Nonadiabatic quantum optimization for crossing quantum phase transitions

Adiabaticity; Control parameters; Finite-time; Kibble-Zurek mechanism; Many-body quantum systems; Non-adiabatic; Optimal controls; Quantum optimization; Quantum-phase transition; Time-scales; Atomic and Molecular Physics, and Optics; Quantum Physics; Physics - Other; Physics - Statistical Mechanics

Abstract :

[en] We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a framework, nonadiabatic quantum optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered nonintegrable model.

Disciplines :

Physics

Author, co-author :

GRABARITS, Andras ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

BALDUCCI, Federico ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Aurélia CHENU ; Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

Sanders, Barry C. ; Institute for Quantum Science and Technology, University of Calgary, Canada

DEL CAMPO ECHEVARRIA, Adolfo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

External co-authors :

yes

Language :

English

Title :

Nonadiabatic quantum optimization for crossing quantum phase transitions

Publication date :

2025

Journal title :

Physical Review. A

ISSN :

2469-9926

eISSN :

2469-9934

Publisher :

American Physical Society

Volume :

111

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevA.111.012215

Funders :

Fonds National de la Recherche Luxembourg
Horizon 2020

Funding text :

We thank P. Chandarana and X. Chen for the insightful discussions. The numerical simulations presented in this work were carried out using the HPC facilities of the University of Luxembourg. This project was supported by the Luxembourg National Research Fund (FNR Grants No. 17132054 and No. 16434093). It has also received funding from the QuantERA II Joint Programme and co-funding from the European Union's Horizon 2020 research and innovation programme.

Commentary :

24 pages, 15 figures, comments welcome

Available on ORBilu :

