MISTER-T: an open-source software package for quantum optimal control of multi-electron systems on arbitrary geometries. (English) Zbl 07867592
Summary: We present an open-source software package, MISTER-T (Manipulating an Interacting System of Total Electrons in Real-Time), for the quantum optimal control of interacting electrons within a time-dependent Kohn-Sham formalism. In contrast to other implementations restricted to simple models on rectangular domains, our method enables quantum optimal control calculations for multi-electron systems (in the effective mass formulation) on nonuniform meshes with arbitrary two-dimensional cross-sectional geometries. Our approach is enabled by forward and backward propagator integration methods to evolve the Kohn-Sham equations with a pseudoskeleton decomposition algorithm for enhanced computational efficiency. We provide several examples of the versatility and efficiency of the MISTER-T code in handling complex geometries and quantum control mechanisms. The capabilities of the MISTER-T code provide insight into the implications of varying propagation times and local control mechanisms to understand a variety of strategies for manipulating electron dynamics in these complex systems.
Keywords:
quantum optimal control; time-dependent Kohn-Sham equation; propagator integration; finite element methodSoftware:
Partial Differential Equation Toolbox; HADOKEN; SHORYUKEN; TRAVOLTA; MISTER-T; COKOSNUT; FINUFFT; NIC-CAGEReferences:
| [1] | Dantus, M.; Lozovoy, V. V., Experimental coherent laser control of physicochemical processes, Chem. Rev., 104, 4, 1813-1860, 2004 |
| [2] | Wollenhaupt, M.; Engel, V.; Baumert, T., Femtosecond laser photoelectron spectroscopy on atoms and small molecules: prototype studies in quantum control, Annu. Rev. Phys. Chem., 56, 25-56, 2005 |
| [3] | Nuernberger, P.; Vogt, G.; Brixner, T.; Gerber, G., Femtosecond quantum control of molecular dynamics in the condensed phase, Phys. Chem. Chem. Phys., 9, 20, 2470-2497, 2007 |
| [4] | Levitt, M. H., Spin Dynamics: Basics of Nuclear Magnetic Resonance, 2013, John Wiley & Sons |
| [5] | Schweiger, A.; Jeschke, G., Principles of Pulse Electron Paramagnetic Resonance, 2001, Oxford University Press |
| [6] | Bernstein, M. A.; King, K. F.; Zhou, X. J., Handbook of MRI Pulse Sequences, 2004, Elsevier |
| [7] | Wang, X.; Okyay, M. S.; Kumar, A.; Wong, B. M., Accelerating quantum optimal control of multi-qubit systems with symmetry-based Hamiltonian transformations, AVS Quantum Sci., 5, 4, 2023 |
| [8] | Verstraete, F.; Wolf, M. M.; Ignacio Cirac, J., Quantum computation and quantum-state engineering driven by dissipation, Nat. Phys., 5, 9, 633-636, 2009 |
| [9] | Heeres, R. W.; Reinhold, P.; Ofek, N.; Frunzio, L.; Jiang, L.; Devoret, M. H.; Schoelkopf, R. J., Implementing a universal gate set on a logical qubit encoded in an oscillator, Nat. Commun., 8, 1, 94, 2017 |
| [10] | Cai, J.; Retzker, A.; Jelezko, F.; Plenio, M. B., A large-scale quantum simulator on a diamond surface at room temperature, Nat. Phys., 9, 3, 168-173, 2013 |
| [11] | Kokail, C.; Maier, C.; van Bijnen, R.; Brydges, T.; Joshi, M. K.; Jurcevic, P.; Muschik, C. A.; Silvi, P.; Blatt, R.; Roos, C. F., Self-verifying variational quantum simulation of lattice models, Nature, 569, 7756, 355-360, 2019 |
| [12] | Neumann, P.; Jakobi, I.; Dolde, F.; Burk, C.; Reuter, R.; Waldherr, G.; Honert, J.; Wolf, T.; Brunner, A.; Shim, J. H., High-precision nanoscale temperature sensing using single defects in diamond, Nano Lett., 13, 6, 2738-2742, 2013 |
