Abstract
Quantum controls realize the unitary or nonunitary operations employed in quantum computers, quantum simulators, quantum communications, and other quantum information devices. They implement the desired quantum dynamics with the help of electric, magnetic, or electromagnetic control fields. Quantum optimal control (QOC) deals with designing an optimal control field modulation that most precisely implements a desired quantum operation with minimum energy consumption and maximum robustness against hardware imperfections as well as external noise. Over the last 2 decades, numerous QOC methods have been proposed. They include asymptotic methods, direct search, gradient methods, variational methods, machine learning methods, etc. In this review, we shall introduce the basic ideas of QOC, discuss practical challenges, and then take an overview of the diverse QOC methods.
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References
Peirce AP, Dahleh MA, Rabitz H (1988) Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys Rev A 37:4950. https://doi.org/10.1103/PhysRevA.37.4950
Kosloff R, Rice S, Gaspard P, Tersigni S, Tannor D (1989) Wavepacket dancing: achieving chemical selectivity by shaping light pulses. Chem Phys 139:201. https://doi.org/10.1016/0301-0104(89)90012-8
Zare RN (1998) Laser control of chemical reactions. Science 279:1875. https://doi.org/10.1126/science.279.5358.1875
Rabitz H, de Vivie-Riedle R, Motzkus M, Kompa K (2000) Whither the Future of Controlling Quantum Phenomena? Science 288:824. https://doi.org/10.1126/science.288.5467.824
Dowling JP, Milburn GJ (2003) Quantum technology: the second quantum revolution. Philos Trans R Soc Lond Ser A Math Phys Eng Sci 361:1655
Cavanagh J, Fairbrother WJ, Palmer III AG, Skelton NJ, Protein NMR spectroscopy: principles and practice. In: Protein NMR spectroscopy: principles and practice. Academic press
Dorai K, Mahesh T, Arvind Kumar A (2000) Quantum computation using NMR. Curr Sci 1447
Kopp RE (1962) Pontryagin maximum principle. In: Mathematics in Science and Engineering, Vol. 5, pp. 255–279. Elsevier
Pontryagin LS (1987) Mathematical theory of optimal processes. In: Mathematical theory of optimal processes. CRC press
Kirk DE (2004) Optimal control theory: an introduction. In: Optimal control theory: an introduction. Courier Corporation
Boscain U, Sigalotti M, Sugny D (2021) Introduction to the pontryagin maximum principle for quantum optimal control. PRX Quant 2:030203
Boscain U, Sigalotti M, Sugny D (2021) Introduction to the Pontryagin maximum principle for quantum optimal control. PRX Quant 2:030203. https://doi.org/10.1103/PRXQuantum.2.030203
Werschnik J, Gross E (2007) Quantum optimal control theory. J Phys B Atom Mol Opt Phys 40:R175
Cong S (2014) Control of quantum systems: theory and methods. In: Control of quantum systems: theory and methods. Wiley
Glaser SJ, Boscain U, Calarco T, Koch CP, Köckenberger W, Kosloff R, Kuprov I, Luy B, Schirmer S, Schulte-Herbrüggen T et al (2015) Training Schrödinger’s cat: quantum optimal control. Eur Phys J D 69:1
d’ Alessandro D (2021) Introduction to quantum control and dynamics. In: Introduction to quantum control and dynamics (Chapman and hall/CRC)
Schäfer F, Fukuhara T, Sugawa S, Takasu Y, Takahashi Y (2020) Tools for quantum simulation with ultracold atoms in optical lattices. Nat Rev Phys 2:411
Häffner H, Roos CF, Blatt R (2008) Quantum computing with trapped ions. Phys Rep 469:155
Veldhorst M, Yang C, Hwang J, Huang W, Dehollain J, Muhonen J, Simmons S, Laucht A, Hudson F, Itoh KM et al (2015) A two-qubit logic gate in silicon. Nature 526:410
Watson T, Philips S, Kawakami E, Ward D, Scarlino P, Veldhorst M, Savage D, Lagally M, Friesen M, Coppersmith S et al (2018) A programmable two-qubit quantum processor in silicon. Nature 555:633
