Model predictive control for robust quantum state preparation

Andy J. Goldschmidt1, Jonathan L. DuBois2, Steven L. Brunton3, and J. Nathan Kutz4

1Department of Physics, University of Washington, Seattle, WA 98195
2Lawrence Livermore National Laboratory, Livermore, CA 94550
3Department of Mechanical Engineering, University of Washington, Seattle, WA 98195
4Department of Applied Mathematics, University of Washington, Seattle, WA 98195

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces $\textit{model predictive control}$ (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

Model predictive control (MPC) is a popular approach for control design in many areas of engineering. This is due to its capability to include constraints, and its robustness against noise and coherent modelling errors. In this work, we adapt classic model predictive control for the design of quantum control sequences to address the problem of planning over mischaracterized models of quantum devices. The MPC perspective is to solve the quantum control problem as if it is an $\textit{online}$ optimization, where the control sequence is optimized sequentially over a receding horizon. We demonstrate the practical benefits of this MPC perspective by studying three representative examples in quantum control engineering.

► BibTeX data

► References

[1] Mohamed Abdelhafez, David I Schuster, and Jens Koch. Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation. Physical Review A, 99 (5): 052327, 2019. https:/​/​doi.org/​10.1103/​PhysRevA.99.052327.
https:/​/​doi.org/​10.1103/​PhysRevA.99.052327

[2] Ian Abraham, Gerardo de la Torre, and Todd Murphey. Model-based control using Koopman operators. In Robotics: Science and Systems XIII. Robotics: Science and Systems Foundation, jul 2017. https:/​/​doi.org/​10.15607/​rss.2017.xiii.052.
https:/​/​doi.org/​10.15607/​rss.2017.xiii.052

[3] Claudio Altafini and Francesco Ticozzi. Modeling and control of quantum systems: An introduction. IEEE Transactions on Automatic Control, 57 (8): 1898–1917, 2012. https:/​/​doi.org/​10.1109/​TAC.2012.2195830.
https:/​/​doi.org/​10.1109/​TAC.2012.2195830

[4] Brian DO Anderson and John B Moore. Optimal control: Linear quadratic methods. Courier Corporation, 2007.

[5] Harrison Ball, Michael Biercuk, Andre Carvalho, Jiayin Chen, Michael Robert Hush, Leonardo A De Castro, Li Li, Per J Liebermann, Harry Slatyer, Claire Edmunds, et al. Software tools for quantum control: Improving quantum computer performance through noise and error suppression. Quantum Science and Technology, 2021. https:/​/​doi.org/​10.1088/​2058-9565/​abdca6.
https:/​/​doi.org/​10.1088/​2058-9565/​abdca6

[6] Yuval Baum, Mirko Amico, Sean Howell, Michael Hush, Maggie Liuzzi, Pranav Mundada, Thomas Merkh, Andre R.R. Carvalho, and Michael J. Biercuk. Experimental deep reinforcement learning for error-robust gate-set design on a superconducting quantum computer. PRX Quantum, 2 (4), nov 2021. https:/​/​doi.org/​10.1103/​prxquantum.2.040324.
https:/​/​doi.org/​10.1103/​prxquantum.2.040324

[7] Thomas Baumeister, Steven L Brunton, and J Nathan Kutz. Deep learning and model predictive control for self-tuning mode-locked lasers. JOSA B, 35 (3): 617–626, 2018. https:/​/​doi.org/​10.1364/​JOSAB.35.000617.
https:/​/​doi.org/​10.1364/​JOSAB.35.000617

[8] Katharina Bieker, Sebastian Peitz, Steven L Brunton, J Nathan Kutz, and Michael Dellnitz. Deep model predictive flow control with limited sensor data and online learning. Theoretical and Computational Fluid Dynamics, pages 1–15, 2020. https:/​/​doi.org/​10.1007/​s00162-020-00520-4.
https:/​/​doi.org/​10.1007/​s00162-020-00520-4

[9] Stephen Boyd, Stephen P Boyd, and Lieven Vandenberghe. Convex optimization. Cambridge University Press, 2004. https:/​/​doi.org/​10.1017/​CBO9780511804441.
https:/​/​doi.org/​10.1017/​CBO9780511804441

