2000 character limit reached
Generation of C-NOT, SWAP, and C-Z Gates for Two Qubits Using Coherent and Incoherent Controls and Stochastic Optimization (2312.05625v1)
Published 9 Dec 2023 in quant-ph
Abstract: In this work, we consider a general form of the dynamics of open quantum systems determined by the Gorini-Kossakowsky-Sudarchhan-Lindblad type master equation with simultaneous coherent and incoherent controls with three particular forms of the two-qubit Hamiltonians. Coherent control enters in the Hamiltonian and incoherent control enters in both the Hamiltonian and the superoperator of dissipation. For these systems, we analyze the control problems of generating two-qubit C-NOT, SWAP, and C-Z gates using with piecewise constant controls and stochastic optimization in the form of an adapted version of the dual annealing algorithm. In the numerical experiment, we analyze the minimal infidelity obtained by the dual annealing for various values of strength of the interaction between the system and the environment.
- G. Kurizki and A. G. Kofman. Thermodynamics and Control of Open Quantum Systems. Cambridge Univ. Press, 2021. https://doi.org/10.1017/9781316798454
- C. Altafini and F. Ticozzi. Modeling and control of quantum systems: An Introduction. IEEE Trans. Automatic Control. 57 (8), 1898–1917 (2012). https://doi.org/10.1109/TAC.2012.2195830
- J. E. Gough. Principles and applications of quantum control engineering. Philos. Trans. Royal Soc. A. 370 (1979), 5241–5258 (2012). https://doi.org/10.1098/rsta.2012.0370
- V. Letokhov. Laser Control of Atoms and Molecules. Oxford Univ. Press, 2007. https://global.oup.com/academic/product/laser-control-of-atoms-and-molecules-9780199697137
- V. A. Kazakov and V. F. Krotov. Optimal control of resonant interaction between light and matter. Automat. Remote Control. 48 (4), 430–434 (1987).
- O. V. Morzhin and A. N. Pechen. Krotov method for optimal control of closed quantum systems. Russian Math. Surveys. 74 (5), 851–908 (2019). https://doi.org/10.1070/RM9835
- O. V. Morzhin and A. N. Pechen. Krotov type optimization of coherent and incoherent controls for open two-qubit systems. Bull. Irkutsk State Univ. Ser. Math. 45, 3–23 (2023). https://doi.org/10.26516/1997-7670.2023.45.3
- W. Zhu and H. Rabitz. A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator. J. Chem. Phys. 109, 385–391 (1998). https://doi.org/10.1063/1.476575
- V. N. Petruhanov and A. N. Pechen. Quantum control landscapes for generation of H𝐻{H}italic_H and T𝑇{T}italic_T gates in an open qubit with both coherent and environmental drive. Photonics. 10 (11), 1200 (2023). https://doi.org/10.3390/photonics10111200
- V. N. Petruhanov and A. N. Pechen. GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls. J. Phys. A: Math. Theor. 56 (30), 305303 (2023). https://doi.org/10.1088/1751-8121/ace13f
- O. V. Morzhin and A. N. Pechen. Maximization of the overlap between density matrices for a two-level open quantum system driven by coherent and incoherent controls. Lobachevskii J. Math. 40 (10), 1532–1548 (2019). https://doi.org/10.1134/S1995080219100202
- O. V. Morzhin and A. N. Pechen. Optimal state manipulation for a two-qubit system driven by coherent and incoherent controls. Quantum Inf. Process. 22, 241 (2023). https://doi.org/10.1007/s11128-023-03946-x
- R. S. Judson and H. Rabitz. Teaching lasers to control molecules. Phys. Rev. Lett. 68, 1500 (1992). https://doi.org/10.1103/PhysRevLett.68.1500
- A. Pechen and H. Rabitz. Teaching the environment to control quantum systems. Phys. Rev. A. 73 (6), 062102 (2006). https://doi.org/10.1103/PhysRevA.73.062102
- A. Pechen. Engineering arbitrary pure and mixed quantum states. Phys. Rev. A. 84 (4), 042106 (2011). https://doi.org/10.1103/PhysRevA.84.042106
- K. A. Valiev. Quantum computers and quantum computations. Physics-Uspekhi. 48 (1), 1–36 (2005). https://doi.org/10.1070/PU2005v048n01ABEH002024
- Dual annealing optimization in SciPy. https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.dual_annealing.html
- D. M. Reich. Efficient Characterisation and Optimal Control of Open Quantum Systems – Mathematical Foundations and Physical Applications: Dissertation. Universität Kassel, 2015. https://kobra.uni-kassel.de/handle/123456789/2015061948576
- C. Tsallis. Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479–487 (1988). https://doi.org/10.1007/BF01016429
- C. Tsallis and D. A. Stariolo. Generalized simulated annealing. Physica A. 233 (1–2), 395–406 (1996). https://doi.org/10.1016/S0378-4371(96)00271-3
- Y. Xiang and X. G. Gong. Efficiency of generalized simulated annealing. Phys. Rev. E. 62 (3), 4473–4476 (2000). https://doi.org/10.1103/PhysRevE.62.4473
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