| [13] | Konzelmann, P.; Rendler, T.; Bergholm, V.; Zappe, A.; Pfannenstill, V.; Garsi, M.; Ziem, F.; Niethammer, M.; Widmann, M.; Lee, S.-Y., Robust and efficient quantum optimal control of spin probes in a complex (biological) environment. Towards sensing of fast temperature fluctuations, New J. Phys., 20, 12, Article 123013 pp., 2018 |
| [14] | Raza, A.; Hong, C.; Wang, X.; Kumar, A.; Shelton, C. R.; Wong, B. M., NIC-CAGE: an open-source software package for predicting optimal control fields in photo-excited chemical systems, Comput. Phys. Commun., 258, Article 107541 pp., 2021 · Zbl 07689009 |
| [15] | Gao, Y.; Wang, X.; Yu, N.; Wong, B. M., Harnessing deep reinforcement learning to construct time-dependent optimal fields for quantum control dynamics, Phys. Chem. Chem. Phys., 24, 24012-24020, 2022 |
| [16] | Koch, C. P.; Boscain, U.; Calarco, T.; Dirr, G.; Filipp, S.; Glaser, S. J.; Kosloff, R.; Montangero, S.; Schulte-Herbrüggen, T.; Sugny, D., Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol., 9, 1, Article 19 pp., 2022 |
| [17] | Lazin, M. F.; Shelton, C. R.; Sandhofer, S. N.; Wong, B. M., High-dimensional multi-fidelity Bayesian optimization for quantum control, Mach. Learn.: Sci. Technol., 4, 4, Article 045014 pp., 2023 |
| [18] | Rodríguez-Borbón, J. M.; Wang, X.; Diéguez, A. P.; Ibrahim, K. Z.; Wong, B. M., TRAVOLTA: GPU acceleration and algorithmic improvements for constructing quantum optimal control fields in photo-excited systems, Comput. Phys. Commun., 296, Article 109017 pp., 2024 · Zbl 1532.81001 |
| [19] | Glaser, S. J.; Boscain, U.; Calarco, T.; Koch, C. P.; Köckenberger, W.; Kosloff, R.; Kuprov, I.; Luy, B.; Schirmer, S.; Schulte-Herbrüggen, T., Training Schrödinger’s cat: quantum optimal control: strategic report on current status, visions and goals for research in Europe, Eur. Phys. J. D, 69, 1-24, 2015 |
| [20] | Boscain, U.; Sigalotti, M.; Sugny, D., Introduction to the Pontryagin maximum principle for quantum optimal control, PRX Quantum, 2, 3, Article 030203 pp., 2021 |
| [21] | Wilhelm, F. K.; Kirchhoff, S.; Machnes, S.; Wittler, N.; Sugny, D., An introduction into optimal control for quantum technologies, 2020, arXiv preprint |
| [22] | Kohn, W.; Sham, L. J., Self-consistent equations including exchange and correlation effects, Phys. Rev., 140, 4A, Article A1133 pp., 1965 |
| [23] | Runge, E.; Gross, E. K., Density-functional theory for time-dependent systems, Phys. Rev. Lett., 52, 12, 997, 1984 |
| [24] | Castro, A., Theoretical shaping of femtosecond laser pulses for ultrafast molecular photo-dissociation with control techniques based on time-dependent density functional theory, ChemPhysChem, 14, 7, 1488-1495, 2013 |
| [25] | Liu, W.-H.; Wang, Z.; Chen, Z.-H.; Luo, J.-W.; Li, S.-S.; Wang, L.-W., Algorithm advances and applications of time-dependent first-principles simulations for ultrafast dynamics, Wiley Interdiscip. Rev. Comput. Mol. Sci., 12, 3, Article e1577 pp., 2022 |
| [26] | Magann, A. B.; Grace, M. D.; Rabitz, H. A.; Sarovar, M., Digital quantum simulation of molecular dynamics and control, Phys. Rev. Res., 3, 2, Article 023165 pp., 2021 |
| [27] | Irani, E.; Anvari, A.; Sadighi-Bonabi, R., Selective photo-dissociative ionization of methane molecule with tddft study, Spectrochim. Acta, Part A, Mol. Biomol. Spectrosc., 171, 325-329, 2017 |
| [28] | Hellgren, M.; Räsänen, E.; Gross, E., Optimal control of strong-field ionization with time-dependent density-functional theory, Phys. Rev. A, 88, 1, Article 013414 pp., 2013 |
| [29] | Castro, A., Theoretical shaping of femtosecond laser pulses for molecular photodissociation with control techniques based on Ehrenfest’s dynamics and time-dependent density functional theory, ChemPhysChem, 17, 11, 1601-1607, 2016 |