Krantz P, Kjaergaard M, Yan F, Orlando TP, Gustavsson S, Oliver WD (2019) A quantum engineer’s guide to superconducting qubits. Appl Phys Rev 6:021318
Bucher DB, Aude Craik DP, Backlund MP, Turner MJ, Ben Dor O, Glenn DR, Walsworth RL (2019) Quantum diamond spectrometer for nanoscale NMR and ESR spectroscopy. Nat Protoc 14:2707
Fortunato EM, Pravia MA, Boulant N, Teklemariam G, Havel TF, Cory DG (2002) Design of strongly modulating pulses to implement precise effective Hamiltonians for quantum information processing. J Chem Phys 116:7599
Khaneja N, Reiss T, Kehlet C, Schulte-Herbrüggen T, Glaser SJ (2005) Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J Magn Reson 172:296
Levitt MH (2013) Spin dynamics: basics of nuclear magnetic resonance. In: Spin dynamics: basics of nuclear magnetic resonance. Wiley
Bayer M, Hawrylak P, Hinzer K, Fafard S, Korkusinski M, Wasilewski Z, Stern O, Forchel A (2001) Coupling and entangling of quantum states in quantum dot molecules. Science 291:451
Tiwari Y, Poonia VS (2021) Universal quantum gates based on quantum dots. arXiv preprint arXiv:2105.07021
Jelezko F, Gaebel T, Popa I, Domhan M, Gruber A, Wrachtrup J (2004) Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Phys Rev Lett 93:130501
Pfender M, Aslam N, Simon P, Antonov D, Thiering G, Burk S, Fávaro de Oliveira F, Denisenko A, Fedder H, Meijer J et al (2017) Protecting a diamond quantum memory by charge state control. Nano Lett 17:5931
Doherty MW, Manson NB, Delaney P, Jelezko F, Wrachtrup J, Hollenberg LC (2013) The nitrogen-vacancy colour centre in diamond. Phys Rep 528:1
Anwar M, Xiao L, Short A, Jones J, Blazina D, Duckett S, Carteret H (2005) Practical implementations of twirl operations. Phys Rev A 71:032327
Bhole G, Anjusha V, Mahesh T (2016) Steering quantum dynamics via bang-bang control: implementing optimal fixed-point quantum search algorithm. Phys Rev A 93:042339
Nielsen MA, Chuang I (2002) Quantum computation and quantum information, “Quantum computation and quantum information,”
Tannús A, Garwood M (1997) Adiabatic pulses, NMR in Biomedicine: an international journal devoted to the development and application of magnetic resonance. In Vivo 10:423
Manu V, Kumar A (2012) Singlet-state creation and universal quantum computation in NMR using a genetic algorithm. Phys Rev A 86:022324
Khurana D, Mahesh T (2017) Bang-bang optimal control of large spin systems: enhancement of 13C–13C singlet-order at natural abundance. J Magn Reson 284:8
Cory DG, Fahmy AF, Havel TF (1997) Ensemble quantum computing by NMR spectroscopy. Proc Natl Acad Sci 94:1634
Suter D, Mahesh T (2008) Spins as qubits: quantum information processing by nuclear magnetic resonance. J Chem Phys 128:052206
Wu R-B, Rabitz H (2012) Control landscapes for open system quantum operations. J Phys A Math Theor 45:485303
Pravia MA, Boulant N, Emerson J, Farid A, Fortunato EM, Havel TF, Martinez R, Cory DG (2003) Robust control of quantum information. J Chem Phys 119:9993
Fletcher R (1983) Penalty functions. Math Program State Art 87
Lucarelli D (2018) Quantum optimal control via gradient ascent in function space and the time-bandwidth quantum speed limit. Phys Rev A 97:062346
Feng G, Cho FH, Katiyar H, Li J, Lu D, Baugh J, Laflamme R (2018) Gradient-based closed-loop quantum optimal control in a solid-state two-qubit system. Phys Rev A 98:052341
Boulant N, Edmonds K, Yang J, Pravia M, Cory D (2003) Experimental demonstration of an entanglement swapping operation and improved control in NMR quantum-information processing. Phys Rev A 68:032305
Möttönen M, de Sousa R, Zhang J, Whaley KB (2006) High-fidelity one-qubit operations under random telegraph noise. Phys Rev A 73:022332
