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arxiv: 2509.20604 · v1 · submitted 2025-09-24 · ⚛️ physics.chem-ph · quant-ph

Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems

Tianchu Li , Pranay Venkatesh , Nanako Shitara , Andr\'es Montoya-Castillo This is my paper

Pith reviewed 2026-05-18 13:29 UTC · model grok-4.3

classification ⚛️ physics.chem-ph quant-ph
keywords quantum dynamicstensor networksmatrix product statesdecoherencespin systemsquantum sensingmolecular magnetscoherence
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0 comments X

The pith

Matrix product states enable numerically exact simulations of decoherence in spin networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a method that uses matrix product states to compute the full quantum dynamics of interacting spin systems without approximations. This yields accurate time evolution for both coherence and state populations across many parameter values relevant to real devices. Accurate dynamics matter because they reveal how decoherence arises and can be controlled in qubits, sensors, and memories. The approach covers solid-state semiconductor spins, molecular magnets, and the effects of repeated light pulses that experiments use to extend coherence times.

Core claim

We leverage a matrix product state representation to introduce a numerically exact and scalable method to achieve this goal. We demonstrate that our method accurately predicts coherence and population dynamics of spin networks across a wide range of parameter regimes, encompassing nuclear spin sensors and qubits in solid-state semiconductors and molecular magnets. Our method further predicts spin dynamics under the influence of repeated light pulses, which are commonly used to mitigate decoherence and perform quantum sensing experiments.

What carries the argument

Matrix product state representation of the quantum state, which compresses the wavefunction to track entanglement growth during time evolution of the spin network.

If this is right

  • Reliable results for moderately sized spin platforms can guide development of faster approximate dynamics methods.
  • The same framework supports direct simulation of pulse sequences used in quantum sensing and coherence protection.
  • Predictions for nuclear spin sensors and molecular magnets supply concrete targets for experimental decoherence studies.
  • The method spans parameter regimes typical of both solid-state qubits and molecular systems in one unified approach.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same tensor-network structure could be adapted to open-system models that include environmental baths beyond the spin bath treated here.
  • Benchmarking against larger system sizes would show where the method remains practical before entanglement growth forces a switch to approximate techniques.
  • Integration with existing pulse-shaping optimization tools could turn the dynamics predictions into design rules for longer-lived qubits.

Load-bearing premise

Matrix product states remain accurate enough to represent the full quantum state without prohibitive cost when entanglement increases during the dynamics of the moderately sized systems studied.

What would settle it

Running the method on small spin clusters where exact diagonalization is still feasible and checking whether the predicted coherence decay matches the exact result to within numerical precision.

Figures

Figures reproduced from arXiv: 2509.20604 by Andr\'es Montoya-Castillo, Nanako Shitara, Pranay Venkatesh, Tianchu Li.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) BSBS molecule with ethyl substituents (BSBS-2Et [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Coherence dynamics for a representative NV center sensor. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Coherence dynamics for a [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Coherence and population dynamics for the BSBS-2Et mol [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
read the original abstract

Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms -- a prerequisite for designing better qubits, sensors, and memories. We leverage a matrix product state representation to introduce a numerically exact and scalable method to achieve this goal. We demonstrate that our method accurately predicts coherence and population dynamics of spin networks across a wide range of parameter regimes, encompassing nuclear spin sensors and qubits in solid-state semiconductors and molecular magnets. Our method further predicts spin dynamics under the influence of repeated light pulses, which are commonly used to mitigate decoherence and perform quantum sensing experiments. Our method thus provides reliable results for moderately-sized spin platforms spanning molecular magnets and solid-state spins that can guide the development of approximate but efficient quantum dynamics methods and enable principled inquiry into decoherence mechanisms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a matrix product state (MPS) representation to simulate the quantum dynamics of interacting spin systems, claiming a numerically exact and scalable method for predicting coherence and population dynamics in spin networks relevant to solid-state semiconductors, molecular magnets, and nuclear spin sensors. It further applies the approach to dynamics under repeated light pulses for decoherence mitigation and quantum sensing.

Significance. If the numerical exactness claim holds with controlled truncation errors for the reported system sizes and timescales, the work would provide a practical tool for moderately sized spin platforms where full Hilbert-space methods become intractable, potentially informing approximate dynamics methods and experimental designs for qubit and sensor development.

