Denoising and Extension of Response Functions in the Time Domain

Kemper, Alexander F.; Yang, Chao; Gull, Emanuel

doi:10.1103/physrevlett.132.160403

Title: Denoising and Extension of Response Functions in the Time Domain

Journal Article · 18 April 2024 · Physical Review Letters

DOI: https://doi.org/10.1103/physrevlett.132.160403 · OSTI ID:2345758

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North Carolina State University, Raleigh, NC (United States); North Carolina State University; North Carolina State University
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Univ. of Michigan, Ann Arbor, MI (United States)

Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

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Research Organization:: North Carolina State University, Raleigh, NC (United States); Univ. of Michigan, Ann Arbor, MI (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: SC0023231; SC0022088

OSTI ID:: 2345758

Alternate ID(s):: OSTI ID: 2473733

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 16 Vol. 132; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (54)

Data for: A linear response framework for simulating bosonic and fermionic correlation functions on quantum computers Kökcü, Efekan; Labib, Heba; Freericks, James K. Dryad https://doi.org/10.5061/dryad.51c59zwcn	dataset	January 2023
Many–Body Quantum Theory in Condensed Matter Physics Bruus, Henrik; Flensberg, Karsten https://doi.org/10.1093/oso/9780198566335.001.0001	book	September 2004
Quantum Monte Carlo Method in the Steady State Erpenbeck, A.; Gull, E.; Cohen, G. Physical Review Letters, Vol. 130, Issue 18 https://doi.org/10.1103/PhysRevLett.130.186301	journal	May 2023
Positivity of the Spectral Densities of Retarded Floquet Green Functions Uhrig, Götz S.; Kalthoff, Mona H.; Freericks, James K. Physical Review Letters, Vol. 122, Issue 13 https://doi.org/10.1103/PhysRevLett.122.130604	journal	April 2019
Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization Bauschke, Heinz H.; Combettes, Patrick L.; Luke, D. Russell Journal of the Optical Society of America A, Vol. 19, Issue 7 https://doi.org/10.1364/JOSAA.19.001334	journal	January 2002
General Principles for the Nonequilibrium Relaxation of Populations in Quantum Materials Kemper, A. F.; Abdurazakov, O.; Freericks, J. K. Physical Review X, Vol. 8, Issue 4 https://doi.org/10.1103/PhysRevX.8.041009	journal	October 2018
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions Georges, Antoine; Kotliar, Gabriel; Krauth, Werner Reviews of Modern Physics, Vol. 68, Issue 1 https://doi.org/10.1103/RevModPhys.68.13	journal	January 1996
Diagrammatic Monte Carlo simulation of nonequilibrium systems Werner, Philipp; Oka, Takashi; Millis, Andrew J. Physical Review B, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevB.79.035320	journal	January 2009
Computing a nearest symmetric positive semidefinite matrix Higham, Nicholas J. Linear Algebra and its Applications, Vol. 103 https://doi.org/10.1016/0024-3795(88)90223-6	journal	May 1988
Lehmann representation of the nonequilibrium self-energy Gramsch, Christian; Potthoff, Michael Physical Review B, Vol. 92, Issue 23 https://doi.org/10.1103/PhysRevB.92.235135	journal	December 2015
A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling Shi, Qiang; Geva, Eitan The Journal of Chemical Physics, Vol. 119, Issue 23 https://doi.org/10.1063/1.1624830	journal	December 2003
�ber den Variabilit�tsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen Carath�odory, C. Mathematische Annalen, Vol. 64, Issue 1 https://doi.org/10.1007/BF01449883	journal	March 1907
Reduced Dynamics of Full Counting Statistics Pollock, Felix; Gull, Emanuel; Modi, Kavan SciPost Physics, Vol. 13, Issue 2 https://doi.org/10.21468/SciPostPhys.13.2.027	journal	August 2022
Antiferromagnetism and d -wave superconductivity in cuprates: A cluster dynamical mean-field theory Lichtenstein, A. I.; Katsnelson, M. I. Physical Review B, Vol. 62, Issue 14 https://doi.org/10.1103/PhysRevB.62.R9283	journal	October 2000
Cellular Dynamical Mean Field Approach to Strongly Correlated Systems Kotliar, Gabriel; Savrasov, Sergej Y.; Pálsson, Gunnar Physical Review Letters, Vol. 87, Issue 18 https://doi.org/10.1103/PhysRevLett.87.186401	journal	October 2001
