Related papers: Precision Bounds on Continuous-Variable State Tomography using Classical Shadows

Precision Bounds on Continuous-Variable State Tomography using Classical Shadows

URL: http://arxiv.org/abs/2211.05149v2
Date: Fri, 15 Dec 2023 20:41:42 GMT
Title: Precision Bounds on Continuous-Variable State Tomography using Classical Shadows
Authors: Srilekha Gandhari, Victor V. Albert, Thomas Gerrits, Jacob M. Taylor, Michael J. Gullans
Abstract summary: We recast experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. numerical and experimental homodyne tomography significantly outperforms our bounds.
Score: 0.46603287532620735
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an $N$-photon density matrix with a high probability, we show that homodyne detection requires an order $\mathcal{O}(N^{4+1/3})$ measurements in the worst case, whereas PNR and photon-parity detection require $\mathcal{O}(N^4)$ measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in $N$. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.

Related papers

Neural Network Enhanced Single-Photon Fock State Tomography [6.434126816101052]
We report the experimental implementation of single-photon quantum state tomography by directly estimating target parameters. Our neural network enhanced quantum state tomography characterizes the photon number distribution for all possible photon number states from the balanced homodyne detectors. Such a fast, robust, and precise quantum state tomography provides us a crucial diagnostic toolbox for the applications with single-photon Fock states and other non-Gaussisan quantum states.
arXiv Detail & Related papers (2024-05-05T04:58:18Z)
Experimental investigation of a multi-photon Heisenberg-limited interferometric scheme: the effect of imperfections [0.0]
We show how to achieve the exact Heisenberg limit (HL) in ab-initio phase estimation with $N=3$ photon-passes. The advantage of the HL over the SNL increases with the number of resources used. We show that the expected usefulness of the prepared triphoton state for HL phase estimation is significantly degraded by even quite small experimental imperfections.
arXiv Detail & Related papers (2024-02-29T12:04:36Z)
Importance sampling for stochastic quantum simulations [68.8204255655161]
We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
arXiv Detail & Related papers (2022-12-12T15:06:32Z)
Retrieving space-dependent polarization transformations via near-optimal quantum process tomography [55.41644538483948]
We investigate the application of genetic and machine learning approaches to tomographic problems. We find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes.
arXiv Detail & Related papers (2022-10-27T11:37:14Z)
Schwinger model on an interval: analytic results and DMRG [0.0]
We show that the conventional Gauss law constraint commonly used in simulations induces a strong boundary effect on the charge density. We obtain by bosonization a number of exact analytic results for local observables in the massless Schwinger model.
arXiv Detail & Related papers (2022-10-01T15:33:06Z)
Lower bounds for learning quantum states with single-copy measurements [3.2590610391507444]
We study the problems of quantum tomography and shadow tomography using measurements performed on individual copies of an unknown $d$-dimensional state. In particular, this rigorously establishes the optimality of the folklore Pauli tomography" algorithm in terms of its complexity.
arXiv Detail & Related papers (2022-07-29T02:26:08Z)
Quantum state tomography with tensor train cross approximation [84.59270977313619]
We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements.
arXiv Detail & Related papers (2022-07-13T17:56:28Z)
Taming numerical errors in simulations of continuous variable non-Gaussian state preparation [1.2891210250935146]
A powerful instrument for such simulation is the numerical computation in the Fock state representation. We analyze the accuracy of several currently available methods for computation of the truncated coherent displacement operator. We then employ the method in analysis of non-Gaussian state preparation scheme based on coherent displacement of a two mode squeezed vacuum with subsequent photon counting measurement.
arXiv Detail & Related papers (2022-02-15T11:41:57Z)
Regularization by Denoising Sub-sampled Newton Method for Spectral CT Multi-Material Decomposition [78.37855832568569]
We propose to solve a model-based maximum-a-posterior problem to reconstruct multi-materials images with application to spectral CT. In particular, we propose to solve a regularized optimization problem based on a plug-in image-denoising function. We show numerical and experimental results for spectral CT materials decomposition.
arXiv Detail & Related papers (2021-03-25T15:20:10Z)
Neural network quantum state tomography in a two-qubit experiment [52.77024349608834]
Machine learning inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states greatly improves the quality of the reconstructed states.
arXiv Detail & Related papers (2020-07-31T17:25:12Z)
Fast approximations in the homogeneous Ising model for use in scene analysis [61.0951285821105]
We provide accurate approximations that make it possible to numerically calculate quantities needed in inference. We show that our approximation formulae are scalable and unfazed by the size of the Markov Random Field. The practical import of our approximation formulae is illustrated in performing Bayesian inference in a functional Magnetic Resonance Imaging activation detection experiment, and also in likelihood ratio testing for anisotropy in the spatial patterns of yearly increases in pistachio tree yields.
arXiv Detail & Related papers (2017-12-06T14:24:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.