major comments (2)
  1. [Methods and Results sections] The central claim of numerical exactness for finite-bond-dimension MPS (abstract and methods) is load-bearing but unsupported without explicit bond-dimension convergence tests or comparisons to exact diagonalization on small instances (N≤10) at the longest times shown; in closed-system spin-bath models, linear entanglement growth typically demands exponentially increasing D, so truncation error control must be demonstrated rather than asserted.
  2. [Results (dynamics plots)] Figures or tables presenting coherence and population dynamics across parameter regimes should include quantitative error bars or D-variation data to confirm that the reported accuracy holds when entanglement accumulates, as the weakest assumption is that finite-D MPS remains faithful without prohibitive cost.
minor comments (2)
  1. [Methods] Clarify the precise form of the spin-bath Hamiltonian and the light-pulse protocol in the methods to allow direct reproduction.
  2. [Results] Ensure all parameter regimes (e.g., coupling strengths, bath sizes) are explicitly tabulated for the demonstrated cases.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help strengthen the presentation of our results. We agree that explicit demonstrations of convergence are important to support the claim of numerical exactness and will revise the manuscript accordingly. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: The central claim of numerical exactness for finite-bond-dimension MPS (abstract and methods) is load-bearing but unsupported without explicit bond-dimension convergence tests or comparisons to exact diagonalization on small instances (N≤10) at the longest times shown; in closed-system spin-bath models, linear entanglement growth typically demands exponentially increasing D, so truncation error control must be demonstrated rather than asserted.

    Authors: We thank the referee for this observation. The MPS representation is formally exact only in the infinite-D limit, and we acknowledge that the manuscript would benefit from explicit evidence of convergence for the finite D values employed. In the revised manuscript we will add bond-dimension convergence tests for the primary systems and timescales reported, together with direct comparisons to exact diagonalization for all instances with N≤10 at the longest simulation times. These additions will quantify the truncation error and demonstrate that the chosen bond dimensions are sufficient to keep errors below the level needed for the claimed accuracy, even when entanglement grows linearly. revision: yes

  2. Referee: Figures or tables presenting coherence and population dynamics across parameter regimes should include quantitative error bars or D-variation data to confirm that the reported accuracy holds when entanglement accumulates, as the weakest assumption is that finite-D MPS remains faithful without prohibitive cost.

    Authors: We agree that quantitative confirmation of accuracy is desirable. In the revision we will augment the dynamics figures with either overlaid results for several bond dimensions or explicit error estimates obtained from D-convergence studies. These data will be shown for representative parameter regimes and at times when entanglement has accumulated, thereby confirming that the reported curves remain stable and that the computational cost remains practical for the system sizes considered. revision: yes

Circularity Check

0 steps flagged

No circularity: numerical method with independent validation claims

full rationale

The paper introduces and demonstrates a tensor-network (MPS) simulation technique for spin-system dynamics. No derivation chain reduces a claimed prediction to a fitted parameter or self-citation by construction; the central statements concern computational accuracy on specific models, which are externally falsifiable via exact diagonalization or larger-D convergence. Self-citations, if present, are not load-bearing for any uniqueness theorem or ansatz. The work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on the standard assumption that the spin systems can be modeled as open quantum systems with Markovian or non-Markovian baths, and that matrix product states suffice for the entanglement structure in the targeted regimes. No free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption Matrix product states can faithfully represent the time-evolved state of the interacting spin network for the system sizes and times considered.
    Central to claiming numerical exactness in the abstract.

pith-pipeline@v0.9.0 · 5691 in / 1126 out tokens · 28550 ms · 2026-05-18T13:29:06.574831+00:00 · methodology

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Reference graph

Works this paper leans on

85 extracted references · 85 canonical work pages · 1 internal anchor

  1. [1]

    author author D. D. \ Awschalom , author R. Hanson , author J. Wrachtrup ,\ and\ author B. B. \ Zhou ,\ title title Quantum technologies with optically interfaced solid-state spins , \ @noop journal journal Nat. Photonics \ volume 12 ,\ pages 516--527 ( year 2018 ) NoStop

    work page 2018

  2. [2]

    author author M. J. \ Graham , author J. M. \ Zadrozny , author M. S. \ Fataftah ,\ and\ author D. E. \ Freedman ,\ title title Forging solid-state qubit design principles in a molecular furnace , \ @noop journal journal Chem. Mat. \ volume 29 ,\ pages 1885--1897 ( year 2017 ) NoStop

    work page 2017

  3. [3]

    author author C. L. \ Degen , author F. Reinhard ,\ and\ author P. Cappellaro ,\ title title Quantum sensing , \ https://doi.org/10.1103/RevModPhys.89.035002 journal journal Rev. Mod. Phys. \ volume 89 ,\ pages 035002 ( year 2017 ) NoStop

    work page internal anchor Pith review doi:10.1103/revmodphys.89.035002 2017

  4. [4]

    Rondin , author J.-P

    author author L. Rondin , author J.-P. \ Tetienne , author T. Hingant , author J.-F. \ Roch , author P. Maletinsky ,\ and\ author V. Jacques ,\ title title Magnetometry with nitrogen-vacancy defects in diamond , \ @noop journal journal Rep. Prog. Phys. \ volume 77 ,\ pages 056503 ( year 2014 ) NoStop

    work page 2014

  5. [5]

