More Like this

1. Bypassing backmapping: Coarse-grained electronic property distributions using heteroscedastic Gaussian processes

   https://doi.org/10.1063/5.0101038  

   Maier, J. Charlie; Jackson, Nicholas E. (November 2022, The Journal of Chemical Physics)

   We employ deep kernel learning electronic coarse-graining (DKL-ECG) with approximate Gaussian processes as a flexible and scalable framework for learning heteroscedastic electronic property distributions as a smooth function of coarse-grained (CG) configuration. The appropriateness of the Gaussian prior on predictive CG property distributions is justified as a function of CG model resolution by examining the statistics of target distributions. The certainties of predictive CG distributions are shown to be limited by CG model resolution with DKL-ECG predictive noise converging to the intrinsic physical noise induced by the CG mapping operator for multiple chemistries. Further analysis of the resolution dependence of learned CG property distributions allows for the identification of CG mapping operators that capture CG degrees of freedom with strong electron–phonon coupling. We further demonstrate the ability to construct the exact quantum chemical valence electronic density of states (EDOS), including behavior in the tails of the EDOS, from an entirely CG model by combining iterative Boltzmann inversion and DKL-ECG. DKL-ECG provides a means of learning CG distributions of all-atom properties that are traditionally “lost” in CG model development, introducing a promising methodological alternative to backmapping algorithms commonly employed to recover all-atom property distributions from CG simulations. 

   more » « less
2. Testing Product Distributions: A Closer Look

   Bhattacharyya, Arnab; Gayen, Sutanu; Kandasamy, Saravanan; Vinodchandran, N. V. (March 2021, International Conference on Algorithmic Learning Theory)

   null (Ed.)

   We study the problems of identity and closeness testing of n-dimensional product distributions. Prior works of Canonne et al. (2017) and Daskalakis and Pan (2017) have established tight sample complexity bounds for non-tolerant testing over a binary alphabet: given two product distributions P and Q over a binary alphabet, distinguish between the cases P = Q and dTV(P;Q) > epsilon . We build on this prior work to give a more comprehensive map of the complexity of testing of product distributions by investigating tolerant testing with respect to several natural distance measures and over an arbitrary alphabet. Our study gives a fine-grained understanding of how the sample complexity of tolerant testing varies with the distance measures for product distributions. In addition, we also extend one of our upper bounds on product distributions to bounded-degree Bayes nets. 

   more » « less
3. Tight Bounds on the Convergence of Noisy Random Circuits to the Uniform Distribution

   https://doi.org/10.1103/PRXQuantum.3.040329  

   Deshpande, Abhinav; Niroula, Pradeep; Shtanko, Oles; Gorshkov, Alexey V.; Fefferman, Bill; Gullans, Michael J. (December 2022, PRX Quantum)

   We study the properties of output distributions of noisy random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the “useless” uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what has been thought prior to this work. 

   more » « less
4. Lower Bounds for Testing Complete Positivity and Quantum Separability

   https://doi.org/10.1007/978-3-030-61792-9_30  

   Bădescu, Costin; O'Donnell, Ryan (December 2020, LATIN 2020: Theoretical Informatics)

   Kohayakawa, Y.; Miyazawa, F.K. (Ed.)

   In this work we are interested in the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given n copies of an unknown mixed quantum state ϱ on Cd⊗Cd , and one wants to test whether ϱ is separable or ϵ -far from all separable states in trace distance. We prove that n=Ω(d2/ϵ2) copies are necessary to test separability, assuming ϵ is not too small, viz. ϵ=Ω(1/d−−√) . We also study completely positive distributions on the grid [d]×[d] , as a classical analogue of separable states. We analogously prove that Ω(d/ϵ2) samples from an unknown distribution p are necessary to decide whether p is completely positive or ϵ -far from all completely positive distributions in total variation distance. 

   more » « less
5. Consistent Sampling With Smoothed Quantum Walk

   https://doi.org/10.1109/QCE60285.2024.00013  

   Zhang, Tianyi; Ke, Yuan (September 2024, IEEE Xplore digital library)

   This paper introduces a novel sampling technique based on the dynamics of a 2-state Quantum Walk (QW) in a one-dimensional space. By leveraging concepts from nonparametric statistics, specifically the kernel smoothing method, our approach addresses two key challenges in Quantum Walk sampling: discontinuities in sampling distributions and potential inaccuracies in limiting distributions. Our innovative method effectively mitigates these issues, leading to significant improvements in density estimation and sampling efficacy compared to traditional Quantum Walk distributions and sampling techniques. 

   more » « less