English
Related papers

Related papers: Sample-optimal classical shadows for pure states

200 papers

Shadow tomography via classical shadows is a state-of-the-art approach for estimating properties of a quantum state. We present a simplified, combinatorial analysis of a recently proposed instantiation of this approach based on the ensemble…

Quantum Physics · Physics 2022-08-01 Bryan O'Gorman

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…

Quantum Physics · Physics 2025-03-28 Robbie King , David Gosset , Robin Kothari , Ryan Babbush

This paper studies quantum supervised learning for classical inference from quantum states. In this model, a learner has access to a set of labeled quantum samples as the training set. The objective is to find a quantum measurement that…

Quantum Physics · Physics 2024-08-26 Mohsen Heidari , Wojciech Szpankowski

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…

Quantum Physics · Physics 2024-10-03 Giacomo De Palma , Tristan Klein , Davide Pastorello

We provide practical and powerful schemes for learning many properties of an unknown n-qubit quantum state using a sparing number of copies of the state. Specifically, we present a depth-modulated randomized measurement scheme that…

We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…

Quantum Physics · Physics 2025-06-12 Angus Lowe , Ashwin Nayak

Quantum state tomography (QST) remains the prevailing method for benchmarking and verifying quantum devices; however, its application to large quantum systems is rendered impractical due to the exponential growth in both the required number…

Quantum Physics · Physics 2025-01-10 Zhen Qin , Joseph M. Lukens , Brian T. Kirby , Zhihui Zhu

Interfacing quantum and classical processors is an important subroutine in full-stack quantum algorithms. The so-called "classical shadow" method efficiently extracts essential classical information from quantum states, enabling the…

Quantum Physics · Physics 2025-09-11 Shuowei Ma , Junyu Liu

We introduce the problem of *shadow tomography*: given an unknown $D$-dimensional quantum mixed state $\rho$, as well as known two-outcome measurements $E_{1},\ldots,E_{M}$, estimate the probability that $E_{i}$ accepts $\rho$, to within…

Quantum Physics · Physics 2018-11-14 Scott Aaronson

We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where the unitary ensemble is invariant under local basis…

Quantum Physics · Physics 2025-10-27 Hong-Ye Hu , Soonwon Choi , Yi-Zhuang You

Accurate estimation of observables in quantum systems is a central challenge in quantum information science, yet practical implementations are fundamentally constrained by the limited number of measurement shots. In this work we explore a…

Quantum Physics · Physics 2025-11-05 Keijo Korhonen , Stefano Mangini , Joonas Malmi , Hetta Vappula , Daniel Cavalcanti

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…

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…

Quantum Physics · Physics 2024-01-23 Pierre-Gabriel Rozon , Ning Bao , Kartiek Agarwal

The rapid development of quantum technology demands efficient characterization of complex quantum many-body states. However, full quantum state tomography requires an exponential number of measurements in system size, preventing its…

Quantum Physics · Physics 2024-12-04 Yadong Wu , Ce Wang , Juan Yao , Hui Zhai , Yi-Zhuang You , Pengfei Zhang

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…

Quantum Physics · Physics 2021-01-20 G. I. Struchalin , Ya. A. Zagorovskii , E. V. Kovlakov , S. S. Straupe , S. P. Kulik

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…

Quantum Physics · Physics 2022-09-08 Weiyuan Gong , Scott Aaronson

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…

Quantum Physics · Physics 2025-09-17 Hyunho Cha , Jungwoo Lee

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…

Quantum Physics · Physics 2023-07-05 You Zhou , Qing Liu

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…

Quantum Physics · Physics 2023-12-27 Jonas Helsen , Michael Walter

Classical shadows are succinct classical representations of quantum states which allow one to encode a set of properties P of a quantum state rho, while only requiring measurements on logarithmically many copies of rho in the size of P. In…

Quantum Physics · Physics 2026-05-28 Georgios Karaiskos , Dorian Rudolph , Johannes Jakob Meyer , Jens Eisert , Sevag Gharibian