[10] Daniel Bruder, Xun Fu, and Ram Vasudevan. Advantages of bilinear Koopman realizations for the modeling and control of systems with unknown dynamics. IEEE Robotics and Automation Letters, 6 (3): 4369–4376, 2021. https:/​/​doi.org/​10.1109/​LRA.2021.3068117.
https:/​/​doi.org/​10.1109/​LRA.2021.3068117

[11] Steven L Brunton, Marko Budišić, Eurika Kaiser, and J Nathan Kutz. Modern Koopman theory for dynamical systems. arXiv preprint arXiv:2102.12086, 2021.
arXiv:2102.12086

[12] Tayfun Çimen. State-dependent Riccati equation (SDRE) control: A survey. IFAC Proceedings Volumes, 41 (2): 3761–3775, 2008. https:/​/​doi.org/​10.3182/​20080706-5-KR-1001.00635.
https:/​/​doi.org/​10.3182/​20080706-5-KR-1001.00635

[13] Domenico d'Alessandro. Introduction to quantum control and dynamics. Chapman and Hall/​CRC, 2021.

[14] Steven Diamond and Stephen Boyd. CVXPY: A Python-embedded modeling language for convex optimization. Journal of Machine Learning Research, 17 (1): 2909–2913, Jan 2016. ISSN 1532-4435.

[15] Daniel J Egger and Frank K Wilhelm. Adaptive hybrid optimal quantum control for imprecisely characterized systems. Physical Review Letters, 112 (24): 240503, 2014. https:/​/​doi.org/​10.1103/​PhysRevLett.112.240503.
https:/​/​doi.org/​10.1103/​PhysRevLett.112.240503

[16] Jens Eisert, Dominik Hangleiter, Nathan Walk, Ingo Roth, Damian Markham, Rhea Parekh, Ulysse Chabaud, and Elham Kashefi. Quantum certification and benchmarking. Nature Reviews Physics, 2 (7): 382–390, 2020. https:/​/​doi.org/​10.1038/​s42254-020-0186-4.
https:/​/​doi.org/​10.1038/​s42254-020-0186-4

[17] Utku Eren, Anna Prach, Başaran Bahadır Koçer, Saša V Raković, Erdal Kayacan, and Behçet Açıkmeşe. Model predictive control in aerospace systems: Current state and opportunities. Journal of Guidance, Control, and Dynamics, 40 (7): 1541–1566, 2017. https:/​/​doi.org/​10.2514/​1.G002507.
https:/​/​doi.org/​10.2514/​1.G002507

[18] Paolo Falcone, Francesco Borrelli, Jahan Asgari, Hongtei Eric Tseng, and Davor Hrovat. Predictive active steering control for autonomous vehicle systems. IEEE Transactions on control systems technology, 15 (3): 566–580, 2007. https:/​/​doi.org/​10.1109/​TCST.2007.894653.
https:/​/​doi.org/​10.1109/​TCST.2007.894653

[19] David D Fan, Ali-akbar Agha-mohammadi, and Evangelos A Theodorou. Deep learning tubes for tube MPC. In Robotics: Science and Systems XVI (2020), 2020. https:/​/​doi.org/​10.15607/​RSS.2020.XVI.087.
https:/​/​doi.org/​10.15607/​RSS.2020.XVI.087

[20] Carl Folkestad and Joel W Burdick. Koopman NMPC: Koopman-based learning and nonlinear model predictive control of control-affine systems. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 7350–7356. IEEE, 2021. https:/​/​doi.org/​10.1109/​ICRA48506.2021.9562002.
https:/​/​doi.org/​10.1109/​ICRA48506.2021.9562002

[21] Dimitris Giannakis, Amelia Henriksen, Joel A Tropp, and Rachel Ward. Learning to forecast dynamical systems from streaming data. arXiv preprint arXiv:2109.09703, 2021.
arXiv:2109.09703

[22] Steffen J Glaser, Ugo Boscain, Tommaso Calarco, Christiane P Koch, Walter Köckenberger, Ronnie Kosloff, Ilya Kuprov, Burkhard Luy, Sophie Schirmer, Thomas Schulte-Herbrüggen, et al. Training Schrödinger’s cat: Quantum optimal control. The European Physical Journal D, 69 (12): 1–24, 2015. https:/​/​doi.org/​10.1140/​epjd/​e2015-60464-1.
https:/​/​doi.org/​10.1140/​epjd/​e2015-60464-1