since 20 May 2025

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Bibliography

S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, 2011).
S. Sachdev, Quantum Phases of Matter (Cambridge University Press, Cambridge, 2023).
J. Dziarmaga, Dynamics of a quantum phase transition and relaxation to a steady state, Adv. Phys. 59, 1063 (2010) 0001-8732 10.1080/00018732.2010.514702.
A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Mod. Phys. 83, 863 (2011) 0034-6861 10.1103/RevModPhys.83.863.
A. del Campo and W. H. Zurek, Universality of phase transition dynamics: Topological defects from symmetry breaking, Int. J. Mod. Phys. A 29, 1430018 (2014) 0217-751X 10.1142/S0217751X1430018X.
T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A: Math. Gen. 9, 1387 (1976) 0305-4470 10.1088/0305-4470/9/8/029.
T. W. B. Kibble, Some implications of a cosmological phase transition, Phys. Rep. 67, 183 (1980) 0370-1573 10.1016/0370-1573(80)90091-5.
W. H. Zurek, Cosmological experiments in superfluid helium Nature (London) 317, 505 (1985) 0028-0836 10.1038/317505a0.
W. H. Zurek, Cosmological experiments in condensed matter systems, Phys. Rep. 276, 177 (1996) 0370-1573 10.1016/S0370-1573(96)00009-9.
A. Polkovnikov, Universal adiabatic dynamics in the vicinity of a quantum critical point, Phys. Rev. B 72, 161201 (R) (2005) 1098-0121 10.1103/PhysRevB.72.161201.
B. Damski, The simplest quantum model supporting the Kibble-Zurek mechanism of topological defect production: Landau-Zener transitions from a new perspective, Phys. Rev. Lett. 95, 035701 (2005) 0031-9007 10.1103/PhysRevLett.95.035701.
J. Dziarmaga, Dynamics of a quantum phase transition: Exact solution of the quantum ising model, Phys. Rev. Lett. 95, 245701 (2005) 0031-9007 10.1103/PhysRevLett.95.245701.
W. H. Zurek, U. Dorner, and P. Zoller, Dynamics of a quantum phase transition, Phys. Rev. Lett. 95, 105701 (2005) 0031-9007 10.1103/PhysRevLett.95.105701.
B. Gardas, J. Dziarmaga, W. H. Zurek et al., Defects in quantum computers, Sci. Rep. 8, 4539 (2018) 2045-2322 10.1038/s41598-018-22763-2.
A. Keesling, A. Omran, H. Levine et al., Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator, Nature (London) 568, 207 (2019) 0028-0836 10.1038/s41586-019-1070-1.
P. Weinberg, M. Tylutki, J. M. Rönkkö et al., Scaling and diabatic effects in quantum annealing with a D-Wave device, Phys. Rev. Lett. 124, 090502 (2020) 0031-9007 10.1103/PhysRevLett.124.090502.
Y. Bando, Y. Susa, H. Oshiyama et al., Probing the universality of topological defect formation in a quantum annealer: Kibble-Zurek mechanism and beyond, Phys. Rev. Res. 2, 033369 (2020) 2643-1564 10.1103/PhysRevResearch.2.033369.
A. D. King, S. Suzuki, J. Raymond et al., Coherent quantum annealing in a programmable 2,000-qubit Ising chain, Nat. Phys. 18, 1324 (2022) 1745-2473 10.1038/s41567-022-01741-6.
A. D. King, A. Nocera, M. M. Rams et al., Computational supremacy in quantum simulation, arXiv:2403.00910.
T. I. Andersen, N. Astrakhantsev, A. H. Karamlou et al., Thermalization and criticality on an analog-digital quantum simulator, arXiv:2405.17385.
M. Demirplak and S. A. Rice, Adiabatic population transfer with control fields, J. Phys. Chem. A 107, 9937 (2003) 1089-5639 10.1021/jp030708a.
M. Demirplak and S. A. Rice, Assisted adiabatic passage revisited, J. Phys. Chem. B 109, 6838 (2005) 1520-6106 10.1021/jp040647w.
M. Demirplak and S. A. Rice, On the consistency, extremal, and global properties of counterdiabatic fields, J. Chem. Phys. 129, 154111 (2008) 0021-9606 10.1063/1.2992152.
M. V. Berry, Transitionless quantum driving, J. Phys. A: Math. Gen. 42, 365303 (2009) 1751-8113 10.1088/1751-8113/42/36/365303.
