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CONTRACTION AND CONCENTRATION OF MEASURES WITH APPLICATIONS TO THEORETICAL NEUROSCIENCE

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arXiv 2025年

作者： Betteti, Simone Bullo, Francesco Department of Information Engineering Università degli Studi di Padova Padova35131 Italy Center for Control Dynamical Systems and Computation University of California at Santa Barbara Santa BarbaraCA93106 IT United States

We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or Br-contracting drift terms. While classical results often assume constant diffusion and gradient-based drifts, we extend the analysis to spatially inhomogeneous diffusion and non-integrable vector fields. We establish sufficient conditions for the existence and uniqueness of stationary measures under global contraction, showing that convergence is preserved when the contraction rate dominates diffusion inhomogeneity. For systems contracting only outside of a compact set and with constant diffusion, we demonstrate mass concentration near the minima of an associated non-convex potential, like in multistable regimes. The theoretical findings are illustrated through Hopfield networks, highlighting implications for memory retrieval dynamics in noisy *** Codes 35Q84, 60G10 © 2025, CC BY.

关键词： Random processes

Enhanced optical nonlinearities under collective strong light-matter coupling

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Physical Review A 2021年第6期103卷 063111-063111页

作者： Raphael F. Ribeiro Jorge A. Campos-Gonzalez-Angulo Noel C. Giebink Wei Xiong Joel Yuen-Zhou Department of Chemistry and Cherry Emerson Center for Scientific Computation Emory University Atlanta Georgia 30322 USA Department of Chemistry and Biochemistry University of California San Diego La Jolla California 92093 USA Department of Electrical Engineering The Pennsylvania State University University Park Pennsylvania 16802 USA Materials Science and Engineering Program University of California San Diego La Jolla California 92093 USA

Optical microcavities and metallic nanostructures have been shown to significantly modulate the dynamics and spectroscopic response of molecular systems. We present a study of the nonlinear optics of a model consisting of N anharmonic multilevel systems (e.g., Morse oscillators) undergoing collective strong coupling with a resonant infrared microcavity. We find that, under experimentally accessible conditions, molecular systems in microcavities may have nonlinear phenomena significantly intensified due to the high quality of polariton resonances and the enhanced microcavity electromagnetic energy density relative to free space. Particularly large enhancement of multiphoton absorption happens when multipolariton states are resonant with bare molecule multiphoton transitions. In particular, our model predicts two-photon absorption cross-section enhancements by several orders of magnitude relative to free space when the Rabi splitting ΩR is approximately equal to the molecular anharmonic shift 2Δ. Our results provide rough upper bounds to resonant nonlinear-response enhancement factors as relaxation to dark states is treated phenomenologically. Notably, ensembles of two-level systems undergoing strong coupling with a cavity (described by the Tavis-Cummings model) show no such optical nonlinearity enhancements, highlighting the rich phenomenology afforded by multilevel anharmonic systems. Similar conclusions are expected to hold for excitonic systems that share features with our model (e.g., molecular dyes with accessible S0→S1→S2 transitions) and strongly interact with a UV-visible cavity.

关键词： Chemical Physics & Physical Chemistry Photonics Polaritons Green's function methods Quantum master equation

Quantum limits on noise for a class of nonlinear amplifiers

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Physical Review A 2021年第5期103卷 052415-052415页

作者： Jeffrey M. Epstein K. Birgitta Whaley Joshua Combes Berkeley Center for Quantum Information and Computation Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA Department of Chemistry University of California Berkeley California 94720 USA Rigetti Computing 775 Heinz Avenue Berkeley California 94710 USA Department of Electrical Computer and Energy Engineering University of Colorado Boulder Boulder Colorado 80309 USA

Nonlinear amplifiers such as the transistor are ubiquitous in classical technology, but their quantum analogs are not well understood. We introduce a class of nonlinear amplifiers that amplify any normal operator and add only a half quantum of vacuum noise at the output. In the large-gain limit, when used in conjunction with a noisy linear detectors, these amplifiers implement ideal measurements of the normal operator.

关键词： Quantum information processing

Errors in stimulated-Raman-induced logic gates in 133Ba+

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arXiv 2022年

作者： Boguslawski, Matthew J. Wall, Zachary J. Vizvary, Samuel R. Moore, Isam Daniel Bareian, Michael Allcock, David T.C. Wineland, David J. Hudson, Eric R. Campbell, Wesley C. Department of Physics and Astronomy University of California Los Angeles Los AngelesCA United States Challenge Institute for Quantum Computation University of California Los Angeles Los AngelesCA United States Department of Physics University of Oregon EugeneOR United States Center for Quantum Science and Engineering University of California Los Angeles Los AngelesCA United States

133Ba+ is illuminated by a laser that is far-detuned from optical transitions, and the resulting spontaneous Raman scattering rate is measured. The observed scattering rate is lower than previous theoretical estimates. The majority of the discrepancy is explained by a more accurate treatment of the scattered photon density of states. This work establishes that, contrary to previous models, there is no fundamental limit to laser-driven quantum gates from laser-induced spontaneous Raman scattering. © 2022, CC BY.

