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The success of modern deep learning hinges on the ability to train neural networks at scale. Through clever reuse of intermediate information, backpropagation facilitates training through gradient computation at a total cost roughly…

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…

Quantum Physics · Physics 2021-04-20 Hsin-Yuan Huang , Richard Kueng , John Preskill

Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…

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…

Quantum Physics · Physics 2024-09-11 Tian-Gang Zhou , Pengfei Zhang

Quantum measurements are slow, while classical processors are fast, yet existing hybrid protocols never exploit this asymmetry. In this work, we propose an alternative formulation of classical estimators as online algorithms that are…

Quantum Physics · Physics 2026-03-30 Marwa Marso , Sabrina Herbst , Jadwiga Wilkens , Vincenzo De Maio , Ivona Brandic , Richard Kueng

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…

Quantum Physics · Physics 2026-05-27 Xun Tang , Haoxuan Chen , Yuehaw Khoo , Lexing Ying

Gradient-based optimizers have been proposed for training variational quantum circuits in settings such as quantum neural networks (QNNs). The task of gradient estimation, however, has proven to be challenging, primarily due to distinctive…

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 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…

Quantum Physics · Physics 2024-06-18 Gregory Boyd , Bálint Koczor , Zhenyu Cai

We propose ShadowGPT, a novel approach for solving quantum many-body problems by learning from randomized measurement data collected from quantum experiments. The model is a generative pretrained transformer (GPT) trained on simulated…

Quantum Physics · Physics 2024-11-20 Jian Yao , Yi-Zhuang You

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be…

Quantum Physics · Physics 2024-05-21 Daniel T. Chen , Zain H. Saleem , Michael A. Perlin

Quantum state tomography (QST) is the art of reconstructing an unknown quantum state through measurements. It is a key primitive for developing quantum technologies. Neural network quantum state tomography (NNQST), which aims to reconstruct…

Quantum Physics · Physics 2024-06-18 Victor Wei , W. A. Coish , Pooya Ronagh , Christine A. Muschik

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

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…

Quantum Physics · Physics 2025-06-04 Maxwell West , Antonio Anna Mele , Martin Larocca , M. Cerezo

Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer…

Quantum Physics · Physics 2023-12-20 Irma Avdic , David A. Mazziotti

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…

Quantum Physics · Physics 2026-05-08 Rebecca Chang , Maureen Krumtünger , Martin Larocca , Maxwell West

Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime by neural-network protocols and classical shadows, while both methods have…

Quantum Physics · Physics 2023-08-23 Yuxuan Du , Yibo Yang , Tongliang Liu , Zhouchen Lin , Bernard Ghanem , Dacheng Tao

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…

Quantum Physics · Physics 2024-01-10 Kaifeng Bu , Dax Enshan Koh , Roy J. Garcia , Arthur Jaffe

We introduce a method to enforce some symmetries starting from a trial wave-function prepared on quantum computers that might not respect these symmetries. The technique eliminates the necessity for performing the projection on the quantum…

Quantum Physics · Physics 2023-11-09 Edgar Andres Ruiz Guzman , Denis Lacroix

The classical simulation of quantum systems typically requires exponential resources. Recently, the introduction of a machine learning-based wavefunction ansatz has led to the ability to solve the quantum many-body problem in regimes that…

Disordered Systems and Neural Networks · Physics 2019-10-24 Joseph Gomes , Keri A. McKiernan , Peter Eastman , Vijay S. Pande