Related papers: New Bounds on Quantum Sample Complexity of Measure…
Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…
We prove that the quantum measurement process contains the same warping mechanism that occurs in categorical perception, a phenomenon ubiquitous in human perception. This warping causes stimuli belonging to the same category to be perceived…
Quantum sensing exploits quantum phenomena to enhance the detection and estimation of classical parameters of physical systems and biological entities, particularly so as to overcome the inefficiencies of its classical counterparts. A…
Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated…
Machine learning models with inputs in a Euclidean space $\mathbb{R}^d$, when implemented on digital computers, generalize, and their generalization gap converges to $0$ at a rate of $c/N^{1/2}$ concerning the sample size $N$. However, the…
Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be…
Beyond computer science, quantum complexity theory can potentially revolutionize multiple branches of physics, ranging from quantum many-body systems to quantum field theory. In this paper, we investigate the relationship between the sample…
Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve…
A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
We explore the role of $\textit{collective measurements}$ on precision in estimation of a single parameter. Collective measurements are represented by observables which commute with all permutations of the probe particles. We show that with…
Measurement uncertainty and experimental error are important concepts taught in undergraduate physics laboratories. Although student ideas about error and uncertainty in introductory classical mechanics lab experiments have been studied…
Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
Classical shadow tomography (CST) involves obtaining enough classical descriptions of an unknown state via quantum measurements to predict the outcome of a set of quantum observables. CST has numerous applications, particularly in…
Learning a hidden property of a quantum system typically requires a series of interactions. In this work, we formalise such multi-round learning processes using a generalisation of classical-quantum states, called classical-quantum combs.…
Classical shadows provide a versatile framework for estimating many properties of quantum states from repeated, randomly chosen measurements without requiring full quantum state tomography. When prior information is available, such as…
Nonclassicality, defined in the quantum optical sense, serves as a resource for photon-based quantum technologies. Therefore, certifying the nonclassicality of a quantum state is crucial for gauging its potential for quantum advantage.…
Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for…
We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…