Nonequilibrium Many-Body Theory of Quantum Systems Stefanucci, Gianluca; van Leeuwen, Robert https://doi.org/10.1017/CBO9781139023979	book	March 2013
Learning Feynman Diagrams with Tensor Trains Núñez Fernández, Yuriel; Jeannin, Matthieu; Dumitrescu, Philipp T. Physical Review X, Vol. 12, Issue 4 https://doi.org/10.1103/PhysRevX.12.041018	journal	November 2022
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem Hedin, Lars Physical Review, Vol. 139, Issue 3A https://doi.org/10.1103/PhysRev.139.A796	journal	August 1965
Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems Cohen, Guy; Gull, Emanuel; Reichman, David R. Physical Review Letters, Vol. 115, Issue 26 https://doi.org/10.1103/PhysRevLett.115.266802	journal	December 2015
Fully self-consistent finite-temperature GW in Gaussian Bloch orbitals for solids Yeh, Chia-Nan; Iskakov, Sergei; Zgid, Dominika Physical Review B, Vol. 106, Issue 23 https://doi.org/10.1103/PhysRevB.106.235104	journal	December 2022
Cutting rules and positivity in finite temperature many-body theory Hyrkäs, M. J.; Karlsson, D.; van Leeuwen, R. Journal of Physics A: Mathematical and Theoretical, Vol. 55, Issue 33 https://doi.org/10.1088/1751-8121/ac802d	journal	August 2022
Tomographically reconstructed master equations for any open quantum dynamics Pollock, Felix A.; Modi, Kavan Quantum, Vol. 2 https://doi.org/10.22331/q-2018-07-11-76	journal	July 2018
Monte Carlo Method for Magnetic Impurities in Metals Hirsch, J. E.; Fye, R. M. Physical Review Letters, Vol. 56, Issue 23 https://doi.org/10.1103/PhysRevLett.56.2521	journal	June 1986
Excitations and spectra from equilibrium real-time Green's functions Dong, Xinyang; Gull, Emanuel; Strand, Hugo U. R. Physical Review B, Vol. 106, Issue 12 https://doi.org/10.1103/PhysRevB.106.125153	journal	September 2022
Quantum cluster theories Maier, Thomas; Jarrell, Mark; Pruschke, Thomas Reviews of Modern Physics, Vol. 77, Issue 3 https://doi.org/10.1103/RevModPhys.77.1027	journal	October 2005
Memory effects in nonequilibrium quantum impurity models Cohen, Guy; Rabani, Eran Physical Review B, Vol. 84, Issue 7 https://doi.org/10.1103/PhysRevB.84.075150	journal	August 2011
Nonlocal dynamical correlations of strongly interacting electron systems Hettler, M. H.; Tahvildar-Zadeh, A. N.; Jarrell, M. Physical Review B, Vol. 58, Issue 12 https://doi.org/10.1103/PhysRevB.58.R7475	journal	September 1998
Continuous-time auxiliary-field Monte Carlo for quantum impurity models Gull, E.; Werner, P.; Parcollet, O. EPL (Europhysics Letters), Vol. 82, Issue 5 https://doi.org/10.1209/0295-5075/82/57003	journal	May 2008
Dynamic Ion Structure Factor of Warm Dense Matter Vorberger, J.; Donko, Z.; Tkachenko, I. M. Physical Review Letters, Vol. 109, Issue 22 https://doi.org/10.1103/PhysRevLett.109.225001	journal	November 2012
Numerically exact long-time behavior of nonequilibrium quantum impurity models Gull, Emanuel; Reichman, David R.; Millis, Andrew J. Physical Review B, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevB.84.085134	journal	August 2011
Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer Steckmann, Thomas; Keen, Trevor; Kökcü, Efekan Physical Review Research, Vol. 5, Issue 2 https://doi.org/10.1103/PhysRevResearch.5.023198	journal	June 2023
Numerically exact long-time magnetization dynamics at the nonequilibrium Kondo crossover of the Anderson impurity model Cohen, Guy; Gull, Emanuel; Reichman, David R. Physical Review B, Vol. 87, Issue 19 https://doi.org/10.1103/PhysRevB.87.195108	journal	May 2013
NESSi: The Non-Equilibrium Systems Simulation package Schüler, Michael; Golež, Denis; Murakami, Yuta Computer Physics Communications, Vol. 257 https://doi.org/10.1016/j.cpc.2020.107484	journal	December 2020
Continuous-Time Solver for Quantum Impurity Models Werner, Philipp; Comanac, Armin; de’ Medici, Luca Physical Review Letters, Vol. 97, Issue 7 https://doi.org/10.1103/PhysRevLett.97.076405	journal	August 2006
Hubbard model in infinite dimensions Georges, Antoine; Kotliar, Gabriel Physical Review B, Vol. 45, Issue 12 https://doi.org/10.1103/PhysRevB.45.6479	journal	March 1992