A. del Campo, M. M. Rams, and W. H. Zurek, Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model, Phys. Rev. Lett. 109, 115703 (2012) 0031-9007 10.1103/PhysRevLett.109.115703.
K. Takahashi, Transitionless quantum driving for spin systems, Phys. Rev. E 87, 062117 (2013) 1539-3755 10.1103/PhysRevE.87.062117.
H. Saberi, T. Opatrný, K. Mølmer et al., Adiabatic tracking of quantum many-body dynamics, Phys. Rev. A 90, 060301 (R) (2014) 1050-2947 10.1103/PhysRevA.90.060301.
B. Damski, Counterdiabatic driving of the quantum Ising model, J. Stat. Mech. (2014) P12019 1742-5468 10.1088/1742-5468/2014/12/P12019.
D. Sels and A. Polkovnikov, Minimizing irreversible losses in quantum systems by local counterdiabatic driving, Proc. Natl. Acad. Sci. USA 114, E3909 (2017) 0027-8424 10.1073/pnas.1619826114.
P. W. Claeys, M. Pandey, D. Sels et al., Floquet-engineering counterdiabatic protocols in quantum many-body systems, Phys. Rev. Lett. 123, 090602 (2019) 0031-9007 10.1103/PhysRevLett.123.090602.
Q. Zhang, N. N. Hegade, A. G. Cadavid et al., Analog counterdiabatic quantum computing, arXiv:2405.14829.
N. N. Hegade, K. Paul, Y. Ding et al., Shortcuts to adiabaticity in digitized adiabatic quantum computing, Phys. Rev. Appl. 15, 024038 (2021) 2331-7019 10.1103/PhysRevApplied.15.024038.
J. Yao, L. Lin, and M. Bukov, Reinforcement learning for many-body ground-state preparation inspired by counterdiabatic driving, Phys. Rev. X 11, 031070 (2021) 2160-3308 10.1103/PhysRevX.11.031070.
P. Chandarana, N. N. Hegade, K. Paul et al., Digitized-counterdiabatic quantum approximate optimization algorithm, Phys. Rev. Res. 4, 013141 (2022) 2643-1564 10.1103/PhysRevResearch.4.013141.
J. Wurtz and P. J. Love, Counterdiabaticity and the quantum approximate optimization algorithm, Quantum 6, 635 (2022) 2521-327X 10.22331/q-2022-01-27-635.
C. Mc Keever and M. Lubasch, Towards adiabatic quantum computing using compressed quantum circuits, PRX Quantum 5, 020362 (2024) 2691-3399 10.1103/PRXQuantum.5.020362.
P. Chandarana, N. N. Hegade, I. Montalban et al., Digitized counterdiabatic quantum algorithm for protein folding, Phys. Rev. Appl. 20, 014024 (2023) 2331-7019 10.1103/PhysRevApplied.20.014024.
P. Chandarana, K. Paul, M. Garcia-de-Andoin, Y. Ban, M. Sanz, and X. Chen, Photonic counterdiabatic quantum optimization algorithm, Commun. Phys. 7, 315 (2024) 10.1038/s42005-024-01807-2.
C. Li, J. Shen, R. Shaydulin et al., Quantum counterdiabatic driving with local control, arXiv:2403.01854.
A. G. Cadavid, A. Dalal, A. Simen et al., Bias-field digitized counterdiabatic quantum optimization, arXiv:2405.13898.
T. W. B. Kibble and G. E. Volovik, On phase ordering behind the propagating front of a second-order transition, J. Exp. Theor. Phys. Lett. 65, 102 (1997) 10.1134/1.567332.
W. H. Zurek, Causality in condensates: Gray solitons as relics of BEC formation, Phys. Rev. Lett. 102, 105702 (2009) 10.1103/PhysRevLett.102.105702.
A. del Campo, G. De Chiara, G. Morigi et al., Structural defects in ion chains by quenching the external potential: The inhomogeneous Kibble-Zurek mechanism, Phys. Rev. Lett. 105, 075701 (2010) 0031-9007 10.1103/PhysRevLett.105.075701.
A. del Campo, A. Retzker, and M. B. Plenio, The inhomogeneous Kibble-Zurek mechanism: Vortex nucleation during Bose-Einstein condensation, New J. Phys. 13, 083022 (2011) 1367-2630 10.1088/1367-2630/13/8/083022.
J. Dziarmaga and M. M. Rams, Dynamics of an inhomogeneous quantum phase transition, New J. Phys. 12, 055007 (2010) 1367-2630 10.1088/1367-2630/12/5/055007.
J. Dziarmaga and M. M. Rams, Adiabatic dynamics of an inhomogeneous quantum phase transition: The case of a (Equation presented) dynamical exponent, New J. Phys. 12, 103002 (2010) 1367-2630 10.1088/1367-2630/12/10/103002.