[23] Michael Goerz, Daniel Basilewitsch, Fernando Gago-Encinas, Matthias G Krauss, Karl P Horn, Daniel M Reich, and Christiane Koch. Krotov: A Python implementation of krotov's method for quantum optimal control. SciPost Physics, 7 (6): 080, 2019. https:/​/​doi.org/​10.21468/​SciPostPhys.7.6.080.
https:/​/​doi.org/​10.21468/​SciPostPhys.7.6.080

[24] Michael H Goerz, Daniel M Reich, and Christiane P Koch. Optimal control theory for a unitary operation under dissipative evolution. New Journal of Physics, 16 (5): 055012, 2014. https:/​/​doi.org/​10.1088/​1367-2630/​16/​5/​055012.
https:/​/​doi.org/​10.1088/​1367-2630/​16/​5/​055012

[25] Andy Goldschmidt, Eurika Kaiser, Jonathan L Dubois, Steven L Brunton, and J Nathan Kutz. Bilinear dynamic mode decomposition for quantum control. New Journal of Physics, 23 (3): 033035, 2021. https:/​/​doi.org/​10.1088/​1367-2630/​abe972.
https:/​/​doi.org/​10.1088/​1367-2630/​abe972

[26] Daniel Görges. Relations between model predictive control and reinforcement learning. IFAC-PapersOnLine, 50 (1): 4920–4928, 2017. https:/​/​doi.org/​10.1016/​j.ifacol.2017.08.747.
https:/​/​doi.org/​10.1016/​j.ifacol.2017.08.747

[27] Sébastien Gros, Mario Zanon, Rien Quirynen, Alberto Bemporad, and Moritz Diehl. From linear to nonlinear MPC: Bridging the gap via the real-time iteration. International Journal of Control, 93 (1): 62–80, 2020. https:/​/​doi.org/​10.1080/​00207179.2016.1222553.
https:/​/​doi.org/​10.1080/​00207179.2016.1222553

[28] Stefanie Günther, N. Anders Petersson, and Jonathan L. DuBois. Quandary: An open-source C++ package for high-performance optimal control of open quantum systems. In 2021 IEEE/​ACM Second International Workshop on Quantum Computing Software (QCS), pages 88–98, 2021. https:/​/​doi.org/​10.1109/​QCS54837.2021.00014.
https:/​/​doi.org/​10.1109/​QCS54837.2021.00014

[29] IN Hincks, CE Granade, Troy W Borneman, and David G Cory. Controlling quantum devices with nonlinear hardware. Physical Review Applied, 4 (2): 024012, 2015. https:/​/​doi.org/​10.1103/​PhysRevApplied.4.024012.
https:/​/​doi.org/​10.1103/​PhysRevApplied.4.024012

[30] Roger A. Horn and Charles R. Johnson. Topics in Matrix Analysis. Cambridge University Press, 1991. https:/​/​doi.org/​10.1017/​CBO9780511840371.
https:/​/​doi.org/​10.1017/​CBO9780511840371

[31] Brian E Jackson, Tarun Punnoose, Daniel Neamati, Kevin Tracy, Rianna Jitosho, and Zachary Manchester. ALTRO-C: A fast solver for conic model-predictive control. In International Conference on Robotics and Automation (ICRA), Xi’an, China, page 8, 2021. https:/​/​doi.org/​10.1109/​ICRA48506.2021.9561438.
https:/​/​doi.org/​10.1109/​ICRA48506.2021.9561438

[32] J Robert Johansson, Paul D Nation, and Franco Nori. QuTiP: An open-source Python framework for the dynamics of open quantum systems. Computer Physics Communications, 183 (8): 1760–1772, 2012. https:/​/​doi.org/​10.1016/​j.cpc.2012.02.021.
https:/​/​doi.org/​10.1016/​j.cpc.2012.02.021