Zhang Y, Lapert M, Sugny D, Braun M, Glaser S (2011) Time-optimal control of spin 1/2 particles in the presence of radiation damping and relaxation. J Chem Phys 134:054103
Tibbetts KWM, Brif C, Grace MD, Donovan A, Hocker DL, Ho T-S, Wu R-B, Rabitz H (2012) Exploring the tradeoff between fidelity and time optimal control of quantum unitary transformations. Phys Rev A 86:062309
Xu X, Wang Z, Duan C, Huang P, Wang P, Wang Y, Xu N, Kong X, Shi F, Rong X et al (2012) Coherence-protected quantum gate by continuous dynamical decoupling in diamond. Phys Rev Lett 109:070502
Zhang J, Souza AM, Brandao FD, Suter D (2014) Protected quantum computing: interleaving gate operations with dynamical decoupling sequences. Phys Rev Lett 112:050502
Viola L, Knill E, Lloyd S (1999) Dynamical decoupling of open quantum systems. Phys Rev Lett 82:2417. https://doi.org/10.1103/PhysRevLett.82.2417
Ram MH, Krithika V, Batra P, Mahesh T (2022) Robust quantum control using hybrid pulse engineering. Phys Rev A 105:042437
Lidar DA, Chuang IL, Whaley KB (1998) Decoherence-free subspaces for quantum computation. Phys Rev Lett 81:2594. https://doi.org/10.1103/PhysRevLett.81.2594
Koch CP (2016) Controlling open quantum systems: tools, achievements, and limitations. J Phys Conden Matter 28:213001
Mahesh T, Suter D (2006) Quantum-information processing using strongly dipolar coupled nuclear spins. Phys Rev A 74:062312
Bhole G, Mahesh T (2017) Rapid exponentiation using discrete operators: applications in optimizing quantum controls and simulating quantum dynamics. arXiv preprint arXiv:1707.02162
Bhole G, Jones JA (2018) Practical pulse engineering: gradient ascent without matrix exponentiation. Front Phys 13:1
Garwood M, DelaBarre L (2001) The return of the frequency sweep: designing adiabatic pulses for contemporary NMR. J Magn Reson 153:155
Messiah A (2014) Quantum mechanics. In: Quantum mechanics. Courier Corporation
Albash T, Lidar DA (2018) Adiabatic quantum computation. Rev Mod Phys 90:015002
Berry M (1988) The geometric phase. Sci Am 259:46
Anandan J (1992) The geometric phase. Nature 360:307
Jones JA, Vedral V, Ekert A, Castagnoli G (2000) Geometric quantum computation using nuclear magnetic resonance. Nature 403:869
Pancharatnam S (1956) Generalized theory of interference and its applications. In: Proceedings of the Indian Academy of Sciences-Section A, Vol. 44 (Springer), pp. 398–417
Berry MV (1987) The adiabatic phase and Pancharatnam’s phase for polarized light. J Mod Opt 34:1401
Suter D, Chingas GC, Harris RA, Pines A (1987) Berry’s phase in magnetic resonance. Mol Phys 61:1327
Ekert A, Ericsson M, Hayden P, Inamori H, Jones JA, Oi DK, Vedral V (2000) Geometric quantum computation. J Mod Opt 47:2501
Zanardi P, Rasetti M (1999) Holonomic quantum computation. Phys Lett A 264:94
Leibfried D, DeMarco B, Meyer V, Lucas D, Barrett M, Britton J, Itano WM, Jelenković B, Langer C, Rosenband T et al (2003) Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422:412
Filipp S, Klepp J, Hasegawa Y, Plonka-Spehr C, Schmidt U, Geltenbort P, Rauch H (2009) Experimental demonstration of the stability of Berry’s phase for a spin-\(1/2\) particle. Phys Rev Lett 102:030404. https://doi.org/10.1103/PhysRevLett.102.030404
Berger S, Pechal M, Abdumalikov AA, Eichler C, Steffen L, Fedorov A, Wallraff A, Filipp S (2013) Exploring the effect of noise on the Berry phase. Phys Rev A 87:060303. https://doi.org/10.1103/PhysRevA.87.060303
Nagata K, Kuramitani K, Sekiguchi Y, Kosaka H (2018) Universal holonomic quantum gates over geometric spin qubits with polarised microwaves. Nat Commun 9:1
Wikipedia Contributors (2021) Control-Lyapunov function — Wikipedia, The Free Encyclopedia”, “Control-lyapunov function — Wikipedia, the free encyclopedia.” [Online; accessed 15-March-2022] . https://en.wikipedia.org/w/index.php?title=Control-Lyapunov_function &oldid=1033346201
