Related papers: Partial Quantum Shadow Tomography for Structured O…
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…
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…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth…
The need to perform quantum state tomography on ever larger systems has spurred a search for methods that yield good estimates from incomplete data. We study the performance of compressed sensing (CS) and least squares (LS) estimators in a…
We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and…
The deployment of intermediate- and large-scale quantum devices necessitates the development of efficient full state tomographical techniques for quantum benchmarks. Here, we introduce a matrix filling-based method for tomography of pure…
Verifying the proper preparation of quantum states is essential in modern quantum information science. Various protocols have been developed to estimate the fidelity of quantum states produced by different parties. Direct fidelity…
Reconstruction of density matrices is important in NMR quantum computing. An analysis is made for a 2-qubit system by using the error matrix method. It is found that the state tomography method determines well the parameters that are…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…
The totality of normalised density matrices of order N forms a convex set Q_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q_N onto a two-plane and show…
Efficient fidelity estimation of multiqubit quantum states is crucial to many applications in quantum information processing. However, to estimate the infidelity $\epsilon$ with multiplicative precision, conventional estimation protocols…
Quantum state tomography (QST) is an essential technique for characterizing quantum states. However, practical implementations of QST are significantly challenged by factors such as shot noise, attenuation, and Raman scattering, especially…
We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements…
Resource-efficient quantum state tomography is one of the key ingredients of future quantum technologies. In this work, we propose a new tomography protocol combining standard quantum state reconstruction methods with an attention-based…
Quantum State Tomography (QST) is a fundamental technique in Quantum Information Processing (QIP) for reconstructing unknown quantum states. However, the conventional QST methods are limited by the number of measurements required, which…
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…
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…
We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the…