[33] J.R. Johansson, P.D. Nation, and Franco Nori. QuTiP 2: A Python framework for the dynamics of open quantum systems. Computer Physics Communications, 184 (4): 1234–1240, apr 2013. https:/​/​doi.org/​10.1016/​j.cpc.2012.11.019.
https:/​/​doi.org/​10.1016/​j.cpc.2012.11.019

[34] Eurika Kaiser, J Nathan Kutz, and Steven L Brunton. Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proceedings of the Royal Society of London A, 474 (2219), 2018. https:/​/​doi.org/​10.1098/​rspa.2018.0335.
https:/​/​doi.org/​10.1098/​rspa.2018.0335

[35] Julian Kelly, Rami Barends, Brooks Campbell, Yu Chen, Zijun Chen, Ben Chiaro, Andrew Dunsworth, Austin G Fowler, I-C Hoi, Evan Jeffrey, et al. Optimal quantum control using randomized benchmarking. Physical Review Letters, 112 (24): 240504, 2014. https:/​/​doi.org/​10.1103/​PhysRevLett.112.240504.
https:/​/​doi.org/​10.1103/​PhysRevLett.112.240504

[36] Navin Khaneja, Timo Reiss, Cindie Kehlet, Thomas Schulte-Herbrüggen, and Steffen J Glaser. Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms. Journal of Magnetic Resonance, 172 (2): 296–305, 2005. https:/​/​doi.org/​10.1016/​j.jmr.2004.11.004.
https:/​/​doi.org/​10.1016/​j.jmr.2004.11.004

[37] Martin Kliesch and Ingo Roth. Theory of quantum system certification. PRX Quantum, 2 (1): 010201, 2021. https:/​/​doi.org/​10.1103/​PRXQuantum.2.010201.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.010201

[38] B. O. Koopman. Hamiltonian systems and transformation in Hilbert space. Proceedings of the National Academy of Sciences, 17 (5): 315–318, may 1931. https:/​/​doi.org/​10.1073/​pnas.17.5.315.
https:/​/​doi.org/​10.1073/​pnas.17.5.315

[39] B. O. Koopman and J. v. Neumann. Dynamical systems of continuous spectra. Proceedings of the National Academy of Sciences, 18 (3): 255–263, mar 1932. https:/​/​doi.org/​10.1073/​pnas.18.3.255.
https:/​/​doi.org/​10.1073/​pnas.18.3.255

[40] Milan Korda and Igor Mezić. Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control. Automatica, 93: 149–160, 2018. https:/​/​doi.org/​10.1016/​j.automatica.2018.03.046.
https:/​/​doi.org/​10.1016/​j.automatica.2018.03.046

[41] Philip Krantz, Morten Kjaergaard, Fei Yan, Terry P Orlando, Simon Gustavsson, and William D Oliver. A quantum engineer's guide to superconducting qubits. Applied Physics Reviews, 6 (2): 021318, 2019. https:/​/​doi.org/​10.1063/​1.5089550.
https:/​/​doi.org/​10.1063/​1.5089550

[42] Jay H Lee and N Lawrence Ricker. Extended Kalman filter based nonlinear model predictive control. Industrial & Engineering Chemistry Research, 33 (6): 1530–1541, 1994.

[43] Boxi Li, Shahnawaz Ahmed, Sidhant Saraogi, Neill Lambert, Franco Nori, Alexander Pitchford, and Nathan Shammah. Pulse-level noisy quantum circuits with qutip. Quantum, 6: 630, 2022. https:/​/​doi.org/​10.22331/​q-2022-01-24-630.
https:/​/​doi.org/​10.22331/​q-2022-01-24-630

[44] Brett T Lopez, Jean-Jacques E Slotine, and Jonathan P How. Dynamic tube MPC for nonlinear systems. In 2019 American Control Conference (ACC), pages 1655–1662. IEEE, 2019. https:/​/​doi.org/​10.23919/​ACC.2019.8814758.
https:/​/​doi.org/​10.23919/​ACC.2019.8814758

[45] Shai Machnes, Elie Assémat, David Tannor, and Frank K Wilhelm. Tunable, flexible, and efficient optimization of control pulses for practical qubits. Physical Review Letters, 120 (15): 150401, 2018. https:/​/​doi.org/​10.1103/​PhysRevLett.120.150401.
https:/​/​doi.org/​10.1103/​PhysRevLett.120.150401

