Related papers: Classical shadows with symmetries
Classical learning of the expectation values of observables for quantum states is a natural variant of learning quantum states or channels. While learning-theoretic frameworks establish the sample complexity and the number of measurement…
In this review we discuss the latest results concerning development of the machine learning algorithms for characterization of the magnetic skyrmions that are topologically-protected magnetic textures originated from the…
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…
Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this work we introduce a method for…
Learning properties of quantum states from measurement data is a fundamental challenge in quantum information. The sample complexity of such tasks depends crucially on the measurement primitive. While shadow tomography achieves…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
A constant number of random Clifford measurements allows the classical shadow protocol to perform direct fidelity estimation (DFE) with high precision. However, estimating properties of an unknown quantum state is expected to be more…
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…
We study various measures of classicality of the states of open quantum systems subject to decoherence. Classical states are expected to be stable in spite of decoherence, and are thought to leave conspicuous imprints on the environment.…
Classical shadows are a versatile tool to probe many-body quantum systems, consisting of a combination of randomised measurements and classical post-processing computations. In a recently introduced version of the protocol, the…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
Verifying whether a quantum device produces a specific state is a fundamental task in many applications of modern quantum technologies. In the conventional framework of quantum state verification, designing an optimal or efficient protocol…
Since symmetry properties of coherent states (CS) on M\"obius strip (MS) and fermions are closely related, CS on MS are naturally associated to the topological properties of fermionic fields. Here we consider CS and superpositions of…
We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…
Classical shadow tomography serves as a potent tool for extracting numerous properties from quantum many-body systems with minimal measurements. Nevertheless, prevailing methods yielding optimal performance for few-body operators…
Quantum computers solve ever more complex tasks using steadily growing system sizes. Characterizing these quantum systems is vital, yet becoming increasingly challenging. The gold-standard is quantum state tomography (QST), capable of fully…
We introduce a variational scheme inspired by classical shadow tomography to compute ground state correlations of quantum spin Hamiltonians. Shadow tomography allows for efficient reconstruction of expectation values of arbitrary…
We introduce a systematic study of "symmetric quantum circuits", a new restricted model of quantum computation that preserves the symmetries of the problems it solves. This model is well-adapted for studying the role of symmetry in quantum…