Isidori A (1995) Local decompositions of control systems. In: Nonlinear control systems (Springer), pp. 1–76
Grivopoulos S, Bamieh B, Lyapunov-based control of quantum systems. In: 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475), Vol. 1 (IEEE, 2003) pp. 434–438
Hou S-C, Khan M, Yi X, Dong D, Petersen IR (2012) Optimal Lyapunov-based quantum control for quantum systems. Phys Revi A 86:022321
Wang L, Hou S, Yi X, Dong D, Petersen IR (2014) Optimal Lyapunov quantum control of two-level systems: convergence and extended techniques. Phys Lett A 378:1074
Ghaeminezhad N, Cong S (2018) Preparation of Hadamard gate for open quantum systems by the Lyapunov control method. IEEE/CAA J Automat Sinica 5:733
Wang Y, Kang Y-H, Hu C-S, Huang B-H, Song J, Xia Y (2022) Quantum control with Lyapunov function and bang-bang solution in the optomechanics system. Front Phys 17:1
Purkayastha A (2022) The Lyapunov equation in open quantum systems and non-Hermitian physics. arXiv preprint arXiv:2201.00677
Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308
Weinstein YS, Havel TF, Emerson J, Boulant N, Saraceno M, Lloyd S, Cory DG (2004) Quantum process tomography of the quantum Fourier transform. J chem Phys 121:6117
Baugh J, Moussa O, Ryan CA, Laflamme R, Ramanathan C, Havel TF, Cory DG (2006) Solid-state NMR three-qubit homonuclear system for quantum-information processing: control and characterization. Phys Rev A 73:022305
Negrevergne C, Mahesh T, Ryan C, Ditty M, Cyr-Racine F, Power W, Boulant N, Havel T, Cory D, Laflamme R (2006) Benchmarking quantum control methods on a 12-qubit system. Phys Rev Lett 96:170501
Černỳ V (1985) Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41
Zhou X, Li S, Feng Y (2020) Quantum circuit transformation based on simulated annealing and heuristic search. IEEE Trans Comput Aided Design Integr Circ Syst 39:4683
Situ H, He Z (2022) Using simulated annealing to learn the SDC quantum protocol. Eur Phys J Plus 137:1
Lloyd S, Montangero S (2014) Information theoretical analysis of quantum optimal control. Phys Rev Lett 113:010502
Doria P, Calarco T, Montangero S (2011) Optimal control technique for many-body quantum dynamics. Phys Rev Lett 106:190501. https://doi.org/10.1103/PhysRevLett.106.190501
Caneva T, Calarco T, Montangero S (2011) Chopped random-basis quantum optimization. Phys Rev A 84:022326. https://doi.org/10.1103/PhysRevA.84.022326
Müller MM, Said RS, Jelezko F, Calarco T, Montangero S (2021) One decade of quantum optimal control in the chopped random basis. arXiv preprint arXiv:2104.07687
Riaz B, Shuang C, Qamar S (2019) Optimal control methods for quantum gate preparation: a comparative study. Quant Inform Process 18:1
Sørensen JJWH, Aranburu MO, Heinzel T, Sherson JF (2018) Quantum optimal control in a chopped basis: applications in control of Bose–Einstein condensates. Phys Rev A 98:022119. https://doi.org/10.1103/PhysRevA.98.022119
Wu S-H, Amezcua M, Wang H (2019) Adiabatic population transfer of dressed spin states with quantum optimal control. Phys Rev A 99:063812. https://doi.org/10.1103/PhysRevA.99.063812
Sørdal VB, Bergli J (2019) Deep reinforcement learning for quantum Szilard engine optimization. Phys Rev A 100:042314. https://doi.org/10.1103/PhysRevA.100.042314
Khurana D, Mahesh T (2017) Bang-bang optimal control of large spin systems: enhancement of 13C–13C singlet-order at natural abundance. J Magn Reson 284:8. https://doi.org/10.1016/j.jmr.2017.09.006
Zahedinejad E, Schirmer S, Sanders BC (2014) Evolutionary algorithms for hard quantum control. Phys Rev A 90:032310. https://doi.org/10.1103/PhysRevA.90.032310