    Balasubramanian , author I

    author author G. Balasubramanian , author I. Chan , author R. Kolesov , author M. Al-Hmoud , author J. Tisler , author C. Shin , author C. Kim , author A. Wojcik , author P. R. \ Hemmer , author A. Krueger , et al. ,\ title title Nanoscale imaging magnetometry with diamond spins under ambient conditions , \ @noop journal journal Nature \ volume 455 ,\ pag...

    work page 2008

  6. [6]

    author author C. E. \ Jackson , author T. Ngendahimana , author C.-Y. \ Lin , author G. R. \ Eaton , author S. S. \ Eaton ,\ and\ author J. M. \ Zadrozny ,\ title title Impact of counter ion methyl groups on spin relaxation in [v (c6h4o2) 3] 2-- , \ @noop journal journal The Journal of Physical Chemistry C \ volume 126 ,\ pages 7169--7176 ( year 2022 ) NoStop

    work page 2022

  7. [7]

    O . \"U ng \

    author author R. Martinez , author C. E. \ Jackson , author \"O . \"U ng \"o r , author J. van Tol ,\ and\ author J. M. \ Zadrozny ,\ title title Impact of ligand chlorination and counterion tuning on high-field spin relaxation in a series of v (iv) complexes , \ @noop journal journal Dalton Trans. \ volume 52 ,\ pages 10805--10816 ( year 2023 ) NoStop

    work page 2023

  8. [8]

    author author K. R. \ Mullin , author D. W. \ Laorenza , author D. E. \ Freedman ,\ and\ author J. M. \ Rondinelli ,\ title title Quantum sensing of magnetic fields with molecular color centers , \ @noop journal journal Phys. Rev. Research \ volume 5 ,\ pages L042023 ( year 2023 ) NoStop

    work page 2023

  9. [9]

    \ Wang \ and\ author S

    author author Z.-H. \ Wang \ and\ author S. Takahashi ,\ title title Spin decoherence and electron spin bath noise of a nitrogen-vacancy center in diamond , \ @noop journal journal Phys. Rev. B \ volume 87 ,\ pages 115122 ( year 2013 ) NoStop

    work page 2013

  10. [10]

    Burkard , author T

    author author G. Burkard , author T. D. \ Ladd , author A. Pan , author J. M. \ Nichol ,\ and\ author J. R. \ Petta ,\ title title Semiconductor spin qubits , \ @noop journal journal Rev. Mod. Phys. \ volume 95 ,\ pages 025003 ( year 2023 ) NoStop

    work page 2023

  11. [11]

    Dreher , author F

    author author L. Dreher , author F. Hoehne , author M. Stutzmann ,\ and\ author M. S. \ Brandt ,\ title title Nuclear spins of ionized phosphorus donors in silicon , \ @noop journal journal Phys. Rev. Lett. \ volume 108 ,\ pages 027602 ( year 2012 ) NoStop

    work page 2012

  12. [12]

    Sessoli , author D

    author author R. Sessoli , author D. Gatteschi , author A. Caneschi ,\ and\ author M. Novak ,\ title title Magnetic bistability in a metal-ion cluster , \ @noop journal journal Nature \ volume 365 ,\ pages 141--143 ( year 1993 ) NoStop

    work page 1993

  13. [13]

    author author M. R. \ Wasielewski , author M. D. \ Forbes , author N. L. \ Frank , author K. Kowalski , author G. D. \ Scholes , author J. Yuen-Zhou , author M. A. \ Baldo , author D. E. \ Freedman , author R. H. \ Goldsmith , author T. Goodson III , et al. ,\ title title Exploiting chemistry and molecular systems for quantum information science , \ @noop...

    work page 2020

  14. [14]

    Gaita-Ari \ n o , author F

    author author A. Gaita-Ari \ n o , author F. Luis , author S. Hill ,\ and\ author E. Coronado ,\ title title Molecular spins for quantum computation , \ @noop journal journal Nat. Chem. \ volume 11 ,\ pages 301--309 ( year 2019 ) NoStop

    work page 2019

  15. [15]

    Prokof'Ev \ and\ author P

    author author N. Prokof'Ev \ and\ author P. Stamp ,\ title title Theory of the spin bath , \ @noop journal journal Rep. Prog. Phys. \ volume 63 ,\ pages 669 ( year 2000 ) NoStop

    work page 2000

  16. [16]

    \ Breuer , author D

    author author H.-P. \ Breuer , author D. Burgarth ,\ and\ author F. Petruccione ,\ title title Non-markovian dynamics in a spin star system: Exact solution and approximation techniques , \ @noop journal journal Phys. Rev. B \ volume 70 ,\ pages 045323 ( year 2004 ) NoStop

    work page 2004

  17. [17]

    author author L. P. \ Lindoy \ and\ author D. E. \ Manolopoulos ,\ title title Simple and accurate method for central spin problems , \ @noop journal journal Phys. Rev. Lett. \ volume 120 ,\ pages 220604 ( year 2018 ) NoStop

    work page 2018

  18. [18]

    author author A. M. \ Lewis , author D. E. \ Manolopoulos ,\ and\ author P. Hore ,\ title title Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions , \ @noop journal journal J. Chem. Phys. \ volume 141 ( year 2014 ) NoStop

    work page 2014

  19. [19]

    author author A. M. \ Lewis , author T. P. \ Fay ,\ and\ author D. E. \ Manolopoulos ,\ title title An efficient quantum mechanical method for radical pair recombination reactions , \ @noop journal journal J. Chem. Phys. \ volume 145 ( year 2016 ) NoStop

    work page 2016

  20. [20]