A. Francuz, J. Dziarmaga, B. Gardas et al., Space and time renormalization in phase transition dynamics, Phys. Rev. B 93, 075134 (2016) 2469-9950 10.1103/PhysRevB.93.075134.
F. J. Gómez-Ruiz and A. del Campo, Universal dynamics of inhomogeneous quantum phase transitions: Suppressing defect formation, Phys. Rev. Lett. 122, 080604 (2019) 0031-9007 10.1103/PhysRevLett.122.080604.
I. Sokolov, F. A. Bayocboc, Jr., M. M. Rams and J. Dziarmaga, Inhomogeneous adiabatic preparation of a quantum critical ground state in two dimensions, Phys. Rev. B 110, 054410 (2024) 10.1103/PhysRevB.110.054410.
A. del Campo, T. W. B. Kibble, and W. H. Zurek, Causality and non-equilibrium second-order phase transitions in inhomogeneous systems, J. Phys.: Condens. Matter 25, 404210 (2013) 0953-8984 10.1088/0953-8984/25/40/404210.
S. Ulm, J. Roßnagel, G. Jacob et al., Observation of the Kibble-Zurek scaling law for defect formation in ion crystals, Nat. Commun. 4, 2290 (2013) 2041-1723 10.1038/ncomms3290.
K. Pyka, J. Keller, H. L. Partner et al., Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals, Nat. Commun. 4, 2291 (2013) 2041-1723 10.1038/ncomms3291.
C.-R. Yi, S. Liu, R.-H. Jiao et al., Exploring inhomogeneous Kibble-Zurek mechanism in a spin-orbit coupled Bose-Einstein condensate, Phys. Rev. Lett. 125, 260603 (2020) 0031-9007 10.1103/PhysRevLett.125.260603.
M. Kim, T. Rabga, Y. Lee et al., Suppression of spontaneous defect formation in inhomogeneous Bose gases, Phys. Rev. A 106, L061301 (2022) 2469-9926 10.1103/PhysRevA.106.L061301.
D. Sen, K. Sengupta, and S. Mondal, Defect production in nonlinear quench across a quantum critical point, Phys. Rev. Lett. 101, 016806 (2008) 0031-9007 10.1103/PhysRevLett.101.016806.
R. Barankov and A. Polkovnikov, Optimal nonlinear passage through a quantum critical point, Phys. Rev. Lett. 101, 076801 (2008) 0031-9007 10.1103/PhysRevLett.101.076801.
M. J. M. Power and G. De Chiara, Dynamical symmetry breaking with optimal control: Reducing the number of pieces, Phys. Rev. B 88, 214106 (2013) 1098-0121 10.1103/PhysRevB.88.214106.
N. Wu, A. Nanduri, and H. Rabitz, Optimal suppression of defect generation during a passage across a quantum critical point, Phys. Rev. B 91, 041115 (R) (2015) 1098-0121 10.1103/PhysRevB.91.041115.
L. M. Garrido and F. J. Sancho, Degree of approximate validity of the adiabatic invariance in quantum mechanics, Physica (Amsterdam) 28, 553 (1962) 0031-8914 10.1016/0031-8914(62)90109-X.
G. Nenciu, Linear adiabatic theory. Exponential estimates, Commun. Math. Phys. 152, 479 (1993) 0010-3616 10.1007/BF02096616.
G. A. Hagedorn and A. Joye, Elementary exponential error estimates for the adiabatic approximation, J. Math. Anal. Appl. 267, 235 (2002) 0022247X 10.1006/jmaa.2001.7765.
D. A. Lidar, A. T. Rezakhani, and A. Hamma, Adiabatic approximation with exponential accuracy for many-body systems and quantum computation, J. Math. Phys. 50, 102106 (2009) 0022-2488 10.1063/1.3236685.
N. Wiebe and N. S. Babcock, Improved error-scaling for adiabatic quantum evolutions, New J. Phys. 14, 013024 (2012) 1367-2630 10.1088/1367-2630/14/1/013024.
Y. Ge, A. Molnár, and J. I. Cirac, Rapid adiabatic preparation of injective projected entangled pair states and Gibbs states, Phys. Rev. Lett. 116, 080503 (2016) 0031-9007 10.1103/PhysRevLett.116.080503.
N. Khaneja, T. Reiss, C. Kehlet et al., Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172, 296 (2005) 1090-7807 10.1016/j.jmr.2004.11.004.
T. Caneva, M. Murphy, T. Calarco et al., Optimal control at the quantum speed limit, Phys. Rev. Lett. 103, 240501 (2009) 0031-9007 10.1103/PhysRevLett.103.240501.
P. Doria, T. Calarco, and S. Montangero, Optimal control technique for many-body quantum dynamics, Phys. Rev. Lett. 106, 190501 (2011) 0031-9007 10.1103/PhysRevLett.106.190501.