| [30] | Andrade, X.; Strubbe, D.; De Giovannini, U.; Larsen, A. H.; Oliveira, M. J.; Alberdi-Rodriguez, J.; Varas, A.; Theophilou, I.; Helbig, N.; Verstraete, M. J., Real-space grids and the octopus code as tools for the development of new simulation approaches for electronic systems, Phys. Chem. Chem. Phys., 17, 47, 31371-31396, 2015 |
| [31] | Rasti, S.; Irani, E.; Sadighi-Bonabi, R., Efficient photo-dissociation of CH_4 and H_2CO molecules with optimized ultra-short laser pulses, AIP Adv., 5, 11, 2015 |
| [32] | Kato, T.; Nobusada, K.; Saito, S., Inverse Kohn-Sham equations derived from the density equation theory, J. Phys. Soc. Jpn., 89, 2, Article 024301 pp., 2020 |
| [33] | Mendes, R. V., Quantum control of quantum triple collisions in a maximally symmetric three-body Coulomb problem, Int. J. Mod. Phys. B, Article 2450143 pp., 2023 |
| [34] | Putaja, A.; Räsänen, E., Ultrafast sequential charge transfer in a double quantum dot, Phys. Rev. B, 82, 16, Article 165336 pp., 2010 |
| [35] | Räsänen, E.; Putaja, A.; Mardoukhi, Y., Optimal control strategies for coupled quantum dots, Open Phys., 11, 9, 1066-1073, 2013 |
| [36] | Castro, A.; Werschnik, J.; Gross, E. K., Controlling the dynamics of many-electron systems from first principles: a combination of optimal control and time-dependent density-functional theory, Phys. Rev. Lett., 109, 15, Article 153603 pp., 2012 |
| [37] | Sprengel, M.; Ciaramella, G.; Borzì, A., A cokosnut code for the control of the time-dependent Kohn-Sham model, Comput. Phys. Commun., 214, 231-238, 2017 · Zbl 1376.93047 |
| [38] | Lehtovaara, L.; Havu, V.; Puska, M., All-electron time-dependent density functional theory with finite elements: time-propagation approach, J. Chem. Phys., 135, 15, 2011 |
| [39] | Bao, G.; Hu, G.; Liu, D., Real-time adaptive finite element solution of time-dependent Kohn-Sham equation, J. Comput. Phys., 281, 743-758, 2015 · Zbl 1354.65187 |
| [40] | Kanungo, B.; Gavini, V., Real time time-dependent density functional theory using higher order finite-element methods, Phys. Rev. B, 100, 11, Article 115148 pp., 2019 |
| [41] | Kanungo, B.; Rufus, N. D.; Gavini, V., Efficient all-electron time-dependent density functional theory calculations using an enriched finite element basis, J. Chem. Theory Comput., 19, 3, 978-991, 2023 |
| [42] | Marques, M. A.; Gross, E. K., Time-dependent density functional theory, (A Primer in Density Functional Theory, 2003, Springer), 144-184 · Zbl 1213.81233 |
| [43] | Gunnarsson, O.; Lundqvist, B. I., Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism, Phys. Rev. B, 13, 10, 4274, 1976 |
| [44] | Glutsch, S., Excitons in Low-Dimensional Semiconductors: Theory Numerical Methods Applications, vol. 141, 2013, Springer Science & Business Media |
| [45] | Ullrich, C. A., Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system, J. Chem. Phys., 125, 23, 2006 |
| [46] | Rehn, D. A., Algorithms for Real-Time Time-Dependent Density Functional Theory and Calculation of Phase Diagrams for Two-Dimensional Phase-Change Materials, 2018, Stanford University |
| [47] | Chen, Y.; Sandhofer, S. N.; Wong, B. M., SHORYUKEN: an open-source software package for calculating nonlocal exchange interactions in nanowires, Comput. Phys. Commun., 300, Article 109197 pp., 2024 · Zbl 07853524 |
| [48] | Yang, Z.-h.; Ullrich, C. A., Direct calculation of exciton binding energies with time-dependent density-functional theory, Phys. Rev. B, 87, 19, Article 195204 pp., 2013 |
| [49] | Qteish, A.; Rinke, P.; Scheffler, M.; Neugebauer, J., Exact-exchange-based quasiparticle energy calculations for the band gap, effective masses, and deformation potentials of scn, Phys. Rev. B, 74, 24, Article 245208 pp., 2006 |
