Related papers: Classical shadows over symmetric spaces
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…
Learning quantum state properties is both a fundamental and practical problem in quantum information theory. Classical shadows have emerged as an efficient method for estimating properties of unknown quantum states, with rigorous…
Classical shadows are a computationally efficient approach to storing quantum states on a classical computer for the purposes of estimating expectation values of local observables, obtained by performing repeated random measurements. In…
Classical shadows (CS) have emerged as a powerful way to estimate many properties of quantum states based on random measurements and classical post-processing. In their original formulation, they come with optimal (or close to) sampling…
Classical shadows provide a versatile framework for estimating many properties of quantum states from repeated, randomly chosen measurements without requiring full quantum state tomography. When prior information is available, such as…
Efficiently learning expectation values of a quantum state using classical shadow tomography has become a fundamental task in quantum information theory. In a classical shadows protocol, one measures a state in a chosen basis W after it has…
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…
The classical shadow estimation protocol is a noise-resilient and sample-efficient quantum algorithm for learning the properties of quantum systems. Its performance depends on the choice of a unitary ensemble, which must be chosen by a user…
Classical Shadow Tomography (Huang, Kueng and Preskill, Nature Physics 2020) is a method for creating a classical snapshot of an unknown quantum state, which can later be used to predict the value of an a-priori unknown observable on that…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
Predicting properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few…
Classical shadows constitute a protocol to estimate the expectation values of a collection of M observables acting on O(1) qubits of an unknown n-qubit state with a number of measurements that is independent of n and that grows only…
Classical shadows are an efficient method for constructing an approximate classical description of a quantum state using very few measurements. In the paper we propose to enhance classical shadow methods using bootstrap resampling methods.…
Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli…
The method of classical shadows heralds unprecedented opportunities for quantum estimation with limited measurements [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020)]. Yet its relationship to established quantum…
Classical shadow tomography has become a powerful tool in learning about quantum states prepared on a quantum computer. Recent works have used classical shadows to variationally enforce N-representability conditions on the 2-particle…
We study the sample complexity of the classical shadows task: what is the fewest number of copies of an unknown state you need to measure to predict expected values with respect to some class of observables? Large joint measurements are…
A crucial subroutine for various quantum computing and communication algorithms is to efficiently extract different classical properties of quantum states. In a notable recent theoretical work by Huang, Kueng, and Preskill [Nat. Phys. 16,…
We study classical shadows protocols based on randomized measurements in $n$-qubit entangled bases, generalizing the random Pauli measurement protocol ($n = 1$). We show that entangled measurements ($n\geq 2$) enable nontrivial and…