T. Caneva, T. Calarco, and S. Montangero, Chopped random-basis quantum optimization, Phys. Rev. A 84, 022326 (2011) 1050-2947 10.1103/PhysRevA.84.022326.
U. Boscain, M. Sigalotti, and D. Sugny, Introduction to the Pontryagin maximum principle for quantum optimal control, PRX Quantum 2, 030203 (2021) 2691-3399 10.1103/PRXQuantum.2.030203.
D. D'Alessandro, Introduction to Quantum Control and Dynamics (CRC Press, Boca Raton, FL, 2007).
J. Roland and N. J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65, 042308 (2002) 1050-2947 10.1103/PhysRevA.65.042308.
A. T. Rezakhani, W.-J. Kuo, A. Hamma et al., Quantum adiabatic brachistochrone, Phys. Rev. Lett. 103, 080502 (2009) 0031-9007 10.1103/PhysRevLett.103.080502.
A. Kazhybekova, S. Campbell, and A. Kiely, Minimal action control method in quantum critical models, J. Phys. Commun. 6, 113001 (2022) 2399-6528 10.1088/2399-6528/aca3fa.
M. M. Müller, R. S. Said, F. Jelezko et al., One decade of quantum optimal control in the chopped random basis, Rep. Prog. Phys. 85, 076001 (2022) 0034-4885 10.1088/1361-6633/ac723c.
S. Suzuki, J. Inoue, and B. Chakrabarti, Quantum Ising Phases and Transitions in Transverse Ising Models, Lecture Notes in Physics (Springer, Berlin, 2012).
A. del Campo, Universal statistics of topological defects formed in a quantum phase transition, Phys. Rev. Lett. 121, 200601 (2018) 0031-9007 10.1103/PhysRevLett.121.200601.
F. Balducci, M. Beau, J. Yang et al., Large deviations beyond the Kibble-Zurek mechanism, Phys. Rev. Lett. 131, 230401 (2023) 0031-9007 10.1103/PhysRevLett.131.230401.
B. Damski and W. H. Zurek, Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again, Phys. Rev. A 73, 063405 (2006) 1050-2947 10.1103/PhysRevA.73.063405.
H.-B. Zeng, C.-Y. Xia, and A. del Campo, Universal breakdown of Kibble-Zurek scaling in fast quenches across a phase transition, Phys. Rev. Lett. 130, 060402 (2023) 0031-9007 10.1103/PhysRevLett.130.060402.
C.-Y. Xia, H.-B. Zeng, A. Grabarits et al., Kibble-Zurek mechanism and beyond: Lessons from a holographic superfluid disk, arXiv:2406.09433.
N. Defenu, G. Morigi, L. Dell'Anna et al., Universal dynamical scaling of long-range topological superconductors, Phys. Rev. B 100, 184306 (2019) 2469-9950 10.1103/PhysRevB.100.184306.
N. Defenu, T. Enss, M. Kastner et al., Dynamical critical scaling of long-range interacting quantum magnets, Phys. Rev. Lett. 121, 240403 (2018) 0031-9007 10.1103/PhysRevLett.121.240403.
F. Gao and L. Han, Implementing the Nelder-Mead simplex algorithm with adaptive parameters, Comput. Optim. Appl. 51, 259 (2012) 0926-6003 10.1007/s10589-010-9329-3.
P. Virtanen, R. Gommers, T. E. Oliphant et al., SciPy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020) 1548-7091 10.1038/s41592-019-0686-2.
D. Vodola, L. Lepori, E. Ercolessi et al., Kitaev chains with long-range pairing, Phys. Rev. Lett. 113, 156402 (2014) 0031-9007 10.1103/PhysRevLett.113.156402.
A. Dutta and A. Dutta, Probing the role of long-range interactions in the dynamics of a long-range Kitaev chain, Phys. Rev. B 96, 125113 (2017) 2469-9950 10.1103/PhysRevB.96.125113.
A. Campa, T. Dauxois, D. Fanelli, Physics of Long-Range Interacting Systems (Oxford University Press, Oxford, 2014).
A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Phys. Usp. 44, 131 (2001) 1468-4780 10.1070/1063-7869/44/10S/S29.
S. M. Albrecht, A. P. Higginbotham, M. Madsen et al., Exponential protection of zero modes in Majorana islands, Nature (London) 531, 206 (2016) 0028-0836 10.1038/nature17162.
V. Mourik, K. Zuo, S. M. Frolov et al., Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices, Science 336, 1003 (2012) 0036-8075 10.1126/science.1222360.