Dynamical response in strongly coupled uniform electron liquids: Observation of plasmon-roton coexistence using nine sum rules, Shannon information entropy, and path-integral Monte Carlo simulations Filinov, A. V.; Ara, J.; Tkachenko, I. M. Physical Review B, Vol. 107, Issue 19 https://doi.org/10.1103/PhysRevB.107.195143	journal	May 2023
Real-Time Path Integral Approach to Nonequilibrium Many-Body Quantum Systems Mühlbacher, Lothar; Rabani, Eran Physical Review Letters, Vol. 100, Issue 17 https://doi.org/10.1103/PhysRevLett.100.176403	journal	May 2008
Continuous-time Monte Carlo methods for quantum impurity models Gull, Emanuel; Millis, Andrew J.; Lichtenstein, Alexander I. Reviews of Modern Physics, Vol. 83, Issue 2 https://doi.org/10.1103/RevModPhys.83.349	journal	May 2011
Nonequilibrium dynamical mean-field theory and its applications Aoki, Hideo; Tsuji, Naoto; Eckstein, Martin Reviews of Modern Physics, Vol. 86, Issue 2 https://doi.org/10.1103/RevModPhys.86.779	journal	June 2014
Multiple emitter location and signal parameter estimation Schmidt, R. IEEE Transactions on Antennas and Propagation, Vol. 34, Issue 3 https://doi.org/10.1109/TAP.1986.1143830	journal	March 1986
Auxiliary Hamiltonian representation of the nonequilibrium Dyson equation Balzer, Karsten; Eckstein, Martin Physical Review B, Vol. 89, Issue 3 https://doi.org/10.1103/PhysRevB.89.035148	journal	January 2014
Monte Carlo calculations of coupled boson-fermion systems. I Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L. Physical Review D, Vol. 24, Issue 8 https://doi.org/10.1103/PhysRevD.24.2278	journal	October 1981
Nevanlinna Analytical Continuation Fei, Jiani; Yeh, Chia-Nan; Gull, Emanuel Physical Review Letters, Vol. 126, Issue 5 https://doi.org/10.1103/PhysRevLett.126.056402	journal	February 2021
Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories Cerrillo, Javier; Cao, Jianshu Physical Review Letters, Vol. 112, Issue 11 https://doi.org/10.1103/PhysRevLett.112.110401	journal	March 2014
Local Linear Convergence for Alternating and Averaged Nonconvex Projections Lewis, A. S.; Luke, D. R.; Malick, J. Foundations of Computational Mathematics, Vol. 9, Issue 4 https://doi.org/10.1007/s10208-008-9036-y	journal	November 2008
Über den zusammenhang der extremen von harmonischen funktionen mit ihren koeffizienten und über den picard-landau’schen satz Caratheodory, C.; Fejér, L. Rendiconti del Circolo Matematico di Palermo, Vol. 32, Issue 1 https://doi.org/10.1007/BF03014796	journal	December 1911
Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data Jarrell, Mark; Gubernatis, J. E. Physics Reports, Vol. 269, Issue 3 https://doi.org/10.1016/0370-1573(95)00074-7	journal	May 1996
Analytical continuation of matrix-valued functions: Carathéodory formalism Fei, Jiani; Yeh, Chia-Nan; Zgid, Dominika Physical Review B, Vol. 104, Issue 16 https://doi.org/10.1103/PhysRevB.104.165111	journal	October 2021
On Projection Algorithms for Solving Convex Feasibility Problems Bauschke, Heinz H.; Borwein, Jonathan M. SIAM Review, Vol. 38, Issue 3 https://doi.org/10.1137/S0036144593251710	journal	September 1996
Continuous-time quantum Monte Carlo method for fermions Rubtsov, A. N.; Savkin, V. V.; Lichtenstein, A. I. Physical Review B, Vol. 72, Issue 3 https://doi.org/10.1103/PhysRevB.72.035122	journal	July 2005
Effect of dynamical spectral weight redistribution on effective interactions in time-resolved spectroscopy Kemper, A. F.; Sentef, M. A.; Moritz, B. Physical Review B, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevB.90.075126	journal	August 2014
Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model Bickers, N. E.; Scalapino, D. J.; White, S. R. Physical Review Letters, Vol. 62, Issue 8 https://doi.org/10.1103/PhysRevLett.62.961	journal	February 1989
Correlated Lattice Fermions in d = ∞ Dimensions Metzner, Walter; Vollhardt, Dieter Physical Review Letters, Vol. 62, Issue 3 https://doi.org/10.1103/PhysRevLett.62.324	journal	January 1989
Superresolution of Green's functions on noisy quantum computers Cruz, Diogo; Magano, Duarte Physical Review A, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevA.108.012618	journal	July 2023

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Title: Denoising and Extension of Response Functions in the Time Domain

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