References

1

A. Acín, I. Bloch, H. Buhrman, T. Calarco, C. Eichler, J. Eisert, D. Esteve, N. Gisin, S. J. Glaser, F. Jelezko, S. Kuhr, M. Lewenstein, M. F. Riedel, P. O. Schmidt, R. Thew, A. Wallraff, I. Walmsley, and F. K. Wilhelm. The quantum technologies roadmap: a European community view. New J. Phys. 20, 080201 (2018). doi:10.1088/1367-2630/aad1ea.

2

M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press (2000).

3

C. L. Degen, F. Reinhard, and P. Cappellaro. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017). doi:10.1103/RevModPhys.89.035002.

4

S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. Köckenberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, T. Schulte-Herbrüggen, D. Sugny, and F. K. Wilhelm. Training Schrödinger's cat: quantum optimal control. Eur. Phys. J. D 69, 279 (2015). doi:10.1140/epjd/e2015-60464-1.

5

D.J. Tannor, V. Kazakov, and V. Orlov. Control of photochemical branching: novel procedures for finding optimal pulses and global upper bounds. In J. Broeckhove and L. Lathouwers, editors, Time-dependent quantum molecular dynamics, pages 347–360. Plenum (1992).

6

P. Gross, D. Neuhauser, and H. Rabitz. Optimal control of curve-crossing systems. J. Chem. Phys. 96, 2834 (1992). doi:10.1063/1.461980.

7

J. B. Murdoch, A. H. Lent, and M. R. Kritzer. Computer-optimized narrowband pulses for multislice imaging. J. Magnet. Res. 74, 226 (1987). doi:10.1016/0022-2364(87)90336-2.

8

S. J. Glaser and G. P. Drobny. The tailored TOCSY experiment: Chemical shift selective coherence transfer. Chem. Phys. Lett. 164, 456 (1989). doi:10.1016/0009-2614(89)85238-8.

9

C. P. Koch. Controlling open quantum systems: tools, achievements, and limitations. J. Phys.: Condens. Matter 28, 213001 (2016). doi:10.1088/0953-8984/28/21/213001.

10

J. Cui, R. van Bijnen, T. Pohl, S. Montangero, and T. Calarco. Optimal control of Rydberg lattice gases. Quantum Sci. Technol. 2, 035006 (2017). doi:10.1088/2058-9565/aa7daf.

11

S. Patsch, D. M. Reich, J.-M. Raimond, M. Brune, S. Gleyzes, and C. P. Koch. Fast and accurate circularization of a Rydberg atom. Phys. Rev. A 97, 053418 (2018). doi:10.1103/PhysRevA.97.053418.

12

C. Lovecchio, F. Schäfer, S. Cherukattil, M. Alí Khan, I. Herrera, F. S. Cataliotti, T. Calarco, S. Montangero, and F. Caruso. Optimal preparation of quantum states on an atom-chip device. Phys. Rev. A 93, 010304 (2016). doi:10.1103/PhysRevA.93.010304.

13

S. van Frank, M. Bonneau, J. Schmiedmayer, S. Hild, C. Gross, M. Cheneau, I. Bloch, T. Pichler, A. Negretti, T. Calarco, and S. Montangero. Optimal control of complex atomic quantum systems. Sci. Rep. 6, 34187 (2016). doi:10.1038/srep34187.

14

N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441 (2016). doi:10.1038/nature18949.

15

J. J. W. H. Sørensen, M. K. Pedersen, M. Munch, P. Haikka, J. H. Jensen, T. Planke, M. G. Andreasen, M. Gajdacz, K. Mølmer, A. Lieberoth, J. F. Sherson, and Q. M. players. Exploring the quantum speed limit with computer games. Nature 532, 210 (2016). doi:10.1038/nature17620.

16

R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, and Michel H. Devoret, and R. J. Schoelkopf. Implementing a universal gate set on a logical qubit encoded in an oscillator. Nature Commun. 8, 94 (2017). doi:10.1038/s41467-017-00045-1.

