Related papers: Triply efficient shadow tomography
The classical shadows protocol is an efficient strategy for estimating properties of an unknown state $\rho$ using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from…
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…
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,…
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…
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…
Improving the performance of quantum algorithms is a fundamental task to achieve quantum advantage. In many cases, extracting information from quantum systems poses an important challenge for practical implementations in real-world quantum…
Full quantum tomography of high-dimensional quantum systems is experimentally infeasible due to the exponential scaling of the number of required measurements on the number of qubits in the system. However, several ideas were proposed…
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…
Detecting multipartite entanglement in many qubit systems is measurement-intensive, motivating protocols that estimate only selected observables with provable efficiency. In this work we use the classical shadow protocol to study the sample…
We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a…
Shadow estimation is an efficient method for predicting many observables of a quantum state with a statistical guarantee. In the multi-shot scenario, one performs projective measurement on the sequentially prepared state for $K$ times after…
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…
In this article we develop a continuous variable (CV) shadow tomography scheme with wide ranging applications in quantum optics. Our work is motivated by the increasing experimental and technological relevance of CV systems in quantum…
Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly,…
Characterising large-scale quantum systems is central to fundamental physics and essential for applications of quantum technologies. While a full characterisation requires exponentially increasing resources, focusing on application-relevant…
Classical shadows (CS) has recently emerged as an important framework to efficiently predict properties of an unknown quantum state. A common strategy in CS protocols is to parametrize the basis in which one measures the state by a random…
We propose a tomographic protocol for estimating any $ k $-body reduced density matrix ($ k $-RDM) of an $ n $-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and…
Fringe projection profilometry has been increasingly sought and applied in dynamic three-dimensional (3D) shape measurement. In this work, a robust and high-efficiency 3D measurement based on Gray-code light is proposed. Unlike the…
Classical shadow tomography has emerged as a powerful framework for predicting properties of quantum many-body systems with favorable sample complexity. Standard theoretical guarantees, however, rely on the assumption that experimental…
The classical shadows protocol, recently introduced by Huang, Kueng, and Preskill [Nat. Phys. 16, 1050 (2020)], is a quantum-classical protocol to estimate properties of an unknown quantum state. Unlike full quantum state tomography, the…