[46] Easwar Magesan and Jay M Gambetta. Effective Hamiltonian models of the cross-resonance gate. Physical Review A, 101 (5): 052308, 2020. https:/​/​doi.org/​10.1103/​PhysRevA.101.052308.
https:/​/​doi.org/​10.1103/​PhysRevA.101.052308

[47] David Q Mayne, James B Rawlings, Christopher V Rao, and Pierre OM Scokaert. Constrained model predictive control: Stability and optimality. Automatica, 36 (6): 789–814, 2000. https:/​/​doi.org/​10.1016/​S0005-1098(99)00214-9.
https:/​/​doi.org/​10.1016/​S0005-1098(99)00214-9

[48] David Q Mayne, María M Seron, and SV Raković. Robust model predictive control of constrained linear systems with bounded disturbances. Automatica, 41 (2): 219–224, 2005. https:/​/​doi.org/​10.1016/​j.automatica.2004.08.019.
https:/​/​doi.org/​10.1016/​j.automatica.2004.08.019

[49] David C McKay, Thomas Alexander, Luciano Bello, Michael J Biercuk, Lev Bishop, Jiayin Chen, Jerry M Chow, Antonio D Córcoles, Daniel Egger, Stefan Filipp, et al. Qiskit backend specifications for OpenQASM and OpenPulse experiments. arXiv preprint arXiv:1809.03452, 2018.
arXiv:1809.03452

[50] Igor Mezić. Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynamics, 41 (1-3): 309–325, 2005. https:/​/​doi.org/​10.1007/​s11071-005-2824-x.
https:/​/​doi.org/​10.1007/​s11071-005-2824-x

[51] Igor Mezic. Analysis of fluid flows via spectral properties of the Koopman operator. Annual Review of Fluid Mechanics, 45: 357–378, 2013. https:/​/​doi.org/​10.1146/​annurev-fluid-011212-140652.
https:/​/​doi.org/​10.1146/​annurev-fluid-011212-140652

[52] Thomas M Moerland, Joost Broekens, and Catholijn M Jonker. Model-based Reinforcement Learning: A survey. arXiv preprint arXiv:2006.16712, 2020.
arXiv:2006.16712

[53] Felix Motzoi, Jay M Gambetta, Patrick Rebentrost, and Frank K Wilhelm. Simple pulses for elimination of leakage in weakly nonlinear qubits. Physical Review Letters, 103 (11): 110501, 2009. https:/​/​doi.org/​10.1103/​PhysRevLett.103.110501.
https:/​/​doi.org/​10.1103/​PhysRevLett.103.110501

[54] Murphy Yuezhen Niu, Sergio Boixo, Vadim N Smelyanskiy, and Hartmut Neven. Universal quantum control through deep reinforcement learning. npj Quantum Information, 5 (1): 1–8, 2019. https:/​/​doi.org/​10.1038/​s41534-019-0141-3.
https:/​/​doi.org/​10.1038/​s41534-019-0141-3

[55] Jorge Nocedal and Stephen Wright. Numerical optimization. Springer Science & Business Media, 2006. https:/​/​doi.org/​10.1007/​b98874.
https:/​/​doi.org/​10.1007/​b98874

[56] Feliks Nüske, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and Karl Worthmann. Finite-data error bounds for Koopman-based prediction and control. arXiv preprint arXiv:2108.07102, 2021.
arXiv:2108.07102

[57] Sebastian Peitz and Stefan Klus. Koopman operator-based model reduction for switched-system control of PDEs. Automatica, 106: 184–191, 2019. https:/​/​doi.org/​10.1016/​j.automatica.2019.05.016.
https:/​/​doi.org/​10.1016/​j.automatica.2019.05.016

[58] Sebastian Peitz, Samuel E Otto, and Clarence W Rowley. Data-driven model predictive control using interpolated Koopman generators. SIAM Journal on Applied Dynamical Systems, 19 (3): 2162–2193, 2020. https:/​/​doi.org/​10.1137/​20M1325678.
https:/​/​doi.org/​10.1137/​20M1325678

