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The numerical emulation of quantum physics and quantum chemistry often involves an intractable number of degrees of freedom and admits no known approximation in general form. In practice, representing quantum-mechanical states using…
Noise and errors are unavoidable in any realistic quantum process, including processes designed to reduce noise and errors in the first place. In particular, quantum thermodynamical protocols for cooling can be significantly affected,…
Diffusion MRI (dMRI) is the only non-invasive technique sensitive to tissue micro-architecture, which can, in turn, be used to reconstruct tissue microstructure and white matter pathways. The accuracy of such tasks is hampered by the low…
We develop generalization error bounds for stochastic gradient descent (SGD) with label noise in non-convex settings under uniform dissipativity and smoothness conditions. Under a suitable choice of semimetric, we establish a contraction in…
Quantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum…
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in…
Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum…
The past decade has witnessed significant advancements in quantum hardware, encompassing improvements in speed, qubit quantity, and quantum volume-a metric defining the maximum size of a quantum circuit effectively implementable on…
In recent proposals of quantum circuit models for generative tasks, the discussion about their performance has been limited to their ability to reproduce a known target distribution. For example, expressive model families such as Quantum…
We report an experimental investigation of the role of measurement in quantum metrology when the states of the probes are mixed. In particular, we investigated optimized local measurements and general global projective measurements,…
The ultimate goal of a supervised learning algorithm is to produce models constructed on the training data that can generalize well to new examples. In classification, functional margin maximization -- correctly classifying as many training…
Quantitative susceptibility mapping (QSM) utilizes MRI signal phase to infer estimates of local tissue magnetism (magnetic susceptibility), which has been shown useful to provide novel image contrast and as biomarkers of abnormal tissue.…
Quantum Neural Networks (QNNs) represent a promising direction within Quantum Machine Learning (QML), yet their realization on noisy intermediate-scale quantum (NISQ) devices remains constrained by decoherence, gate imperfections,…
Supervised deep learning involves the training of neural networks with a large number $N$ of parameters. For large enough $N$, in the so-called over-parametrized regime, one can essentially fit the training data points. Sparsity-based…
Finding solid and practical quantum advantages via noisy quantum devices without error correction is a critical but challenging problem. Conversely, comprehending the fundamental limitations of the state-of-the-art is equally crucial. In…
Variational quantum eigensolver (VQE) is promising to show quantum advantage on near-term noisy-intermediate-scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially the physical noise on realistic…
While Quantum Machine Learning (QML) holds great potential, its practical realization on Noisy Intermediate-Scale Quantum (NISQ) hardware has been hindered by the limitations of variational quantum circuits (VQCs). Recent evidence suggests…
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features…
Quantum technology has entered the era of noisy intermediate-scale quantum (NISQ) information processing. The technological revolution of machine learning represented by generative models heralds a great prospect of artificial intelligence,…
We study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data. We show that…