Related papers: Classical shadows with arbitrary group representat…
Deep learning has seen substantial achievements, with numerical and theoretical evidence suggesting that singularities of statistical models are considered a contributing factor to its performance. From this remarkable success of classical…
State smoothing is a technique to estimate a state at a particular time, conditioned on information obtained both before (past) and after (future) that time. For a classical system, the smoothed state is a normalized product of the…
Learning latent representations from complex data is central to modern machine learning, spanning temporal, multimodal, and partially observed systems. In such settings, representations are better understood as latent states capturing…
"Classical shadows" are estimators of an unknown quantum state, constructed from suitably distributed random measurements on copies of that state [Nature Physics 16, 1050-1057]. Here, we analyze classical shadows obtained using random…
With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short…
Transmitting information about quantum states over classical noisy channels is an important problem with applications to science, computing, and sensing. This task, however, poses fundamental challenges due to the exponential scaling of…
Transmission of classical information over a quantum state-dependent channel is considered, when the encoder can measure channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. In…
This paper presents an original ABC algorithm, "ABC Shadow", that can be applied to sample posterior densities that are continuously differentiable. The proposed method uses the ideas given by the auxiliary variable MH of (M\o ller and…
Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from future measurements (smoothing). While classical smoothing is…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly…
We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory we identify all cases when the criterion can be computed exactly in terms of the spectrum of a…
Shadow tomography via classical shadows is a state-of-the-art approach for estimating properties of a quantum state. We present a simplified, combinatorial analysis of a recently proposed instantiation of this approach based on the ensemble…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from…
This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that…
Applied statistical problems often come with pre-specified groupings to predictors. It is natural to test for the presence of simultaneous group-wide signal for groups in isolation, or for multiple groups together. Classical tests for the…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representation. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be…
Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible…
Generalized Coherent States (GCS) are constructed (and discussed) in order to study quasiclassical behaviour of quantum spin models of the Heisenberg type. Several such models are taken to their semiclassical limits, whose form depends on…