    Rowan , author E

    author author L. Rowan , author E. Hahn ,\ and\ author W. Mims ,\ title title Electron-spin-echo envelope modulation , \ @noop journal journal Phys. Rev. \ volume 137 ,\ pages A61 ( year 1965 ) NoStop

    work page 1965

  21. [21]

    Zhao , author J

    author author N. Zhao , author J. Honert , author B. Schmid , author M. Klas , author J. Isoya , author M. Markham , author D. Twitchen , author F. Jelezko , author R. B. \ Liu , author H. Fedder ,\ and\ author J. Wrachtrup ,\ title title Sensing single remote nuclear spins , \ https://doi.org/10.1038/nnano.2012.152 journal journal Nat. Nanotechnol \ volu...

    work page doi:10.1038/nnano.2012.152 2012

  22. [22]

    Maze , author J

    author author J. Maze , author J. Taylor ,\ and\ author M. Lukin ,\ title title Electron spin decoherence of single nitrogen-vacancy defects in diamond , \ @noop journal journal Phys. Rev. B \ volume 78 ,\ pages 094303 ( year 2008 ) NoStop

    work page 2008

  23. [23]

    Sza \' n kowski , author G

    author author P. Sza \' n kowski , author G. Ramon , author J. Krzywda , author D. Kwiatkowski ,\ and\ author . Cywi \' n ski ,\ title title Environmental noise spectroscopy with qubits subjected to dynamical decoupling , \ https://doi.org/10.1088/1361-648x/aa7648 journal journal J. Condens. Matter Phys. \ volume 29 ,\ pages 333001 ( year 2017 ) NoStop

    work page doi:10.1088/1361-648x/aa7648 2017

  24. [24]

    Yang \ and\ author R.-B

    author author W. Yang \ and\ author R.-B. \ Liu ,\ title title Quantum many-body theory of qubit decoherence in a finite-size spin bath , \ https://doi.org/10.1103/PhysRevB.78.085315 journal journal Phys. Rev. B \ volume 78 ,\ pages 085315 ( year 2008 ) NoStop

    work page doi:10.1103/physrevb.78.085315 2008

  25. [25]

    Yang \ and\ author R.-B

    author author W. Yang \ and\ author R.-B. \ Liu ,\ title title Quantum many-body theory of qubit decoherence in a finite-size spin bath. ii. ensemble dynamics , \ https://doi.org/10.1103/PhysRevB.79.115320 journal journal Phys. Rev. B \ volume 79 ,\ pages 115320 ( year 2009 ) NoStop

    work page doi:10.1103/physrevb.79.115320 2009

  26. [26]

    Yang , author W.-L

    author author W. Yang , author W.-L. \ Ma ,\ and\ author R.-B. \ Liu ,\ title title Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths. \ @noop journal journal Rep. Prog. Phys. \ volume 80 1 ,\ pages 016001 ( year 2017 ) NoStop

    work page 2017

  27. [27]

    \ Ma , author G

    author author W.-L. \ Ma , author G. Wolfowicz , author N. Zhao , author S.-S. \ Li , author J. J. \ Morton ,\ and\ author R.-B. \ Liu ,\ title title Uncovering many-body correlations in nanoscale nuclear spin baths by central spin decoherence , \ @noop journal journal Nat. Commun. \ volume 5 ,\ pages 4822 ( year 2014 ) NoStop

    work page 2014

  28. [28]

    author author S. J. \ Balian , author G. Wolfowicz , author J. J. L. \ Morton ,\ and\ author T. S. \ Monteiro ,\ title title Quantum-bath-driven decoherence of mixed spin systems , \ https://doi.org/10.1103/PhysRevB.89.045403 journal journal Phys. Rev. B \ volume 89 ,\ pages 045403 ( year 2014 ) NoStop

    work page doi:10.1103/physrevb.89.045403 2014

  29. [29]

    Seo , author A

    author author H. Seo , author A. L. \ Falk , author P. V. \ Klimov , author K. C. \ Miao , author G. Galli ,\ and\ author D. D. \ Awschalom ,\ title title Quantum decoherence dynamics of divacancy spins in silicon carbide , \ @noop journal journal Nat. Commun. \ volume 7 ,\ pages 12935 ( year 2016 ) NoStop

    work page 2016

  30. [30]