关键词： Logic gates

Photon scattering errors during stimulated Raman transitions in trapped-ion qubits

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arXiv 2022年

作者： Moore, I.D. Campbell, W.C. Hudson, E.R. Boguslawski, M.J. Wineland, D.J. Allcock, D.T.C. Department of Physics University of Oregon EugeneOR United States Department of Physics and Astronomy University of California Los Angeles Los AngelesCA United States Center for Quantum Science and Engineering University of California Los Angeles Los AngelesCA United States Challenge Institute for Quantum Computation University of California Los Angeles Los AngelesCA United States

We study photon scattering errors in stimulated Raman driven quantum logic gates. For certain parameter regimes, we find that previous, simplified models of the process significantly overestimate the gate error rate due to photon scattering. This overestimate is shown to be due to previous models neglecting the detuning dependence of the scattered photon frequency and Lamb-Dicke parameter, a second scattering process, interference effects on scattering rates to metastable manifolds, and the counter-rotating contribution to the Raman transition rate. The resulting improved model shows that there is no fundamental limit on gate error due to photon scattering for electronic ground state qubits in commonly-used trapped-ion species when the Raman laser beams are red detuned from the main optical transition. Additionally, photon scattering errors are studied for qubits encoded in metastable D5/2manifold, showing that gate errors below 10-4are achievable for all commonly-used trapped ions. Copyright © 2022, The Authors. All rights reserved.

关键词： Trapped ions

Learning Robust Data-based LQG controllers from Noisy Data

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arXiv 2023年

作者： Liu, Wenjie Sun, Jian Wang, Gang Bullo, Francesco Chen, Jie The National Key Lab of Autonomous Intelligent Unmanned Systems School of Automation Beijing Institute of Technology Beijing100081 China The Beijing Institute of Technology Chongqing Innovation Center Chongqing401120 China The Mechanical Engineering Department The Center of Control Dynamical Systems and Computation UC Santa Barbara CA93106-5070 United States The Department of Control Science and Engineering Tongji University Shanghai201804 China The National Key Lab of Autonomous Intelligent Unmanned Systems Beijing Institute of Technology Beijing100081 China

This paper addresses the joint state estimation and control problems for unknown linear time-invariant systems subject to both process and measurement noise. The aim is to redesign the linear quadratic Gaussian (LQG) controller based solely on data. The LQG controller comprises a linear quadratic regulator (LQR) and a steady-state Kalman observer;while the data-based LQR design problem has been previously studied, constructing the Kalman gain and the LQG controller from noisy data presents a novel challenge. In this work, a data-based formulation for computing the steady-state Kalman gain is proposed based on semi-definite programming (SDP) using some noise-free input-state-output data. Additionally, a data-based LQG controller is developed, which is shown to be equivalent to the model-based LQG controller. For cases where offline data are corrupted by noise, a robust data-based observer gain is constructed by tackling a relaxed SDP. The proposed controllers are proven to achieve robust global exponential stability (RGES) for state estimation and input-to-state practical stability (ISpS) under standard conditions. Finally, numerical tests are conducted to validate the proposed controllers' correctness and effectiveness. © 2023, CC BY.

关键词： Linear time-invariant system

Virtual Staining of Label-Free Tissue in Imaging Mass Spectrometry

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arXiv 2024年

作者： Zhang, Yijie Huang, Luzhe Pillar, Nir Li, Yuzhu Migas, Lukasz G. Van de Plas, Raf Spraggins, Jeffrey M. Ozcan, Aydogan Electrical and Computer Engineering Department University of California Los AngelesCA90095 United States Bioengineering Department University of California Los AngelesCA90095 United States University of California Los AngelesCA90095 United States Mass Spectrometry Research Center Vanderbilt University NashvilleTN37232 United States Delft Center for Systems and Control Delft University of Technology Delft2628 Netherlands Department of Cell and Developmental Biology Vanderbilt University NashvilleTN37232 United States Department of Chemistry Vanderbilt University NashvilleTN37232 United States Department of Biochemistry Vanderbilt University NashvilleTN37232 United States Department of Pathology Microbiology and Immunology Vanderbilt University Medical Center NashvilleTN37232 United States Department of Surgery University of California Los AngelesCA90095 United States