[59] Seth D Pendergrass, J Nathan Kutz, and Steven L Brunton. Streaming GPU singular value and dynamic mode decompositions. arXiv preprint arXiv:1612.07875, 2016.
arXiv:1612.07875

[60] Minh Q Phan and Seyed Mahdi B Azad. Model predictive Q-learning (MPQ-L) for bilinear systems. In Modeling, Simulation and Optimization of Complex Processes HPSC 2018, pages 97–115. Springer, 2021. https:/​/​doi.org/​10.1007/​978-3-030-55240-4_5.
https:/​/​doi.org/​10.1007/​978-3-030-55240-4_5

[61] Thomas Propson, Brian E Jackson, Jens Koch, Zachary Manchester, and David I Schuster. Robust quantum optimal control with trajectory optimization. Physical Review Applied, 17 (1): 014036, 2022. https:/​/​doi.org/​10.1103/​PhysRevApplied.17.014036.
https:/​/​doi.org/​10.1103/​PhysRevApplied.17.014036

[62] S Joe Qin and Thomas A Badgwell. A survey of industrial model predictive control technology. Control engineering practice, 11 (7): 733–764, 2003. https:/​/​doi.org/​10.1016/​S0967-0661(02)00186-7.
https:/​/​doi.org/​10.1016/​S0967-0661(02)00186-7

[63] Saša V Raković and William S Levine. Handbook of model predictive control. Springer, 2018. https:/​/​doi.org/​10.1007/​978-3-319-77489-3.
https:/​/​doi.org/​10.1007/​978-3-319-77489-3

[64] Mohan Sarovar, Timothy Proctor, Kenneth Rudinger, Kevin Young, Erik Nielsen, and Robin Blume-Kohout. Detecting crosstalk errors in quantum information processors. Quantum, 4: 321, 2020. https:/​/​doi.org/​10.22331/​q-2020-09-11-321.
https:/​/​doi.org/​10.22331/​q-2020-09-11-321

[65] Manuel Schaller, Karl Worthmann, Friedrich Philipp, Sebastian Peitz, and Feliks Nüske. Towards efficient and reliable prediction-based control using eDMD. arXiv preprint arXiv:2202.09084, 2022.
arXiv:2202.09084

[66] Yunong Shi, Nelson Leung, Pranav Gokhale, Zane Rossi, David I Schuster, Henry Hoffmann, and Frederic T Chong. Optimized compilation of aggregated instructions for realistic quantum computers. In Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, pages 1031–1044, 2019. https:/​/​doi.org/​10.1145/​3297858.3304018.
https:/​/​doi.org/​10.1145/​3297858.3304018

[67] Henrique Silvério, Sebastián Grijalva, Constantin Dalyac, Lucas Leclerc, Peter J Karalekas, Nathan Shammah, Mourad Beji, Louis-Paul Henry, and Loïc Henriet. Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays. Quantum, 6: 629, 2022. https:/​/​doi.org/​10.22331/​q-2022-01-24-629.
https:/​/​doi.org/​10.22331/​q-2022-01-24-629

[68] B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd. OSQP: An operator splitting solver for quadratic programs. Mathematical Programming Computation, 12 (4): 637–672, 2020. https:/​/​doi.org/​10.1007/​s12532-020-00179-2.
https:/​/​doi.org/​10.1007/​s12532-020-00179-2

[69] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17: 261–272, 2020. https:/​/​doi.org/​10.1038/​s41592-019-0686-2.
https:/​/​doi.org/​10.1038/​s41592-019-0686-2

[70] John von Neumann, Robert T. Beyer, and Nicholas A. Wheeler. Mathematical foundations of quantum mechanics. Princeton University Press, 2018 edition, 1932. ISBN 9780691178561. https:/​/​doi.org/​10.1515/​9781400889921.
https:/​/​doi.org/​10.1515/​9781400889921

[71] Yang Wang and Stephen Boyd. Fast model predictive control using online optimization. IEEE Transactions on control systems technology, 18 (2): 267–278, 2009. https:/​/​doi.org/​10.1109/​TCST.2009.2017934.
https:/​/​doi.org/​10.1109/​TCST.2009.2017934

[72] Manuel Watter, Jost Springenberg, Joschka Boedecker, and Martin Riedmiller. Embed to Control: A locally linear latent dynamics model for control from raw images. Advances in Neural Information Processing Systems, 28, 2015.