17

R. Heck, O. Vuculescu, J. J. Sørensen, J. Zoller, M. G. Andreasen, M. G. Bason, P. Ejlertsen, O. Elíasson, P. Haikka, J. S. Laustsen, L. L. Nielsen, A. Mao, R. Müller, M. Napolitano, M. K. Pedersen, A. R. Thorsen, C. Bergenholtz, T. Calarco, S. Montangero, and J. F. Sherson. Remote optimization of an ultracold atoms experiment by experts and citizen scientists. Proc. Nat. Acad. Sci. 115, E11231 (2018). doi:10.1073/pnas.1716869115.

18

G. Feng, F. H. Cho, H. Katiyar, J. Li, D. Lu, J. Baugh, and R. Laflamme. Gradient-based closed-loop quantum optimal control in a solid-state two-qubit system. Phys. Rev. A 98, 052341 (2018). doi:10.1103/PhysRevA.98.052341.

19

A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin. Generation and manipulation of Schrödinger cat states in Rydberg atom arrays. Science 365, 570 (2019). doi:10.1126/science.aax9743.

20

A. Larrouy, S. Patsch, and others. in preparation.

21

N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magnet. Res. 172, 296 (2005). doi:10.1016/j.jmr.2004.11.004.

22

D. M. Reich, M. Ndong, and C. P. Koch. Monotonically convergent optimization in quantum control using Krotov's method. J. Chem. Phys. 136, 104103 (2012). doi:10.1063/1.3691827.

23

R. Eitan, M. Mundt, and D. J. Tannor. Optimal control with accelerated convergence: combining the Krotov and quasi-Newton methods. Phys. Rev. A 83, 053426 (2011). doi:10.1103/PhysRevA.83.053426.

24

T. Caneva, T. Calarco, and S. Montangero. Chopped random-basis quantum optimization. Phys. Rev. A 84, 022326 (2011). doi:10.1103/PhysRevA.84.022326.

25

M. M. Müller, H. Haakh, T. Calarco, C. P. Koch, and C. Henkel. Prospects for fast Rydberg gates on an atom chip. Quantum Inf. Process. 10, 771 (2011). doi:10.1007/s11128-011-0296-0.

26

M. H. Goerz, E. J. Halperin, J. M. Aytac, C. P. Koch, and K. B. Whaley. Robustness of high-fidelity Rydberg gates with single-site addressability. Phys. Rev. A 90, 032329 (2014). doi:10.1103/PhysRevA.90.032329.

27

M. H. Goerz, D. M. Reich, and C. P. Koch. Optimal control theory for a unitary operation under dissipative evolution. New J. Phys. 16, 055012 (2014). doi:10.1088/1367-2630/16/5/055012.

28

P. Watts, J. Vala, M. M. Müller, T. Calarco, K. B. Whaley, D. M. Reich, M. H. Goerz, and C. P. Koch. Optimizing for an arbitrary perfect entangler: I. Functionals. Phys. Rev. A 91, 062306 (2015). doi:10.1103/PhysRevA.91.062306.

29

M. H. Goerz, G. Gualdi, D. M. Reich, C. P. Koch, F. Motzoi, K. B. Whaley, J. Vala, M. M. Müller, S. Montangero, and T. Calarco. Optimizing for an arbitrary perfect entangler. II. Application. Phys. Rev. A 91, 062307 (2015). doi:10.1103/PhysRevA.91.062307.

30

D. Basilewitsch, R. Schmidt, D. Sugny, S. Maniscalco, and C. P. Koch. Beating the limits with initial correlations. New J. Phys. 19, 113042 (2017). doi:10.1088/1367-2630/aa96f8.

31

J. Preskill. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018). doi:10.22331/q-2018-08-06-79.

32

M. H. Goerz, K. B. Whaley, and C. P. Koch. Hybrid optimization schemes for quantum control. EPJ Quantum Technol. 2, 21 (2015). doi:10.1140/epjqt/s40507-015-0034-0.

33

M. H. Goerz, F. Motzoi, K. B. Whaley, and C. P. Koch. Charting the circuit-QED design landscape using optimal control theory. npj Quantum Inf. 3, 37 (2017). doi:10.1038/s41534-017-0036-0.