Ma H, Chen C, Dong D (2015) Differential evolution with equally-mixed strategies for robust control of open quantum systems. In: 2015 IEEE international conference on systems, man, and cybernetics (IEEE) pp. 2055–2060
Rowland B, Jones JA (2012) Implementing quantum logic gates with gradient ascent pulse engineering: principles and practicalities. Philos Trans R Soc A Math Phys Eng Sci 370:4636
Batra P, Krithika V, Mahesh T (2020) Push–pull optimization of quantum controls. Phys Rev Res 2:013314
Boutin S, Andersen CK, Venkatraman J, Ferris AJ, Blais A (2017) Resonator reset in circuit QED by optimal control for large open quantum systems. Phys Rev A 96:042315
Egger DJ, Wilhelm FK (2014) Optimal control of a quantum measurement. Phys Rev A 90:052331. https://doi.org/10.1103/PhysRevA.90.052331
De Fouquieres P, Schirmer S, Glaser S, Kuprov I (2011) Second order gradient ascent pulse engineering. J Magn Reson 212:412
Machnes S, Assémat E, Tannor D, Wilhelm FK (2018) Tunable, flexible, and efficient optimization of control pulses for practical qubits. Phys Rev Lett 120:150401. https://doi.org/10.1103/PhysRevLett.120.150401
Kirchhoff S, Keßler T, Liebermann PJ, Assémat E, Machnes S, Motzoi F, Wilhelm FK (2018) Optimized cross-resonance gate for coupled transmon systems. Phys Rev A 97:042348
Krotov V (1995) Global methods in optimal control theory. Global methods in optimal control theory, Vol. 195. CRC Press
Maximov II, Tošner Z, Nielsen NC (2008) Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms. J Chem Phys 128:184505. https://doi.org/10.1063/1.2903458
Reich DM, Ndong M, Koch CP (2012) Monotonically convergent optimization in quantum control using Krotov’s method. J Chem Phys 136:104103. https://doi.org/10.1063/1.3691827
Vinding MS, Maximov II, Tošner Z, Nielsen NC (2012) Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods. J Chem Phys 137:054203
Hwang B, Goan H-S (2012) Optimal control for non-Markovian open quantum systems. Phys Rev A 85:032321. https://doi.org/10.1103/PhysRevA.85.032321
Jäger G, Reich DM, Goerz MH, Koch CP, Hohenester U (2014) Optimal quantum control of Bose–Einstein condensates in magnetic microtraps: comparison of gradient-ascent-pulse-engineering and Krotov optimization schemes. Phys Rev A 90:033628. https://doi.org/10.1103/PhysRevA.90.033628
Sutton RS, Barto AG (2018) Reinforcement learning: an introduction. Reinforcement learning. MIT press, Cambridge
Bukov M, Day AGR, Sels D, Weinberg P, Polkovnikov A, Mehta P (2018) Reinforcement learning in different phases of quantum control. Phys Rev X 8:031086. https://doi.org/10.1103/PhysRevX.8.031086
An Z, Zhou DL (2019) Deep reinforcement learning for quantum gate control. EPL (Europhys Lett) 126:60002. https://doi.org/10.1209/0295-5075/126/60002
Zhang X-M, Wei Z, Asad R, Yang X-C, Wang X (2019) When does reinforcement learning stand out in quantum control? A comparative study on state preparation. NPJ Quant Inform 5:1
Baum Y, Amico M, Howell S, Hush M, Liuzzi M, Mundada P, Merkh T, Carvalho AR, Biercuk MJ (2021) Experimental deep reinforcement learning for error-robust gate-set design on a superconducting quantum computer. PRX Quant 2:040324
Niu MY, Boixo S, Smelyanskiy VN, Neven H (2019) Universal quantum control through deep reinforcement learning. NPJ Quant Inform 5:1
An Z, Song H-J, He Q-K, Zhou DL (2021) Quantum optimal control of multilevel dissipative quantum systems with reinforcement learning. Phys Rev A 103:012404. https://doi.org/10.1103/PhysRevA.103.012404
Wu R-B, Ding H, Dong D, Wang X (2019) Learning robust and high-precision quantum controls. Phys Rev A 99:042327. https://doi.org/10.1103/PhysRevA.99.042327
Zeng Y, Shen J, Hou S, Gebremariam T, Li C (2020) Quantum control based on machine learning in an open quantum system. Phys Lett A 384:126886. https://doi.org/10.1016/j.physleta.2020.126886