[73] Max Werninghaus, Daniel J Egger, Federico Roy, Shai Machnes, Frank K Wilhelm, and Stefan Filipp. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Information, 7 (1): 1–6, 2021. https:/​/​doi.org/​10.1038/​s41534-020-00346-2.
https:/​/​doi.org/​10.1038/​s41534-020-00346-2

[74] Nicolas Wittler, Federico Roy, Kevin Pack, Max Werninghaus, Anurag Saha Roy, Daniel J Egger, Stefan Filipp, Frank K Wilhelm, and Shai Machnes. Integrated tool set for control, calibration, and characterization of quantum devices applied to superconducting qubits. Physical Review Applied, 15 (3): 034080, 2021. https:/​/​doi.org/​10.1103/​PhysRevApplied.15.034080.
https:/​/​doi.org/​10.1103/​PhysRevApplied.15.034080

[75] Xian Wu, SL Tomarken, N Anders Petersson, LA Martinez, Yaniv J Rosen, and Jonathan L DuBois. High-fidelity software-defined quantum logic on a superconducting qudit. Physical Review Letters, 125 (17): 170502, 2020. https:/​/​doi.org/​10.1103/​PhysRevLett.125.170502.
https:/​/​doi.org/​10.1103/​PhysRevLett.125.170502

[76] Hao Zhang, Clarence W Rowley, Eric A Deem, and Louis N Cattafesta. Online dynamic mode decomposition for time-varying systems. SIAM Journal on Applied Dynamical Systems, 18 (3): 1586–1609, 2019. https:/​/​doi.org/​10.1137/​18M1192329.
https:/​/​doi.org/​10.1137/​18M1192329

[77] Tianhao Zhang, Gregory Kahn, Sergey Levine, and Pieter Abbeel. Learning deep control policies for autonomous aerial vehicles with MPC-guided policy search. In 2016 IEEE international conference on robotics and automation (ICRA), pages 528–535. IEEE, 2016. https:/​/​doi.org/​10.1109/​ICRA.2016.7487175.
https:/​/​doi.org/​10.1109/​ICRA.2016.7487175

Cited by

[1] Lennart Maximilian Seifert, Ziqian Li, Tanay Roy, David I. Schuster, Frederic T. Chong, and Jonathan M. Baker, "Exploring ququart computation on a transmon using optimal control", Physical Review A 108 6, 062609 (2023).

[2] Ettore Canonici, Stefano Martina, Riccardo Mengoni, Daniele Ottaviani, and Filippo Caruso, "Machine Learning based Noise Characterization and Correction on Neutral Atoms NISQ Devices", Advanced Quantum Technologies 7 1, 2300192 (2024).

[3] Yuzuru Kato and Hiroya Nakao, 2023 62nd IEEE Conference on Decision and Control (CDC) 5912 (2023) ISBN:979-8-3503-0124-3.

[4] Jason D. Chadwick and Frederic T. Chong, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 1286 (2023) ISBN:979-8-3503-4323-6.

[5] Maison Clouatre, Mark Balas, Vinod Gehlot, and John Valasek, "Linear Quantum State Observers", IEEE Transactions on Quantum Engineering 3, 1 (2022).

[6] Yuzuru Kato and Hiroya Nakao, 2022 IEEE 61st Conference on Decision and Control (CDC) 5141 (2022) ISBN:978-1-6654-6761-2.

[7] Christiane P. Koch, Ugo Boscain, Tommaso Calarco, Gunther Dirr, Stefan Filipp, Steffen J. Glaser, Ronnie Kosloff, Simone Montangero, Thomas Schulte-Herbrüggen, Dominique Sugny, and Frank K. Wilhelm, "Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe", arXiv:2205.12110, (2022).

[8] Jason D. Chadwick and Frederic T. Chong, "Efficient control pulses for continuous quantum gate families through coordinated re-optimization", arXiv:2302.01553, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-03-29 09:55:35) and SAO/NASA ADS (last updated successfully 2024-03-29 09:55:36). The list may be incomplete as not all publishers provide suitable and complete citation data.