a symmetry group to assess resourcefulness in compact Lie-group quantum resource theories (QRTs). The family of Stratonovich-Weyl quantum phase space (QPS) representations, parameterized by the Cahill-Glauber s, functions as a tunable group Fourier filter: s=-1 emphasizes low-dimensional irreps dominant in free states, s=0 preserves the spectrum, and s=1 highlights high-dimensional irreps indicative of resources. QPS spectra are fully characterized by norms of free state Fourier components, with an s-duality linking free and Haar-random resourceful state spectra.

Quantum Kernel Methods Leverage Hilbert Space Equivalence to Boost Classical ML Classifiers

Kernel methods in ML define similarity measures between data points via positive semi-definite functions, equivalent to inner products in a high-dimensional Hilbert feature space, enabling nonlinear classification through the kernel trick in algorithms like SVMs and Gaussian processes. Quantum theory mirrors this kernel structure due to shared Hilbert space foundations, allowing quantum feature maps to generate expressive kernels for hybrid quantum-classical ML. This equivalence expands feature spaces to simplify separable data problems unachievable by linear models.

Hybrid Quantum Transfer Learning Augments Pre-Trained Classical Networks with Quantum Circuits for Efficient NISQ Processing

The paper extends transfer learning to hybrid classical-quantum neural networks by pre-training classical networks on high-dimensional data like images and augmenting them with final variational quantum circuits. This leverages classical preprocessing to embed informative features into quantum processors, ideal for noisy intermediate-scale quantum (NISQ) devices. Proof-of-concept demonstrations include image recognition and quantum state classification, experimentally validated on IBM and Rigetti quantum computers using PennyLane.

Strawberry Fields Applications Layer Enables Easy GBS Algorithm Implementation for Near-Term Photonic Quantum Computing

Gaussian Boson Sampling (GBS) serves as a near-term photonic quantum computing platform with algorithms for graph problems, point processes, and molecular vibronic spectra. The Strawberry Fields library introduces a new applications layer that allows users to design and implement GBS algorithms using minimal code. This software acts as both an introduction with examples and a review of state-of-the-art GBS applications.

Duality Links Gaussian Boson Sampling Probabilities to Prism Graph Matching Polynomials

Gaussian boson sampling (GBS) photon-number probabilities for graph G define coefficients of a new displaced GBS polynomial. This polynomial exhibits a duality with the matching polynomial of the prism graph G □ P₂(x), the Cartesian product of G with a weighted edge. The duality enables novel classical simulation methods for GBS and underpins recent coarse-grained quantum feature maps.

Stochastic Gradient Descent Emerges from Few-Shot Expectation Value Estimation in Hybrid Quantum-Classical Optimization

Quantum hardware estimation of expectation values in parameterized quantum circuits induces stochastic gradient descent (SGD) for hybrid quantum-classical optimizers like VQE, QAOA, and quantum classifiers. Using as few as k=1 measurement shots per expectation value yields algorithms with provable convergence guarantees. For gradients as linear combinations of expectations (e.g., Hamiltonian terms, parameter-shift rules, dataset sums), doubly stochastic variants via term sampling further reduce measurements while maintaining rigorous convergence. Numerical benchmarks demonstrate state-of-the-art performance with drastically fewer circuit executions.

Gaussian Boson Samplers Enable Hardware-Efficient Graph Kernels for Quantum Machine Learning

Gaussian Boson Samplers (GBS), proposed for near-term quantum advantage demonstrations, are leveraged to construct a graph kernel via feature maps derived from sampling outputs. This kernel measures graph similarity by linking GBS probability distributions to subgraph matching numbers, enabling graph isomorphism testing and competitive performance on benchmark datasets against classical kernels. The approach frames kernels as quantum hardware-efficient feature mappings, opening applications for Noisy Intermediate-Scale Quantum devices in graph analysis.

Machine Learning's Symbiotic Integration with Physical Sciences: Insights, Applications, and Architectures

Machine learning algorithms, informed by physical principles like statistical physics, enhance understanding of ML methods while enabling applications across particle physics, cosmology, quantum many-body systems, quantum computing, and materials science. The review highlights bidirectional exchanges, including physics-motivated conceptual advances in ML and domain-specific ML successes tackling unique challenges. It also covers novel hardware architectures designed to accelerate ML computations.

Efficient Gradient Estimation for Quantum Circuits on Near-Term Hardware

Gradients of expectation values in parametrized quantum circuits can be estimated using nearly identical hardware architectures to the original circuit. For many cases, a single gate parameter shift and two circuit runs suffice for each gradient component. The approach generalizes to continuous-variable systems and uses ancilla conditioning for broader scenarios, enabling optimization in hybrid quantum-classical algorithms.

PennyLane Enables Differentiable Programming for Hybrid Quantum-Classical Computations

PennyLane is a Python 3 framework for differentiable programming of quantum computers, supporting qubit and continuous-variable devices. It computes gradients of variational quantum circuits compatibly with classical backpropagation, extending automatic differentiation to hybrid quantum-classical models. Plugins integrate with quantum hardware like Xanadu Cloud, Amazon Braket, and IBM Quantum, plus ML libraries including TensorFlow, PyTorch, JAX, and Autograd.