    Bourassa , author C

    author author A. Bourassa , author C. P. \ Anderson , author K. C. \ Miao , author M. Onizhuk , author H. Ma , author A. L. \ Crook , author H. Abe , author J. Ul-Hassan , author T. Ohshima , author N. T. \ Son , et al. ,\ title title Entanglement and control of single nuclear spins in isotopically engineered silicon carbide , \ @noop journal journal Nat....

    work page 2020

  31. [31]

    Onizhuk , author K

    author author M. Onizhuk , author K. C. \ Miao , author J. P. \ Blanton , author H. Ma , author C. P. \ Anderson , author A. Bourassa , author D. D. \ Awschalom ,\ and\ author G. Galli ,\ title title Probing the coherence of solid-state qubits at avoided crossings , \ https://doi.org/10.1103/PRXQuantum.2.010311 journal journal PRX Quantum \ volume 2 ,\ pa...

    work page doi:10.1103/prxquantum.2.010311 2021

  32. [32]

    Jeschke , author N

    author author G. Jeschke , author N. Wili , author Y. Wu , author S. Kuzin , author H. Karas , author H. Hintz ,\ and\ author A. Godt ,\ title title Electron-spin decoherence in trityl radicals in the absence and presence of microwave irradiation , \ @noop journal journal Magn. Reson. \ volume 6 ,\ pages 15--32 ( year 2025 ) NoStop

    work page 2025

  33. [33]

    author author S. M. \ Jahn , author R. K. \ Stowell ,\ and\ author S. Stoll ,\ title title The contribution of methyl groups to electron spin decoherence of nitroxides in glassy matrices , \ @noop journal journal J. Chem. Phys. \ volume 161 ( year 2024 ) NoStop

    work page 2024

  34. [34]

    Bahrenberg , author S

    author author T. Bahrenberg , author S. M. \ Jahn , author A. Feintuch , author S. Stoll ,\ and\ author D. Goldfarb ,\ title title The decay of the refocused hahn echo in double electron--electron resonance (deer) experiments , \ https://doi.org/10.5194/mr-2-161-2021 journal journal Magn. Reson. \ volume 2 ,\ pages 161--173 ( year 2021 ) NoStop

    work page doi:10.5194/mr-2-161-2021 2021

  35. [35]

    author author E. R. \ Canarie , author S. M. \ Jahn ,\ and\ author S. Stoll ,\ title title Quantitative structure-based prediction of electron spin decoherence in organic radicals , \ @noop journal journal J. Phys. Chem. Lett. \ volume 11 ,\ pages 3396--3400 ( year 2020 ) NoStop

    work page 2020

  36. [36]

    Kveder , author B

    author author M. Kveder , author B. Rakvin ,\ and\ author J. You ,\ title title A quantum many body model for the embedded electron spin decoherence in organic solids , \ @noop journal journal J. Chem. Phys. \ volume 151 ( year 2019 ) NoStop

    work page 2019

  37. [37]

    author author W. M. \ Witzel , author M. S. \ Carroll , author . Cywi \'n ski ,\ and\ author S. Das Sarma ,\ title title Quantum decoherence of the central spin in a sparse system of dipolar coupled spins , \ https://doi.org/10.1103/PhysRevB.86.035452 journal journal Phys. Rev. B \ volume 86 ,\ pages 035452 ( year 2012 ) NoStop

    work page doi:10.1103/physrevb.86.035452 2012

  38. [38]

    Onizhuk , author Y.-X

    author author M. Onizhuk , author Y.-X. \ Wang , author J. Nagura , author A. A. \ Clerk ,\ and\ author G. Galli ,\ title title Understanding central spin decoherence due to interacting dissipative spin baths , \ @noop journal journal Phys. Rev. Lett. \ volume 132 ,\ pages 250401 ( year 2024 ) NoStop

    work page 2024

  39. [39]

    Sch \"a tzle , author R

    author author P. Sch \"a tzle , author R. Ghassemizadeh , author D. F. \ Urban , author T. Wellens , author P. Knittel , author F. Reiter , author J. Jeske ,\ and\ author W. Hahn ,\ title title Spin coherence in strongly coupled spin baths in quasi-two-dimensional layers , \ @noop journal journal Physical Review B \ volume 110 ,\ pages L220302 ( year 2024...

    work page 2024

  40. [40]

    Verstraete , author V

    author author F. Verstraete , author V. Murg ,\ and\ author J. I. \ Cirac ,\ title title Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , \ @noop journal journal Adv. Phys. \ volume 57 ,\ pages 143--224 ( year 2008 ) NoStop

    work page 2008

  41. [41]