34

J. Bezanson, A. Edelman, S. Karpinski, and V. Shah. Julia: a fresh approach to numerical computing. SIAM Rev. 59, 65 (2017). doi:10.1137/141000671.

35

J. Akeret, L. Gamper, A. Amara, and A. Refregier. HOPE: a Python just-in-time compiler for astrophysical computations. Astron. Comput. 10, 1 (2015). doi:10.1016/j.ascom.2014.12.001.

36

H. Eichhorn, J. L. Cano, F. McLean, and R. Anderl. A comparative study of programming languages for next-generation astrodynamics systems. CEAS Space J. 10, 115 (2018). doi:10.1007/s12567-017-0170-8.

37

D. J. Tannor and S. A. Rice. Control of selectivity of chemical reaction via control of wave packet evolution. J. Chem. Phys. 83, 5013 (1985). doi:10.1063/1.449767.

38

R. Bellman. Dynamic Programming. Princeton University Press, Princeton, NJ (1957).

39

L. S. Pontryagin, V. G. Boltyanskii, G. R. V., and E. F. Mishchenko. The Mathematical Theory of Optimal Processes. Interscience, New York, NY (1962).

40

V. F. Krotov and I. N. Fel'dman. An iterative method for solving optimal-control problems. Engrg. Cybernetics 21, 123 (1983). doi:.

41

V. F. Krotov. A technique of global bounds in optimal control theory. Control and Cybernetics 17, 115 (1988). doi:.

42

V. Krotov. Global Methods in Optimal Control Theory. CRC Press (1995).

43

A.I. Konnov and V. F. Krotov. On global methods of successive improvement of controlled processes. Autom. Rem. Contr. 60, 1427 (1999).

44

J. Somlói, V. A. Kazakov, and D. J. Tannor. Controlled dissociation of I2 via optical transitions between the X and B electronic states. Chem. Phys. 172, 85 (1993). doi:10.1016/0301-0104(93)80108-L.

45

A. Bartana, R. Kosloff, and D. J. Tannor. Laser cooling of internal degrees of freedom. II. J. Chem. Phys. 106, 1435 (1997). doi:10.1063/1.473973.

46

S. E. Sklarz and D. J. Tannor. Loading a Bose-Einstein condensate onto an optical lattice: an application of optimal control theory to the nonlinear Schrödinger equation. Phys. Rev. A 66, 053619 (2002). doi:10.1103/PhysRevA.66.053619.

47

J. P. Palao and R. Kosloff. Optimal control theory for unitary transformations. Phys. Rev. A 68, 062308 (2003). doi:10.1103/PhysRevA.68.062308.

48

A. Kaiser and V. May. Optimal control theory for a target state distributed in time: optimizing the probe-pulse signal of a pump-probe-scheme. J. Chem. Phys. 121, 2528 (2004). doi:10.1063/1.1769370.

49

I. Serban, J. Werschnik, and E. K. U. Gross. Optimal control of time-dependent targets. Phys. Rev. A 71, 053810 (2005). doi:10.1103/PhysRevA.71.053810.

50

J. P. Palao, R. Kosloff, and C. P. Koch. Protecting coherence in optimal control theory: state-dependent constraint approach. Phys. Rev. A 77, 063412 (2008). doi:10.1103/PhysRevA.77.063412.

51

A. Bartana, R. Kosloff, and D. J. Tannor. Laser cooling of molecular internal degrees of freedom by a series of shaped pulses. J. Chem. Phys. 99, 196 (1993). doi:10.1063/1.465797.

52

Y. Ohtsuki, W. Zhu, and H. Rabitz. Monotonically convergent algorithm for quantum optimal control with dissipation. J. Chem. Phys. 110, 9825 (1999). doi:10.1063/1.478036.

53

M. H. Goerz and K. Jacobs. Efficient optimization of state preparation in quantum networks using quantum trajectories. Quantum Sci. Technol. 3, 045005 (2018). doi:10.1088/2058-9565/aace16.