Universal Continuous-Variable Quantum Neural Networks via Layered Gaussian and Non-Gaussian Gates

The paper presents variational quantum circuits in the continuous-variable (CV) architecture as universal neural networks, using layered Gaussian gates for affine transformations and non-Gaussian gates for nonlinear activations. These CV-QNNs encode highly nonlinear transformations unitarily, support embeddings of classical networks including convolutional, recurrent, and residual variants. Experiments with Strawberry Fields demonstrate applications like fraud detection classification, Tetris image generation, and hybrid classical-quantum autoencoders.

Low-Depth Variational Quantum Classifiers with Poly-Log Parameters for Noisy Quantum Hardware

Proposes a variational quantum classifier encoding input features into quantum state amplitudes, processed by a shallow circuit of parameterized single- and two-qubit gates followed by single-qubit measurement. The architecture scales learnable parameters poly-logarithmically with input dimension, enabling deployment on limited-qubit, error-prone devices. Quantum-classical training uses analytical gradient estimation via circuit perturbations; simulations show strong performance on classical benchmarks with fewer parameters than alternatives, plus noise resilience via quantum dropout.

Quantum Kernel Methods Mirror Feature Maps to Hilbert Spaces

Quantum computing parallels kernel methods by enabling efficient computation in high-dimensional Hilbert spaces via nonlinear feature maps that encode classical data into quantum states. Two quantum ML approaches emerge: (1) quantum estimation of intractable kernel inner products for classical algorithms like SVMs; (2) variational quantum circuits as linear classifiers directly in feature Hilbert space. Demonstrated with continuous-variable squeezing feature maps on 2D benchmark data.

Quantum Ensembles Enable Exponentially Large Untrained Classifier Aggregates via Parallel Evaluation

Quantum ensembles of quantum classifiers form by preparing a superposition state that encodes multiple classifiers, allowing parallel evaluation on a quantum computer followed by a single-qubit measurement for the collective decision. This approach supports exponentially large ensembles without individual training, akin to Bayesian averaging. An example weights classifiers by training performance, yielding novel quantum and classical machine learning results.

Quantum Interference Circuit Enables Simple Distance-Based Classification

Researchers implement a distance-based classifier using a minimal quantum circuit consisting of state preparation, a single Hadamard gate, and two single-qubit measurements. The circuit computes distances between data points in quantum parallel, bypassing complex subroutines like Hamiltonian simulation. Numerical simulations and IBM Quantum Experience demonstrations show strong performance on simple benchmark tasks.

Quantum Algorithms for Gradient Descent and Newton's Method Enable Efficient Constrained Polynomial Optimization

Quantum gradient descent and Newton's method optimize unit-norm constrained polynomials using quantum phase estimation, adapted quantum PCA, and quantum matrix operations. These algorithms scale polylogarithmically with solution vector dimension but exponentially with iteration count. They offer advantages for high-dimensional problems requiring few iterations, relevant to machine learning optimization.

Quantum Linear Regression Enables Direct Prediction via Single Qubit Measurement

The algorithm performs least-squares linear regression on quantum computers, prioritizing prediction of outputs for new inputs over parameter readout. It handles non-sparse data via low-rank approximations, reducing condition number dependence. Runtime is logarithmic in input dimension when data is quantum-encoded, with results accessible via one qubit measurement for further processing.

Quantum Algorithm Leverages Hamming Distance for Enhanced Pattern Classification

This paper introduces a quantum machine learning approach to pattern classification by adapting Trugenberger's quantum Hamming distance measurement method. The algorithm aims to exploit quantum computing's known advantages over classical methods for specific tasks within machine learning. It demonstrates potential benefits using handwritten digit recognition from the MNIST dataset as a benchmark.

Quantum Perceptron via Phase Estimation Mimics Classical Step Activation with Linear Resources

The paper proposes a quantum perceptron model that simulates the step-activation function of classical perceptrons using the quantum phase estimation algorithm. It processes inputs of size n with O(n) resource requirements, enabling efficient scaling. This foundational unit supports development of trainable quantum neural networks in quantum machine learning.

Systematic Overview of Quantum Machine Learning Approaches

Quantum machine learning explores enhancing classical ML algorithms using quantum computing, from efficient execution of costly subroutines to reformulating stochastic methods in quantum terms. The field addresses tasks like image/speech recognition and optimization relevant to IT. This paper provides an accessible systematic review of approaches, technical details, and prospects for a quantum learning theory.

No Existing Quantum Neural Network Fully Merges Neural Nonlinearity with Quantum Unitary Dynamics

Quantum Neural Networks (QNNs) aim to fuse neural computing's nonlinear, dissipative dynamics with quantum computing's linear, unitary evolution, but current proposals fall short. The paper systematically reviews QNN research, defines key requirements, and finds no model fully leverages both quantum advantages and neural properties. It proposes Open Quantum Neural Networks via dissipative quantum computing as a promising path forward.

Quantum Walks Model Associative Memory in Qubit-Based Neural Networks

Proposes quantum neural networks (QNNs) using qubits instead of binary neurons to leverage quantum computing. Models QNN dynamics via stochastic quantum walks on global firing state graphs, replicating classical associative memory. Biased discrete Hadamard walks from biological neuron updates fail unitarity, but stochastic walks succeed with modest quantum speed-up in select regimes.