Related papers: An infinite hierarchy of multi-copy quantum learni…
Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with…
We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown $d$-dimensional quantum state $\rho$ and a known set of observables $\{O_i\}_{i=1}^m$, the goal is to…
A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the…
Randomised measurements can efficiently characterise many-body quantum states by learning the expectation values of observables with low Pauli weights. In this paper, we generalise the theoretical tools of classical shadow tomography to the…
Quantum computers can efficiently sample from probability distributions that are believed to be classically intractable, providing a foundation for quantum generative modeling. However, practical training of such models remains challenging,…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases, generalizing the random Pauli measurement protocol ($n = 1$). We show that entangled measurements ($n\geq 2$) enable nontrivial and…
The computational cost of preparing a quantum state can be substantial depending on the structure of data to be encoded. Many quantum algorithms require repeated sampling to find the answer, mandating reconstruction of the same input state…
The hidden subgroup problem ($\mathsf{HSP}$) has been attracting much attention in quantum computing, since several well-known quantum algorithms including Shor algorithm can be described in a uniform framework as quantum methods to address…
We provide a general machine learning methodology that integrates classical shadow representations with unsupervised principal component analysis (PCA) to explore various quantum phase transitions. By sampling spin configurations from…
Quantum metrology of an incoherent signal is a canonical sensing problem related to superresolution and noise spectroscopy. We show that quantum computing can accelerate searches for a weak incoherent signal when the signal and noise are…
We study model-agnostic copies of machine learning classifiers. We develop the theory behind the problem of copying, highlighting its differences with that of learning, and propose a framework to copy the functionality of any classifier…
We describe a new shadow tomography algorithm that uses $n=\Theta(\sqrt{m}\log m/\epsilon^2)$ samples, for $m$ measurements and additive error $\epsilon$, which is independent of the dimension of the quantum state being learned. This stands…
Nonclassical phenomena tied to entangled states are the focus of foundational studies and powerful resources in many applications. By contrast, the counterparts in quantum measurements are still poorly understood. Notably, genuine…
The ability of modern quantum simulators--both digital and analogue--to generate large ensembles of single-shot projective "snapshots" has opened a data-rich avenue for the study of quantum many-body systems. Unsupervised machine learning…
Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require…
In the past decade, the field of quantum machine learning has drawn significant attention due to the prospect of bringing genuine computational advantages to now widespread algorithmic methods. However, not all domains of machine learning…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…
Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state…