    Schollw \"o ck ,\ title title The density-matrix renormalization group in the age of matrix product states , \ @noop journal journal Ann

    author author U. Schollw \"o ck ,\ title title The density-matrix renormalization group in the age of matrix product states , \ @noop journal journal Ann. Phys. \ volume 326 ,\ pages 96--192 ( year 2011 ) NoStop

    work page 2011

  42. [42]

    author author R. Or \'u s ,\ title title A practical introduction to tensor networks: Matrix product states and projected entangled pair states , \ https://doi.org/10.1016/j.aop.2014.06.013 journal journal Ann. Phys. \ volume 349 ,\ pages 117--158 ( year 2014 a ) NoStop

    work page doi:10.1016/j.aop.2014.06.013 2014

  43. [43]

    Qin , author T

    author author M. Qin , author T. Sch \"a fer , author S. Andergassen , author P. Corboz ,\ and\ author E. Gull ,\ title title The hubbard model: A computational perspective , \ @noop journal journal Annu. Rev. Condens. Matter Phys. \ volume 13 ,\ pages 275--302 ( year 2022 ) NoStop

    work page 2022

  44. [44]

    Naber , author S

    author author W. Naber , author S. Faez ,\ and\ author W. G. \ van der Wiel ,\ title title Organic spintronics , \ @noop journal journal J. Phys. D: Appl. Phys. \ volume 40 ,\ pages R205 ( year 2007 ) NoStop

    work page 2007

  45. [45]

    author author V. A. \ Dediu , author L. E. \ Hueso , author I. Bergenti ,\ and\ author C. Taliani ,\ title title Spin routes in organic semiconductors , \ @noop journal journal Nat. Mater. \ volume 8 ,\ pages 707--716 ( year 2009 ) NoStop

    work page 2009

  46. [46]

    Sanvito ,\ title title Spintronics goes plastic , \ @noop journal journal Nat

    author author S. Sanvito ,\ title title Spintronics goes plastic , \ @noop journal journal Nat. Mater. \ volume 6 ,\ pages 803--804 ( year 2007 ) NoStop

    work page 2007

  47. [47]

    author author A. Lunghi ,\ title title Insights into the spin-lattice dynamics of organic radicals beyond molecular tumbling: A combined molecular dynamics and machine-learning approach , \ @noop journal journal Appl. Magn. Reson. \ volume 51 ,\ pages 1343--1356 ( year 2020 ) NoStop

    work page 2020

  48. [48]

    Neese , author F

    author author F. Neese , author F. Wennmohs , author U. Becker ,\ and\ author C. Riplinger ,\ title title The orca quantum chemistry program package , \ @noop journal journal The Journal of chemical physics \ volume 152 ( year 2020 ) NoStop

    work page 2020

  49. [49]

    author author J. P. \ Perdew , author K. Burke ,\ and\ author M. Ernzerhof ,\ title title Generalized gradient approximation made simple , \ @noop journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 3865 ( year 1996 ) NoStop

    work page 1996

  50. [50]

    Grimme , author J

    author author S. Grimme , author J. Antony , author S. Ehrlich ,\ and\ author H. Krieg ,\ title title A consistent and accurate ab initio parametrization of density functional dispersion correction (dft-d) for the 94 elements h-pu , \ @noop journal journal J. Chem. Phys. \ volume 132 ( year 2010 ) NoStop

    work page 2010

  51. [51]

    Adamo \ and\ author V

    author author C. Adamo \ and\ author V. Barone ,\ title title Toward reliable density functional methods without adjustable parameters: The pbe0 model , \ @noop journal journal J. Chem. Phys. \ volume 110 ,\ pages 6158--6170 ( year 1999 ) NoStop

    work page 1999

  52. [52]

    author author R. Or \'u s ,\ title title A practical introduction to tensor networks: Matrix product states and projected entangled pair states , \ @noop journal journal Annals of physics \ volume 349 ,\ pages 117--158 ( year 2014 b ) NoStop

    work page 2014

  53. [53]

    Guan , author P

    author author W. Guan , author P. Bao , author J. Peng , author Z. Lan ,\ and\ author Q. Shi ,\ title title mpsqd: A matrix product state based python package to simulate closed and open system quantum dynamics , \ @noop journal journal J. Chem. Phys. \ volume 161 ( year 2024 ) NoStop

    work page 2024

  54. [54]

    Shi , author Y

    author author Q. Shi , author Y. Xu , author Y. Yan ,\ and\ author M. Xu ,\ title title Efficient propagation of the hierarchical equations of motion using the matrix product state method , \ @noop journal journal J. Chem. Phys. \ volume 148 ( year 2018 ) NoStop

    work page 2018

  55. [55]

    Ke , author R

    author author Y. Ke , author R. Borrelli ,\ and\ author M. Thoss ,\ title title Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space , \ @noop journal journal J. Chem. Phys. \ volume 156 ( year 2022 ) NoStop

    work page 2022

  56. [56]

    Jaschke , author S

    author author D. Jaschke , author S. Montangero ,\ and\ author L. D. \ Carr ,\ title title One-dimensional many-body entangled open quantum systems with tensor network methods , \ @noop journal journal Quantum Sci. Technol. \ volume 4 ,\ pages 013001 ( year 2018 ) NoStop

    work page 2018

  57. [57]

