Related papers: Classical shadows with arbitrary group representat…
Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting…
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 introduce a post-processing technique for classical shadow measurement data that enhances the precision of ground state estimation through high-dimensional subspace expansion; the dimensionality is only limited by the amount of classical…
We argue that to solve the foundational problems of quantum theory one has to first understand what it means to quantize a classical system. We then propose a quantization method based on replacement of deterministic c-numbers by…
Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum…
Snapshot compressed sensing (CS) refers to compressive imaging systems in which multiple frames are mapped into a single measurement frame. Each pixel in the acquired frame is a noisy linear mapping of the corresponding pixels in the frames…
Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this…
Given copies of a quantum state $\rho$, a shadow tomography protocol aims to learn all expectation values from a fixed set of observables, to within a given precision $\epsilon$. We say that a shadow tomography protocol is triply efficient…
In this paper, we investigate state estimation and opacity verification problems within a decentralized observation architecture. Specifically, we consider a discrete event system whose behavior is recorded by a set of observation sites.…
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…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
Shadow estimation provides an efficient framework for estimating observable expectation values using randomized measurements. While originally developed for discrete-variable systems, its recent extensions to continuous-variable (CV)…
Measuring properties of quantum systems is a fundamental problem in quantum mechanics. We provide a simple method for estimating the expectation value of observables with an unknown quantum state. The idea is to use a data structure to…
The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum…
We give the first tight sample complexity bounds for shadow tomography and classical shadows in the regime where the target error is below some sufficiently small inverse polynomial in the dimension of the Hilbert space. Formally we give a…
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates,…
Efficiently estimating properties of large and strongly coupled quantum systems is a central focus in many-body physics and quantum information theory. While quantum computers promise speedups for many such tasks, near-term devices are…
Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as {importance sampling,} observable…
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…
In this tutorial I intend to present some of the results I obtained through my PhD work in the "quantum optics group of the University of Isfahan" under consideration Dr. R. Roknizadeh and Prof. S. Twareque Ali as my supervisor and advisor,…