Huang T, Ban Y, Sherman EY, Chen X (2022) Machine-learning-assisted quantum control in a random environment. Phys Rev Appl 17:024040. https://doi.org/10.1103/PhysRevApplied.17.024040
Schäfer F, Kloc M, Bruder C, Lörch N (2020) A differentiable programming method for quantum control. Mach Learn Sci Technol 1:035009. https://doi.org/10.1088/2632-2153/ab9802
Khait I, Carrasquilla J, Segal D (2021) Optimal control of quantum thermal machines using machine learning. arXiv preprint arXiv:2108.12441
Coopmans L, Kiely A, De Chiara G, Campbell S (2022) Optimal control in disordered quantum systems. arXiv preprint arXiv:2201.02029
Machnes S, Sander U, Glaser SJ, de Fouquieres P, Gruslys A, Schirmer S, Schulte-Herbrüggen T (2011) Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework. Phys Rev A 84:022305
Batra P, Ram MH, Mahesh T (2022) Recommender system expedited quantum control optimization. arXiv preprint arXiv:2201.12550
Eitan R, Mundt M, Tannor DJ (2011) Optimal control with accelerated convergence: combining the Krotov and quasi-Newton methods. Phys. Rev. A 83:053426
Sørensen J, Aranburu M, Heinzel T, Sherson J (2018) Quantum optimal control in a chopped basis: applications in control of Bose–Einstein condensates. Phys Rev A 98:022119
Lu D, Li K, Li J, Katiyar H, Park AJ, Feng G, Xin T, Li H, Long G, Brodutch A et al (2017) Enhancing quantum control by bootstrapping a quantum processor of 12 qubits. NPJ Quant Inform 3:1
Policharla G-V, Vinjanampathy S (2021) Algorithmic primitives for quantum-assisted quantum control. Phys Rev Lett 127:220504. https://doi.org/10.1103/PhysRevLett.127.220504
Tošner Z, Vosegaard T, Kehlet C, Khaneja N, Glaser SJ, Nielsen NC (2009) Optimal control in NMR spectroscopy: numerical implementation in SIMPSON. J Magn Reson 197:120
Machnes S, Sander U, Glaser SJ, de Fouquières P, Gruslys A, Schirmer S, Schulte-Herbrüggen T (2011) Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework. Phys Rev A 84:022305. https://doi.org/10.1103/PhysRevA.84.022305
Johansson JR, Nation PD, Nori F (2012) QuTiP: an open-source python framework for the dynamics of open quantum systems. Comput Phys Commun 183:1760
Johansson J, Nation P, Nori F (2013) QuTiP 2: a python framework for the dynamics of open quantum systems. Comput Phys Commun 184:1234. https://doi.org/10.1016/j.cpc.2012.11.019
Goerz MH, Basilewitsch D, Gago-Encinas F, Krauss MG, Horn KP, Reich DM, Koch CP (2019) Krotov: A Python implementation of Krotov’s method for quantum optimal control. Sci Post Phys 7: 80. https://doi.org/10.21468/SciPostPhys.7.6.080
Teske JD, Cerfontaine P, Bluhm H (2022) qopt: an experiment-oriented software package for qubit simulation and quantum optimal control. Phys Rev Appl 17:034036. https://doi.org/10.1103/PhysRevApplied.17.034036
Sørensen J, Jensen J, Heinzel T, Sherson J (2019) QEngine: A C++ library for quantum optimal control of ultracold atoms. Comput Phys Commun 243:135. https://doi.org/10.1016/j.cpc.2019.04.020
Acknowledgements
This review is dedicated to the 80th birthday of Prof. Anil Kumar, IISc, Bangalore, who is noted for his pioneering contributions to NMR spectroscopy as well as NMR quantum computation. PB acknowledges support from the Prime Ministers Research Fellowship (PMRF) of the Government of India. TSM acknowledges funding from DST/ICPS/QuST/2019/Q67.
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The funding has been received from DST INDIA with Grant no. DST/ICPS/QuST/2019/Q67.
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Mahesh, T.S., Batra, P. & Ram, M.H. Quantum Optimal Control: Practical Aspects and Diverse Methods. J Indian Inst Sci 103, 591–607 (2023). https://doi.org/10.1007/s41745-022-00311-2
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DOI: https://doi.org/10.1007/s41745-022-00311-2