    Li , author Y

    author author Q. Li , author Y. Gao , author Y.-Y. \ He , author Y. Qi , author B.-B. \ Chen ,\ and\ author W. Li ,\ title title Tangent space approach for thermal tensor network simulations of the 2d hubbard model , \ @noop journal journal Phys. Rev. Lett. \ volume 130 ,\ pages 226502 ( year 2023 ) NoStop

    work page 2023

  58. [58]

    Haegeman , author C

    author author J. Haegeman , author C. Lubich , author I. Oseledets , author B. Vandereycken ,\ and\ author F. Verstraete ,\ title title Unifying time evolution and optimization with matrix product states , \ @noop journal journal Physical Review B \ volume 94 ,\ pages 165116 ( year 2016 ) NoStop

    work page 2016

  59. [59]

    Haegeman , author J

    author author J. Haegeman , author J. I. \ Cirac , author T. J. \ Osborne , author I. Pi z orn , author H. Verschelde ,\ and\ author F. Verstraete ,\ title title Time-dependent variational principle for quantum lattices , \ @noop journal journal Phys. Rev. Lett. \ volume 107 ,\ pages 070601 ( year 2011 ) NoStop

    work page 2011

  60. [60]

    Lubich , author I

    author author C. Lubich , author I. V. \ Oseledets ,\ and\ author B. Vandereycken ,\ title title Time integration of tensor trains , \ @noop journal journal SIAM J. Numer. Anal. \ volume 53 ,\ pages 917--941 ( year 2015 ) NoStop

    work page 2015

  61. [61]

    Yang \ and\ author S

    author author M. Yang \ and\ author S. R. \ White ,\ title title Time-dependent variational principle with ancillary krylov subspace , \ @noop journal journal Phys. Rev. B \ volume 102 ,\ pages 094315 ( year 2020 ) NoStop

    work page 2020

  62. [62]

    Hackl , author T

    author author L. Hackl , author T. Guaita , author T. Shi , author J. Haegeman , author E. Demler ,\ and\ author J. I. \ Cirac ,\ title title Geometry of variational methods: dynamics of closed quantum systems , \ @noop journal journal SciPost Phys. \ volume 9 ,\ pages 048 ( year 2020 ) NoStop

    work page 2020

  63. [63]

    author author I. V. \ Oseledets ,\ title title Tensor-train decomposition , \ @noop journal journal SIAM J. Sci. Comput. \ volume 33 ,\ pages 2295--2317 ( year 2011 ) NoStop

    work page 2011

  64. [64]

    author author S. M. \ Greene \ and\ author V. S. \ Batista ,\ title title Tensor-train split-operator fourier transform (tt-soft) method: Multidimensional nonadiabatic quantum dynamics , \ @noop journal journal J. Chem. Theory Comput. \ volume 13 ,\ pages 4034--4042 ( year 2017 ) NoStop

    work page 2017

  65. [65]

    Onizhuk \ and\ author G

    author author M. Onizhuk \ and\ author G. Galli ,\ title title Bath-limited dynamics of nuclear spins in solid-state spin platforms , \ https://doi.org/10.1103/PhysRevB.108.075306 journal journal Phys. Rev. B \ volume 108 ,\ pages 075306 ( year 2023 ) NoStop

    work page doi:10.1103/physrevb.108.075306 2023

  66. [66]

    \ Zhang , author W.-L

    author author G.-L. \ Zhang , author W.-L. \ Ma ,\ and\ author R.-B. \ Liu ,\ title title Cluster correlation expansion for studying decoherence of clock transitions in spin baths , \ https://doi.org/10.1103/PhysRevB.102.245303 journal journal Phys. Rev. B \ volume 102 ,\ pages 245303 ( year 2020 ) NoStop

    work page doi:10.1103/physrevb.102.245303 2020

  67. [67]

    author author P. L. \ Stanwix , author L. M. \ Pham , author J. R. \ Maze , author D. Le Sage , author T. K. \ Yeung , author P. Cappellaro , author P. R. \ Hemmer , author A. Yacoby , author M. D. \ Lukin ,\ and\ author R. L. \ Walsworth ,\ title title Coherence of nitrogen-vacancy electronic spin ensembles in diamond , \ @noop journal journal Phys. Rev....

    work page 2010

  68. [68]

    author author J. R. \ Maze , author P. L. \ Stanwix , author J. S. \ Hodges , author S. Hong , author J. M. \ Taylor , author P. Cappellaro , author L. Jiang , author M. G. \ Dutt , author E. Togan , author A. Zibrov , et al. ,\ title title Nanoscale magnetic sensing with an individual electronic spin in diamond , \ @noop journal journal Nature \ volume 4...

    work page 2008

  69. [69]