54

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208 (2000). doi:10.1103/PhysRevLett.85.2208.

55

M. M. Müller, D. M. Reich, M. Murphy, H. Yuan, J. Vala, K. B. Whaley, T. Calarco, and C. P. Koch. Optimizing entangling quantum gates for physical systems. Phys. Rev. A 84, 042315 (2011). doi:10.1103/PhysRevA.84.042315.

56

P. Watts, M. O'Connor, and J. Vala. Metric structure of the space of two-qubit gates, perfect entanglers and quantum control. Entropy 15, 1963 (2013). doi:10.3390/e15061963.

57

M. Musz, M. Kuś, and K. Życzkowski. Unitary quantum gates, perfect entanglers, and unistochastic maps. Phys. Rev. A 87, 022111 (2013). doi:10.1103/PhysRevA.87.022111.

58

M. B. Plenio and P. L. Knight. The quantum-jump approach to dissipative dynamics in quantum optics. Rev. Mod. Phys. 70, 101 (1998). doi:10.1103/RevModPhys.70.101.

59

D. M. Reich, J. P. Palao, and C. P. Koch. Optimal control under spectral constraints: enforcing multi-photon absorption pathways. J. Mod. Opt. 61, 822 (2014). doi:10.1080/09500340.2013.844866.

60

M. M. Müller, D. M. Reich, M. Murphy, H. Yuan, J. Vala, K. B. Whaley, T. Calarco, and C. P. Koch. Optimizing entangling quantum gates for physical systems. Phys. Rev. A 84, 042315 (2011). doi:10.1103/PhysRevA.84.042315.

61

R. Kosloff, S.A. Rice, P. Gaspard, S. Tersigni, and D.J. Tannor. Wavepacket dancing: achieving chemical selectivity by shaping light pulses. Chem. Phys. 139, 201 (1989). doi:10.1016/0301-0104(89)90012-8.

62

S. Shi and H. Rabitz. Quantum mechanical optimal control of physical observables in microsystems. J. Chem. Phys. 92, 364 (1990). doi:10.1063/1.458438.

63

S. Shi and H. Rabitz. Optimal control of bond selectivity in unimolecular reactions. Comput. Phys. Commun. 63, 71 (1991). doi:10.1016/0010-4655(91)90239-H.

64

D. J. Tannor and Y. Jin. Design of femtosecond pulse sequences to control photochemical products. In Mode Selective Chemistry, pages 333–345. Springer (1991).

65

W. Zhu, J. Botina, and H. Rabitz. Rapidly convergent iteration methods for quantum optimal control of population. J. Chem. Phys. 108, 1953 (1998). doi:10.1063/1.475576.

66

Y. Maday and G. Turinici. New formulations of monotonically convergent quantum control algorithms. J. Chem. Phys. 118, 8191 (2003). doi:10.1063/1.1564043.

67

Y. Ohtsuki, G. Turinici, and H. Rabitz. Generalized monotonically convergent algorithms for solving quantum optimal control problems. J. Chem. Phys. 120, 5509 (2004). doi:10.1063/1.1650297.

68

J. Werschnik and E. K. U. Gross. Quantum optimal control theory. J. Phys. B 40, R175 (2007). doi:10.1088/0953-4075/40/18/r01.

69

B. Schmidt and C. Hartmann. WavePacket: a Matlab package for numerical quantum dynamics. II: open quantum systems, optimal control, and model reduction. Comput. Phys. Commun. 228, 229 (2018). doi:10.1016/j.cpc.2018.02.022.

70

S. G. Schirmer and P. de Fouquieres. Efficient algorithms for optimal control of quantum dynamics: the krotov method unencumbered. New J. Phys. 13, 073029 (2011). doi:10.1088/1367-2630/13/7/073029.

71

S. Machnes, U. Sander, S. J. Glaser, P. de Fouquières, A. Gruslys, S. Schirmer, and T. Schulte-Herbrüggen. Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework. Phys. Rev. A 84, 022305 (2011). doi:10.1103/PhysRevA.84.022305.