| [50] | Chao, C. Y.-P.; Chuang, S. L., Resonant tunneling of holes in the multiband effective-mass approximation, Phys. Rev. B, 43, 9, 7027, 1991 |
| [51] | Wijewardane, H. O.; Ullrich, C. A., Real-time electron dynamics with exact-exchange time-dependent density-functional theory, Phys. Rev. Lett., 100, 5, Article 056404 pp., 2008 |
| [52] | Wijewardane, H. O.; Ullrich, C. A., Time-dependent Kohn-Sham theory with memory, Phys. Rev. Lett., 95, 8, Article 086401 pp., 2005 |
| [53] | Flick, J.; Ruggenthaler, M.; Appel, H.; Rubio, A., Kohn-Sham approach to quantum electrodynamical density-functional theory: exact time-dependent effective potentials in real space, Proc. Natl. Acad. Sci., 112, 50, 15285-15290, 2015 |
| [54] | Gil, H.; Papakonstantinou, P.; Hyun, C. H.; Oh, Y., From homogeneous matter to finite nuclei: role of the effective mass, Phys. Rev. C, 99, 6, Article 064319 pp., 2019 |
| [55] | Bhattacharyya, A.; Furnstahl, R., The kinetic energy density in Kohn-Sham density functional theory, Nucl. Phys. A, 747, 2, 268-294, 2005 |
| [56] | Eich, F. G.; Di Ventra, M.; Vignale, G., Density-functional theory of thermoelectric phenomena, Phys. Rev. Lett., 112, 19, Article 196401 pp., 2014 |
| [57] | Sprengel, M.; Ciaramella, G.; Borzì, A., Investigation of optimal control problems governed by a time-dependent Kohn-Sham model, J. Dyn. Control Syst., 24, 657-679, 2018 · Zbl 1407.35170 |
| [58] | Borzì, A.; Ciaramella, G.; Sprengel, M., Formulation and Numerical Solution of Quantum Control Problems, 2017, SIAM · Zbl 1402.81006 |
| [59] | Tröltzsch, F., Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, vol. 112, 2010, American Mathematical Soc. · Zbl 1195.49001 |
| [60] | Chiu, J.; Demanet, L., Sublinear randomized algorithms for skeleton decompositions, SIAM J. Matrix Anal. Appl., 34, 3, 1361-1383, 2013 · Zbl 1277.68296 |
| [61] | Engquist, B.; Ying, L., A fast directional algorithm for high frequency acoustic scattering in two dimensions, J. Comput. Phys., 2009 · Zbl 1182.65178 |
| [62] | Gao, Y.; Mayfield, J.; Luo, S., A second-order fast Huygens sweeping method for time-dependent Schrödinger equations with perfectly matched layers, J. Sci. Comput., 88, 1-26, 2021 · Zbl 1490.65230 |
| [63] | Barnett, A. H.; Magland, J.; af Klinteberg, L., A parallel nonuniform fast Fourier transform library based on an “exponential of semicircle” kernel, SIAM J. Sci. Comput., 41, 5, C479-C504, 2019 · Zbl 07123199 |
| [64] | Barnett, A. H., Aliasing error of the kernel in the nonuniform fast Fourier transform, Appl. Comput. Harmon. Anal., 51, 1-16, 2021 · Zbl 1464.65295 |
| [65] | Chevalier, C.; Wong, B. M., HADOKEN: an open-source software package for predicting electron confinement effects in various nanowire geometries and configurations, Comput. Phys. Commun., 274, Article 108299 pp., 2022 · Zbl 07699269 |
| [66] | Hager, W. W.; Zhang, H., A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM J. Optim., 16, 1, 170-192, 2005 · Zbl 1093.90085 |
| [67] | Bender, C. M.; Orszag, S. A., Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, vol. 1, 1999, Springer Science & Business Media · Zbl 0938.34001 |
| [68] | Goreinov, S. A.; Tyrtyshnikov, E. E.; Zamarashkin, N. L., A theory of pseudoskeleton approximations, Linear Algebra Appl., 261, 1-3, 1-21, 1997 · Zbl 0877.65021 |
| [69] | Goreinov, S. A.; Zamarashkin, N. L.; Tyrtyshnikov, E. E., Pseudo-skeleton approximations by matrices of maximal volume, Math. Notes, 62, 4, 515-519, 1997 · Zbl 0916.65040 |
| [70] | MathWorks, Partial Differential Equation Toolbox User’s Guide, 2023, The MathWorks Inc. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