Imaging mass spectrometry (IMS) is a powerful tool for untargeted, highly multiplexed molecular mapping of tissue in biomedical research. IMS offers a means of mapping the spatial distributions of molecular species in biological tissue with unparalleled chemical specificity and sensitivity. However, most IMS platforms are not able to achieve microscopy-level spatial resolution and lack cellular morphological contrast, necessitating subsequent histochemical staining, microscopic imaging and advanced image registration steps to enable molecular distributions to be linked to specific tissue features and cell types. Here, we present a virtual histological staining approach that enhances spatial resolution and digitally introduces cellular morphological contrast into mass spectrometry images of label-free human tissue using a diffusion model. Blind testing on human kidney tissue demonstrated that the virtually stained images of label-free samples closely match their histochemically stained counterparts (with Periodic Acid-Schiff staining), showing high concordance in identifying key renal pathology structures despite utilizing IMS data with 10-fold larger pixel size. Additionally, our approach employs an optimized noise sampling technique during the diffusion model’s inference process to reduce variance in the generated images, yielding reliable and repeatable virtual staining. We believe this virtual staining method will significantly expand the applicability of IMS in life sciences and open new avenues for mass spectrometry-based biomedical research. Copyright © 2024, The Authors. All rights reserved.

关键词： Tissue

Quantum Algorithm for Petz Recovery Channels and Pretty Good Measurements

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Physical Review Letters 2022年第22期128卷 220502-220502页

作者： András Gilyén Seth Lloyd Iman Marvian Yihui Quek Mark M. Wilde Institute for Quantum Information and Matter California Institute of Technology Pasadena California 91125 USA Simons Institute for the Theory of Computing Berkeley California 94720 USA Department of Mechanical Engineering and Research Laboratory of Electronics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics and Department of Electrical and Computer Engineering Duke University Durham North Carolina 27708 USA Information Systems Laboratory Stanford University Stanford California 94305 USA Hearne Institute for Theoretical Physics Department of Physics and Astronomy and Center for Computation and Technology Louisiana State University Baton Rouge Louisiana 70803 USA Stanford Institute for Theoretical Physics Stanford University Stanford California 94305 USA

The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for near-optimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient method to implement them. This Letter sets out to rectify this lack: Using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, we provide a quantum algorithm to implement the Petz recovery channel when given the ability to perform the channel that one wishes to reverse. Moreover, we prove that, in some sense, our quantum algorithm’s usage of the channel implementation cannot be improved by more than a quadratic factor. Our quantum algorithm also provides a procedure to perform pretty good measurements when given multiple copies of the states that one is trying to distinguish.

关键词： Quantum algorithms Quantum channels Quantum error correction

A spinless crystal for a high-performance solid-state 229Th nuclear clock

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arXiv 2025年

作者： Morgan, Harry W.T. Terhune, James E.S. Elwell, Ricky Tan, Hoang Bao Tran Perera, Udeshika C. Derevianko, Andrei Hudson, Eric R. Alexandrova, Anastassia N. Department of Chemistry and Biochemistry University of California Los Angeles Los AngelesCA90095 United States Department of Chemistry University of Manchester Oxford Road ManchesterM13 9PL United Kingdom Department of Physics and Astronomy University of California Los AngelesCA90095 United States Department of Physics University of Nevada RenoNV89557 United States Los Alamos National Laboratory P.O. Box 1663 Los AlamosNM87545 United States Challenge Institute for Quantum Computation University of California Los Angeles Los AngelesCA United States Center for Quantum Science and Engineering University of California Los Angeles Los AngelesCA United States

Solid-state 229Th nuclear clocks require a host material whose band gap is larger than the 8.4 eV nuclear transition energy. As such, excitation of the 229Th nuclear state has so far only been demonstrated in metal fluorides, specifically CaF2, LiSrAlF6, and ThF4, where the large electronegativity of the halogen leads to sufficient band gaps. However, it is expected that the nuclear magnetic moment of the fluorine gives rise to a leading order broadening mechanism that limits the clock stability. Here, we use concepts of molecular design to identify a polyatomic anion, SO42– , that is both nuclear spin free and of sufficient electron affinity to result in a high band gap metal sulfate system. Using state-of-the-art calculations, we find that the band gap of Th(SO4)2 is approximately 9 eV, large enough for direct laser excitation of 229Th. Low concentrations of 229Th in the otherwise spinless 232Th(SO4)2 crystal mitigate 229Th-229Th interactions. Furthermore, the introduction of 229Th does not modify the material band gap nor introduce electronic states associated with nuclear quenching. By removing one of the primary sources of nuclear line broadening in the crystal, the nuclear magnetic dipole-dipole interaction, a nuclear clock with instability as low as σ = 4.6 × 10−23/√τ, where τ is the averaging time, may be realized. This is roughly six orders of magnitude lower than previously thought possible. © 2025, CC BY-NC-SA.

关键词： Laser excitation