    Dolde , author H

    author author F. Dolde , author H. Fedder , author M. W. \ Doherty , author T. N \"o bauer , author F. Rempp , author G. Balasubramanian , author T. Wolf , author F. Reinhard , author L. C. \ Hollenberg , author F. Jelezko , et al. ,\ title title Electric-field sensing using single diamond spins , \ @noop journal journal Nat. Phys. \ volume 7 ,\ pages 459...

    work page 2011

  70. [70]

    \ Liu , author X

    author author G.-Q. \ Liu , author X. Feng , author N. Wang , author Q. Li ,\ and\ author R.-B. \ Liu ,\ title title Coherent quantum control of nitrogen-vacancy center spins near 1000 kelvin , \ @noop journal journal Nat. Commun. \ volume 10 ,\ pages 1344 ( year 2019 ) NoStop

    work page 2019

  71. [71]

    Nemoto , author M

    author author K. Nemoto , author M. Trupke , author S. J. \ Devitt , author B. Scharfenberger , author K. Buczak , author J. Schmiedmayer ,\ and\ author W. J. \ Munro ,\ title title Photonic quantum networks formed from nv- centers , \ @noop journal journal Sci. Rep. \ volume 6 ,\ pages 26284 ( year 2016 ) NoStop

    work page 2016

  72. [72]

    \ Yang , author Y.-X

    author author Z.-S. \ Yang , author Y.-X. \ Wang , author M.-J. \ Tao , author W. Yang , author M. Zhang , author Q. Ai ,\ and\ author F.-G. \ Deng ,\ title title Longitudinal relaxation of a nitrogen-vacancy center in a spin bath by generalized cluster-correlation expansion method , \ @noop journal journal Ann. Phys. \ volume 413 ,\ pages 168063 ( year 2...

    work page 2020

  73. [73]

    Onizhuk \ and\ author G

    author author M. Onizhuk \ and\ author G. Galli ,\ title title Pycce: A python package for cluster correlation expansion simulations of spin qubit dynamics , \ @noop journal journal Adv. Theory Simul. \ volume 4 ,\ pages 2100254 ( year 2021 ) NoStop

    work page 2021

  74. [74]

    author author B. E. \ Kane ,\ title title A silicon-based nuclear spin quantum computer , \ @noop journal journal Nature \ volume 393 ,\ pages 133--137 ( year 1998 ) NoStop

    work page 1998

  75. [75]

    author author J. J. \ Morton , author A. M. \ Tyryshkin , author R. M. \ Brown , author S. Shankar , author B. W. \ Lovett , author A. Ardavan , author T. Schenkel , author E. E. \ Haller , author J. W. \ Ager ,\ and\ author S. Lyon ,\ title title Solid-state quantum memory using the 31p nuclear spin , \ @noop journal journal Nature \ volume 455 ,\ pages ...

    work page 2008

  76. [76]

    author author J. M. \ Zadrozny , author J. Niklas , author O. G. \ Poluektov ,\ and\ author D. E. \ Freedman ,\ title title Millisecond coherence time in a tunable molecular electronic spin qubit , \ @noop journal journal ACS Cent. Sci. \ volume 1 ,\ pages 488--492 ( year 2015 ) NoStop

    work page 2015

  77. [77]

    Schott , author E

    author author S. Schott , author E. R. \ McNellis , author C. B. \ Nielsen , author H.-Y. \ Chen , author S. Watanabe , author H. Tanaka , author I. McCulloch , author K. Takimiya , author J. Sinova ,\ and\ author H. Sirringhaus ,\ title title Tuning the effective spin-orbit coupling in molecular semiconductors , \ @noop journal journal Nat. Commun. \ vol...

    work page 2017

  78. [78]

    Mukamel ,\ @noop title Principles of Nonlinear Optical Spectroscopy ,\ series Oxford Series in Optical and Imaging Sciences , Vol

    author author S. Mukamel ,\ @noop title Principles of Nonlinear Optical Spectroscopy ,\ series Oxford Series in Optical and Imaging Sciences , Vol. volume 6 \ ( publisher Oxford University Press ,\ year 1995 ) NoStop

    work page 1995

  79. [79]

    Mukamel ,\ title title Fluorescence and absorption of large anharmonic molecules - spectroscopy without eigenstates , \ https://doi.org/10.1021/j100253a008 journal journal J

    author author S. Mukamel ,\ title title Fluorescence and absorption of large anharmonic molecules - spectroscopy without eigenstates , \ https://doi.org/10.1021/j100253a008 journal journal J. Phys. Chem. \ volume 89 ,\ pages 1077--1087 ( year 1985 ) NoStop

    work page doi:10.1021/j100253a008 1985

  80. [80]

    author author G. S. \ Uhrig ,\ title title Keeping a quantum bit alive by optimized -pulse sequences , \ @noop journal journal Phys. Rev. Lett. \ volume 98 ,\ pages 100504 ( year 2007 ) NoStop

    work page 2007

Showing first 80 references.