Predicting many properties of a quantum system from very few measurements

By Hsin-Yuan Huang, Richard Kueng, John Preskill. Nature Physics, 2020

1,650 citations recorded by the source corpus.

Predicting the 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 measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order log(M)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{log}}\,(M)$$\end{document} measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods. An efficient method has been proposed through which the properties of a complex, large-scale quantum system can be predicted without fully characterizing the quantum state.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3986bbdcf8784101bf7a0389948cda48f71ac5f3

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Citations in the corpus

Quantum error mitigation (2022, methodology): “In the more general case, one can imagine either unitar-ily transforming O to a single-qubit observable (if possible) or linearly decomposing it into a sum of simpler terms (which is always possible). of operators using shadow tomography (Hu et al. , 2022; Huang et al. , 2020; Seif et al. , 2023).”
The randomized measurement toolbox (2022, methodology): “Asymptotic scalings M ∝ 2 w / ε 2 have been rigorously shown for equation (4) 24,36 and also observed for equation (3) 23,35,44 .”
Provably efficient machine learning for quantum many-body problems (2021, methodology): “We begin with an overview of the randomized measurement toolbox ( 31 , 32 , 42 – 45 ), rele-gating further details to section S1 ( 46 ).”
Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States (2024, neutral): “…average of a local charged operator if the original state ρ has SW-SSB: The inequalities above came from the joint concavity of fidelity: It is straightforward to show that the above result on local detectability of explicit strong symmetry breaking for ρ + is also valid in the R´enyi-2 sense.”
Quantum computing with Qiskit (2024, background): “Quantum computing is an active area of research [46], and major advances in many areas are needed to solve interesting and classically intractable problems.”
Emergent Quantum State Designs from Individual Many-Body Wave Functions (2021, background): “Further, our work could lead to novel experimental quantum tomography protocols [17,34], cryptographic protocols for hiding information [14], the design of unforgeable quantum encryption [15], and also new methods for quantum device verification [18,19].”
Variational quantum algorithms (2020, background): “Another promising approach to efficient measurements is the construction of classical shadows [197], also know as shadow tomography.”