Skip to main content
SpringerLink
Log in

Incoherent GRAPE for Optimization of Quantum Systems with Environmentally Assisted Control

  • QUANTUM INFORMATICS: COMPUTING
  • Published:
Russian Microelectronics Aims and scope Submit manuscript

Abstract

In this work, we review several results on development and application of incoherent version of GRAPE (Gradient Ascent Pulse Engineering) approach to optimization for open quantum systems driven by both coherent and incoherent controls. In the incoherent control approach, the environment serves as a control together with coherent field, and decoherence rates become generally time-dependent. For a qubit, explicit analytic expressions for evolution of the density matrix were obtained by solving a cubic equation via Cardano method. We discuss applications of incoherent GRAPE method (inGRAPE) to high fidelity gate generation for open one- and two-qubit systems and surprising properties of the underlying control landscapes, forming two groups — smooth single peak landscapes for Hadamard, C-NOT and C-Z gates, and more complicated with two peaks for T (or π/8) gate. For a qutrit, a formulation of the environment-assisted incoherent control with time-dependent decoherence rates is provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.

REFERENCES

  1. Koch, C.P., Boscain, U., Calarco, T., Dirr, G., Filipp, S., Glaser, S.J., Kosloff, R., Montangero, S., Schulte-Herbrüggen, T., Sugny, D., and Wilhelm, F.K., Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe, EPJ Quantum Technol., 2022, vol. 9, no. 1, p. 19. https://doi.org/10.1140/epjqt/s40507-022-00138-x

    Article  Google Scholar 

  2. Rice, S.A. and Zhao, M., Optical Control of Molecular Dynamics, Wiley, 2000.

    Google Scholar 

  3. Tannor, D.J., Introduction to Quantum Mechanics: A Time-Dependent Perspective, University Science Books, 2007.

    Google Scholar 

  4. Shapiro, M. and Brumer, P., Quantum Control of Molecular Processes, Wiley, 2011. https://doi.org/10.1002/9783527639700

    Book  Google Scholar 

  5. Pechen, A. and Rabitz, H., Teaching the environment to control quantum systems, Phys. Rev. A, 2006, vol. 73, no. 6, p. 062102. https://doi.org/10.1103/physreva.73.062102

    Article  Google Scholar 

  6. Pechen, A., Engineering arbitrary pure and mixed quantum states, Phys. Rev. A, 2011, vol. 84, no. 4, p. 042106. https://doi.org/10.1103/physreva.84.042106

    Article  Google Scholar 

  7. Judson, R.S. and Rabitz, H., Teaching lasers to control molecules, Phys. Rev. Lett., 1992, vol. 68, no. 10, pp. 1500–1503. https://doi.org/10.1103/physrevlett.68.1500

    Article  Google Scholar 

  8. Eitan, R., Mundt, M., and Tannor, D.J., Optimal control with accelerated convergence: Combining the Krotov and quasi-Newton methods, Phys. Rev. A, 2011, vol. 83, no. 5, p. 053426. https://doi.org/10.1103/physreva.83.053426

    Article  Google Scholar 

  9. Baturina, O.V. and Morzhin, O.V., Optimal control of the spin system on a basis of the global improvement method, Autom. Remote Control, 2011, vol. 72, no. 6, pp. 1213–1220. https://doi.org/10.1134/s0005117911060075

    Article  MathSciNet  Google Scholar 

  10. Caneva, T., Calarco, T., and Montangero, S., Chopped random-basis quantum optimization, Phys. Rev. A, 2011, vol. 84, no. 2, p. 022326. https://doi.org/10.1103/physreva.84.022326

    Article  Google Scholar 

  11. Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T., and Glaser, S.J., Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson., 2005, vol. 172, no. 2, pp. 296–305. https://doi.org/10.1016/j.jmr.2004.11.004

    Article  Google Scholar 

  12. De Fouquieres, P., Schirmer, S.G., Glaser, S.J., and Kuprov, I., Second order gradient ascent pulse engineering, J. Magn. Reson., 2011, vol. 212, no. 2, pp. 412–417. https://doi.org/10.1016/j.jmr.2011.07.023

    Article  Google Scholar 

  13. Pechen, A.N. and Tannor, D.J., Quantum control landscape for a Λ-atom in the vicinity of second-order traps, Isr. J. Chem., 2012, vol. 52, no. 5, pp. 467–472. https://doi.org/10.1002/ijch.201100165

    Article  Google Scholar 

  14. Petruhanov, V.N. and Pechen, A.N., GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls, J. Phys. A: Math. Theor., 2023, vol. 56, no. 30, p. 305303. https://doi.org/10.1088/1751-8121/ace13f

    Article  MathSciNet  Google Scholar 

  15. Petruhanov, V.N. and Pechen, A.N., Quantum gate generation in two-level open quantum systems by coherent and incoherent photons found with gradient search, Photonics, 2023, vol. 10, no. 2, p. 220. https://doi.org/10.3390/photonics10020220

    Article  Google Scholar 

  16. Petruhanov, V.N. and Pechen, A.N., Quantum control landscapes for generation of H and T gates in an open qubit with both coherent and environmental drive, Photonics, 2023, vol. 10, no. 11, p. 1200. https://doi.org/10.3390/photonics10111200

    Article  Google Scholar 

  17. Petruhanov, V.N. and Pechen, A.N., Optimal control for state preparation in twoqubit open quantum systems driven by coherent and incoherent controls via grape approach, Int. J. Mod. Phys. A, 2022, vol. 37, no. 20n21, p. 2243017. https://doi.org/10.1142/S0217751X22430175

  18. Davies, E.B., Quantum Theory of Open Systems, Academic, 1976.

    Google Scholar 

  19. Accardi, L., Volovich, I., and Lu, Yu.G., Quantum Theory and Its Stochastic Limit, Berlin: Springer, 2002. https://doi.org/10.1007/978-3-662-04929-7

    Book  Google Scholar 

  20. Pechen, A.N., Petruhanov, V.N., Morzhin, O.V., and Volkov, B.O., Control landscapes for high-fidelity generation of C-NOT and C-PHASE gates with coherent and environmental drive, 2023 (in press).

  21. Popov, A., Kiktenko, E., Fedorov, A., and Man’ko, V.I., Information processing using three-qubit and qubit–qutrit encodings of noncomposite quantum systems, J. Russ. Laser Res., 2016, vol. 37, no. 6, pp. 581–590. https://doi.org/10.1007/s10946-016-9610-8

    Article  Google Scholar 

  22. Morzhin, O.V. and Pechen, A.N., Optimization of time-dependent decoherence rates and coherent control for a qutrit system, Proc. Steklov Math. Institute (in press), arXiv Preprint, 2023. https://doi.org/10.48550/arXiv.2308.03976

Download references

Funding

Section 4 of this work was performed in Steklov Mathematical Institute of Russian Academy of Sciences within the Russian Science Foundation grant no. 22-11-00330, https://rscf.ru/en/project/22-11-00330/.

Author information

Authors and Affiliations

  1. Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    V. Petruhanov & A. Pechen

  2. Quantum Engineering Research and Education Center, University of Science and Technology MISIS, 119991, Moscow, Russia

    V. Petruhanov & A. Pechen

Authors
  1. V. Petruhanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Pechen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. Petruhanov or A. Pechen.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Petruhanov, V., Pechen, A. Incoherent GRAPE for Optimization of Quantum Systems with Environmentally Assisted Control. Russ Microelectron 52 (Suppl 1), S424–S427 (2023). https://doi.org/10.1134/S1063739723600784

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063739723600784

Keywords:

Search

Navigation