O. Viyuela, L. Fu, and M. A. Martin-Delgado, Chiral topological superconductors enhanced by long-range interactions, Phys. Rev. Lett. 120, 017001 (2018) 0031-9007 10.1103/PhysRevLett.120.017001.
A. Alecce and L. Dell'Anna, Extended Kitaev chain with longer-range hopping and pairing, Phys. Rev. B 95, 195160 (2017) 2469-9950 10.1103/PhysRevB.95.195160.
M. Singh, S. Dhara, and S. Gangadharaiah, Driven one-dimensional noisy Kitaev chain, Phys. Rev. B 107, 014303 (2023) 2469-9950 10.1103/PhysRevB.107.014303.
C. Nayak, S. H. Simon, A. Stern et al., Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008) 0034-6861 10.1103/RevModPhys.80.1083.
L. Mazza, M. Rizzi, M. D. Lukin et al., Robustness of quantum memories based on Majorana zero modes, Phys. Rev. B 88, 205142 (2013) 1098-0121 10.1103/PhysRevB.88.205142.
J. A. Kjäll, J. H. Bardarson, and F. Pollmann, Many-body localization in a disordered quantum Ising chain, Phys. Rev. Lett. 113, 107204 (2014) 0031-9007 10.1103/PhysRevLett.113.107204.
A. Lucas, Ising formulations of many NP problems, Front. Phys. 2 (2014) 2296-424X 10.3389/fphy.2014.00005.
A. B. Harris, Effect of random defects on the critical behaviour of Ising models, J. Phys. C: Solid State Phys. 7, 1671 (1974) 0022-3719 10.1088/0022-3719/7/9/009.
J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics (Cambridge University Press, Cambridge, 1996).
D. S. Fisher, Random transverse field Ising spin chains, Phys. Rev. Lett. 69, 534 (1992) 0031-9007 10.1103/PhysRevLett.69.534.
D. S. Fisher, Critical behavior of random transverse-field Ising spin chains, Phys. Rev. B 51, 6411 (1995) 0163-1829 10.1103/PhysRevB.51.6411.
J. Dziarmaga, Dynamics of a quantum phase transition in the random Ising model: Logarithmic dependence of the defect density on the transition rate, Phys. Rev. B 74, 064416 (2006) 1098-0121 10.1103/PhysRevB.74.064416.
A. P. Young, S. Knysh, and V. N. Smelyanskiy, Size dependence of the minimum excitation gap in the quantum adiabatic algorithm, Phys. Rev. Lett. 101, 170503 (2008) 0031-9007 10.1103/PhysRevLett.101.170503.
A. P. Young, S. Knysh, and V. N. Smelyanskiy, First-order phase transition in the quantum adiabatic algorithm, Phys. Rev. Lett. 104, 020502 (2010) 0031-9007 10.1103/PhysRevLett.104.020502.
P. Bader, S. Blanes, F. Casas et al., An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation, Math. Comput. Simul. 194, 383 (2022) 0378-4754 10.1016/j.matcom.2021.12.002.
L. Zeng, J. Zhang, and M. Sarovar, Schedule path optimization for adiabatic quantum computing and optimization, J. Phys. A: Math. Theor. 49, 165305 (2016) 1751-8113 10.1088/1751-8113/49/16/165305.
J. Côté, F. Sauvage, M. Larocca et al., Diabatic quantum annealing for the frustrated ring model, Quantum Sci. Technol. 8, 045033 (2023) 2058-9565 10.1088/2058-9565/acfbaa.
G. Quiroz, Robust quantum control for adiabatic quantum computation, Phys. Rev. A 99, 062306 (2019) 2469-9926 10.1103/PhysRevA.99.062306.
A. G. R. Day, M. Bukov, P. Weinberg et al., Glassy phase of optimal quantum control, Phys. Rev. Lett. 122, 020601 (2019) 0031-9007 10.1103/PhysRevLett.122.020601.
X. Ge, R.-B. Wu, and H. Rabitz, The optimization landscape of hybrid quantum-classical algorithms: From quantum control to NISQ applications, Annu. Rev. Control. 54, 314 (2022) 1367-5788 10.1016/j.arcontrol.2022.06.001.
M. Dalgaard, F. Motzoi, and J. Sherson, Predicting quantum dynamical cost landscapes with deep learning, Phys. Rev. A 105, 012402 (2022) 2469-9926 10.1103/PhysRevA.105.012402.
N. Beato, P. Patil, and M. Bukov, Towards a theory of phase transitions in quantum control landscapes, arXiv:2408.11110.
S. Hernández-Gómez, F. Balducci, G. Fasiolo et al., Optimal control of a quantum sensor: A fast algorithm based on an analytic solution, SciPost Phys. 17, 004 (2024) 2542-4653 10.21468/SciPostPhys.17.1.004.