72

J. P. Palao and R. Kosloff. Quantum computing by an optimal control algorithm for unitary transformations. Phys. Rev. Lett. 89, 188301 (2002). doi:10.1103/PhysRevLett.89.188301.

73

M. Goerz. Optimizing Robust Quantum Gates in Open Quantum Systems. PhD thesis, Universität Kassel, (2015). URL: https://kobra.bibliothek.uni-kassel.de/handle/urn:nbn:de:hebis:34-2015052748381.

74

S. Schirmer. Implementation of quantum gates via optimal control. J. Mod. Opt. 56, 831 (2009). doi:10.1080/09500340802344933.

75

F. F. Floether, P. de Fouquières, and S. G. Schirmer. Robust quantum gates for open systems via optimal control: markovian versus non-markovian dynamics. New J. Phys. 14, 073023 (2012). doi:10.1088/1367-2630/14/7/073023.

76

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu. A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16, 1190 (1995). doi:10.1137/0916069.

77

C. Zhu, R. H. Byrd, P. Lu, and J. Nocedal. Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Softw. 23, 550 (1997). doi:10.1145/279232.279236.

78

P. de Fouquières, S.G. Schirmer, S.J. Glaser, and I. Kuprov. Second order gradient ascent pulse engineering. J. Magnet. Res. 212, 412 (2011). doi:10.1016/j.jmr.2011.07.023.

79

E. Jones, T. Oliphant, P. Peterson, and others. SciPy: open source scientific tools for Python. (2001–). URL: http://www.scipy.org/.

80

G. Jäger, D. M. Reich, M. H. Goerz, C. P. Koch, and U. Hohenester. Optimal quantum control of Bose-Einstein condensates in magnetic microtraps: comparison of GRAPE and Krotov optimization schemes. Phys. Rev. A 90, 033628 (2014). doi:10.1103/PhysRevA.90.033628.

81

J. L. Neves, B. Heitmann, N. Khaneja, and S. J. Glaser. Heteronuclear decoupling by optimal tracking. J. Magnet. Res. 201, 7 (2009). doi:10.1016/j.jmr.2009.07.024.

82

T. T. Nguyen and S. J. Glaser. An optimal control approach to design entire relaxation dispersion experiments. J. Magnet. Res. 282, 142 (2017). doi:10.1016/j.jmr.2017.07.010.

83

Q. Ansel, M. Tesch, S. J. Glaser, and D. Sugny. Optimizing fingerprinting experiments for parameter identification: application to spin systems. Phys. Rev. A 96, 053419 (2017). doi:10.1103/PhysRevA.96.053419.

84

P. E. Spindler, Y. Zhang, B. Endeward, N. Gershernzon, T. E. Skinner, S. J. Glaser, and T. F. Prisner. Shaped optimal control pulses for increased excitation bandwidth in epr. J. Magnet. Res. 218, 49 (2012). doi:10.1016/j.jmr.2012.02.013.

85

Z. Tošner, R. Sarkar, J. Becker-Baldus, C. Glaubitz, S. Wegner, F. Engelke, S. J. Glaser, and B. Reif. Overcoming volume selectivity of dipolar recoupling in biological solid-state NMR spectroscopy. Angew. Chem. Int. Ed. 57, 14514 (2018). doi:10.1002/anie.201805002.

86

N. Leung, M. Abdelhafez, J. Koch, and D. Schuster. Speedup for quantum optimal control from automatic differentiation based on graphics processing units. Phys. Rev. A 95, 042318 (2017). doi:10.1103/PhysRevA.95.042318.

87

M. Abdelhafez, D. I. Schuster, and J. Koch. Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation. Phys. Rev. A 99, 052327 (2019). doi:10.1103/PhysRevA.99.052327.

88

G. v. Winckel and A. Borzì. Computational techniques for a quantum control problem with H¹-cost. Inverse Problems 24, 034007 (2008). doi:10.1088/0266-5611/24/3/034007.

