References#
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.
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.
Niklas Rach, Matthias M Müller, Tommaso Calarco, and Simone Montangero. Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape. Physical Review A, 92(6):062343, 2015.
Jens Jakob WH Sørensen, MO Aranburu, Till Heinzel, and Jacob F Sherson. Quantum optimal control in a chopped basis: applications in control of bose-einstein condensates. Physical Review A, 98(2):022119, 2018.
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Yash Katariya, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang. JAX: composable transformations of Python+NumPy programs. 2018. URL: jax-ml/jax.
H. Tal‐Ezer and R. Kosloff. An accurate and efficient scheme for propagating the time dependent schrödinger equation. The Journal of Chemical Physics, 81(9):3967–3971, 11 1984. URL: https://doi.org/10.1063/1.448136, arXiv:https://pubs.aip.org/aip/jcp/article-pdf/81/9/3967/18950222/3967_1_online.pdf, doi:10.1063/1.448136.
Patrick Kidger. On Neural Differential Equations. PhD thesis, University of Oxford, 2021.
James H Verner. Numerically optimal runge–kutta pairs with interpolants. Numerical Algorithms, 53(2):383–396, 2010.
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. doi:10.1038/s41592-019-0686-2.
Neill Lambert, Eric Giguère, Paul Menczel, Boxi Li, Patrick Hopf, Gerardo Suárez, Marc Gali, Jake Lishman, Rushiraj Gadhvi, Rochisha Agarwal, and others. Qutip 5: the quantum toolbox in python. Physics Reports, 1153:1–62, 2026.
Michael H Goerz, Sebastián C Carrasco, and Vladimir S Malinovsky. Quantum optimal control via semi-automatic differentiation. Quantum, 6:871, 2022.
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.
Bobak Shahriari, Kevin Swersky, Ziyu Wang, Ryan P Adams, Nando De Freitas, and others. Taking the human out of the loop: a review of bayesian optimization. Proc. Ieee, 104(1):148–175, 2016.
Matthias M Müller, Ressa S Said, Fedor Jelezko, Tommaso Calarco, and Simone Montangero. One decade of quantum optimal control in the chopped random basis. Reports on progress in physics, 85(7):076001, 2022.
Jens Koch, Terri M Yu, Jay Gambetta, Andrew A Houck, David I Schuster, Johannes Majer, Alexandre Blais, Michel H Devoret, Steven M Girvin, and Robert J Schoelkopf. Charge-insensitive qubit design derived from the cooper pair box. Physical Review A—Atomic, Molecular, and Optical Physics, 76(4):042319, 2007.
Sarah Sheldon, Easwar Magesan, Jerry M Chow, and Jay M Gambetta. Procedure for systematically tuning up cross-talk in the cross-resonance gate. Physical Review A, 93(6):060302, 2016.
Goran Lindblad. On the generators of quantum dynamical semigroups. Communications in mathematical physics, 48(2):119–130, 1976.
Daniel Manzano. A short introduction to the lindblad master equation. Aip advances, 2020.
Reinier W Heeres, Philip Reinhold, Nissim Ofek, Luigi Frunzio, Liang Jiang, Michel H Devoret, and Robert J Schoelkopf. Implementing a universal gate set on a logical qubit encoded in an oscillator. Nature communications, 8(1):94, 2017.
Alec Eickbusch, Volodymyr Sivak, Andy Z Ding, Salvatore S Elder, Shantanu R Jha, Jayameenakshi Venkatraman, Baptiste Royer, Steven M Girvin, Robert J Schoelkopf, and Michel H Devoret. Fast universal control of an oscillator with weak dispersive coupling to a qubit. Nature Physics, 18(12):1464–1469, 2022.
Alexandre Blais, Arne L Grimsmo, Steven M Girvin, and Andreas Wallraff. Circuit quantum electrodynamics. Reviews of Modern Physics, 93(2):025005, 2021.
Jun Zhang and K Birgitta Whaley. Generation of quantum logic operations from physical hamiltonians. Physical Review A—Atomic, Molecular, and Optical Physics, 71(5):052317, 2005.
Paul Watts, Jiří Vala, Matthias M Müller, Tommaso Calarco, K Birgitta Whaley, Daniel M Reich, Michael H Goerz, and Christiane P Koch. Optimizing for an arbitrary perfect entangler. i. functionals. Physical Review A, 91(6):062306, 2015.
Yuriy Makhlin. Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum computations. Quantum Information Processing, 1(4):243–252, 2002.
Michael A Nielsen. A simple formula for the average gate fidelity of a quantum dynamical operation. Physics Letters A, 303(4):249–252, 2002.
Nikolaus Hansen, Sibylle D Müller, and Petros Koumoutsakos. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (cma-es). Evolutionary computation, 11(1):1–18, 2003.
Nikolaus Hansen. The cma evolution strategy: a tutorial. arXiv preprint arXiv:1604.00772, 2016.
Pierre de Fouquieres, Sophie G Schirmer, Steffen J Glaser, and Ilya Kuprov. Second order gradient ascent pulse engineering. Journal of Magnetic Resonance, 212(2):412–417, 2011.
Awad H Al-Mohy and Nicholas J Higham. Computing the fréchet derivative of the matrix exponential, with an application to condition number estimation. SIAM Journal on Matrix Analysis and Applications, 30(4):1639–1657, 2009.
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, 2019.