89

T. E. Skinner and N. I. Gershenzon. Optimal control design of pulse shapes as analytic functions. J. Magnet. Res. 204, 248 (2010). doi:10.1016/j.jmr.2010.03.002.

90

F. Motzoi, J. M. Gambetta, S. T. Merkel, and F. K. Wilhelm. Optimal control methods for rapidly time-varying hamiltonians. Phys. Rev. A 84, 022307 (2011). doi:10.1103/PhysRevA.84.022307.

91

D. Lucarelli. Quantum optimal control via gradient ascent in function space and the time-bandwidth quantum speed limit. Phys. Rev. A 97, 062346 (2018). doi:10.1103/physreva.97.062346.

92

J. J. W. H. Sørensen, M. O. Aranburu, T. Heinzel, and J. F. Sherson. Quantum optimal control in a chopped basis: applications in control of Bose-Einstein condensates. Phys. Rev. A 98, 022119 (2018). doi:10.1103/PhysRevA.98.022119.

93

J. J. Sørensen, J. H. M. Jensen, T. Heinzel, and J. F. Sherson. QEngine: a C++ library for quantum optimal control of ultracold atoms. Comput. Phys. Commun. 243, 135 (2019). doi:10.1016/j.cpc.2019.04.020.

94

S. Machnes, E. Assémat, D. Tannor, and F. K. Wilhelm. Tunable, flexible, and efficient optimization of control pulses for practical qubits. Phys. Rev. Lett. 120, 150401 (2018). doi:10.1103/PhysRevLett.120.150401.

95

N. Rach, M. M. Müller, T. Calarco, and S. Montangero. Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape. Phys. Rev. A 92, 062343 (2015). doi:10.1103/PhysRevA.92.062343.

96

R. E. Goetz, A. Karamatskou, R. Santra, and C. P. Koch. Quantum optimal control of photoelectron spectra and angular distributions. Phys. Rev. A 93, 013413 (2016). doi:10.1103/PhysRevA.93.013413.

97

K. P. Horn, F. Reiter, Y. Lin, D. Leibfried, and C. P. Koch. Quantum optimal control of the dissipative production of a maximally entangled state. New J. Phys. 20, 123010 (2018). doi:10.1088/1367-2630/aaf360.

98

P. Doria, T. Calarco, and S. Montangero. Optimal control technique for many-body quantum dynamics. Phys. Rev. Lett. 106, 190501 (2011). doi:10.1103/PhysRevLett.106.190501.

99

T. Caneva, T. Calarco, and S. Montangero. Chopped random-basis quantum optimization. Phys. Rev. A 84, 022326 (2011). doi:10.1103/PhysRevA.84.022326.

100

S. G. Johnson. The NLopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt.

101

J. Rapin and O. Teytaud. Nevergrad - A gradient-free optimization platform. https://GitHub.com/FacebookResearch/Nevergrad, (2018).

102

I.R. Petersen. Quantum control theory and applications: a survey. IET Control Theory & Applications 4, 2651 (2010). doi:10.1049/iet-cta.2009.0508.

103

M. H. Goerz, F. Motzoi, K. B. Whaley, and C. P. Koch. Charting the circuit QED design landscape using optimal control theory. npj Quantum Information 3, 37 (2017). doi:10.1038/s41534-017-0036-0.

104

T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, and G. E. Santoro. Optimal control at the quantum speed limit. Phys. Rev. Lett. 103, 240501 (2009). doi:10.1103/PhysRevLett.103.240501.

105

M. H. Goerz, T. Calarco, and C. P. Koch. The quantum speed limit of optimal controlled phasegates for trapped neutral atoms. J. Phys. B 44, 154011 (2011). doi:10.1088/0953-4075/44/15/154011.

106

J.R. Johansson, P.D. Nation, and F. Nori. QuTiP: an open-source Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 183, 1760 (2012). doi:10.1016/j.cpc.2012.02.021.

107

J.R. Johansson, P.D. Nation, and F. Nori. QuTiP 2: a Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 184, 1234 (2013). URL: http://qutip.org, doi:10.1016/j.cpc.2012.11.019.