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A numerical approach for calculating exact non-adiabatic terms in quantum dynamics (2401.10985v2)

Published 19 Jan 2024 in quant-ph and cond-mat.str-el

Abstract: Understanding how non-adiabatic terms affect quantum dynamics is fundamental to improving various protocols for quantum technologies. We present a novel approach to computing the Adiabatic Gauge Potential (AGP), which gives information on the non-adiabatic terms that arise from time dependence in the Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an appropriate basis of the AGP, which can be easily truncated to give an approximate form when the exact result is intractable. We use this approach to study the AGP obtained for the transverse field Ising model on a variety of graphs, showing how the different underlying graph structures can give rise to very different scaling for the number of terms required in the AGP.

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References (70)
  1. M. Born and V. Fock, Beweis des adiabatensatzes, Zeitschrift für Physik 51(3-4), 165 (1928), 10.1007/BF01343193.
  2. T. Kato, On the adiabatic theorem of quantum mechanics, Journal of the Physical Society of Japan 5(6), 435 (1950), 10.1143/JPSJ.5.435.
  3. Quantum computation by adiabatic evolution, arXiv preprint quant-ph/0001106 (2000).
  4. Adiabatic quantum computation is equivalent to standard quantum computation, SIAM review 50(4), 755 (2008), 10.1137/080734479.
  5. T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018), 10.1103/RevModPhys.90.015002.
  6. G. E. Santoro and E. Tosatti, Optimization using quantum mechanics: quantum annealing through adiabatic evolution, Journal of Physics A: Mathematical and General 39(36), R393 (2006), 10.1088/0305-4470/39/36/R01.
  7. A. Das and B. K. Chakrabarti, Colloquium: Quantum annealing and analog quantum computation, Rev. Mod. Phys. 80, 1061 (2008), 10.1103/RevModPhys.80.1061.
  8. T. H. Johnson, S. R. Clark and D. Jaksch, What is a quantum simulator?, EPJ Quantum Technology 1(1), 1 (2014), 10.1140/epjqt10.
  9. Quantum simulators: Architectures and opportunities, PRX Quantum 2, 017003 (2021), 10.1103/PRXQuantum.2.017003.
  10. Quantum simulation, Rev. Mod. Phys. 86, 153 (2014), 10.1103/RevModPhys.86.153.
  11. Fast quantum gates for neutral atoms, Phys. Rev. Lett. 85, 2208 (2000), 10.1103/PhysRevLett.85.2208.
  12. One bound to rule them all: from adiabatic to zeno, Quantum 6, 737 (2022), 10.22331/q-2022-06-14-737.
  13. Shortcuts to adiabaticity, In Advances in atomic, molecular, and optical physics, vol. 62, pp. 117–169. Elsevier, 10.1016/B978-0-12-408090-4.00002-5 (2013).
  14. Shortcuts to adiabaticity: Concepts, methods, and applications, Rev. Mod. Phys. 91, 045001 (2019), 10.1103/RevModPhys.91.045001.
  15. J. Werschnik and E. Gross, Quantum optimal control theory, Journal of Physics B: Atomic, Molecular and Optical Physics 40(18), R175 (2007), 10.1088/0953-4075/40/18/R01.
  16. Training schrödinger’s cat: quantum optimal control, Eur. Phys. J. D 69(12), 1 (2015), 10.1140/epjd/e2015-60464-1.
  17. Quantum optimal control in quantum technologies. strategic report on current status, visions and goals for research in europe, EPJ Quantum Technology 9(1), 19 (2022), 10.1140/epjqt/s40507-022-00138-x.
  18. A tutorial on optimal control and reinforcement learning methods for quantum technologies, Physics Letters A 434, 128054 (2022), 10.1016/j.physleta.2022.128054.
  19. E. Crosson and D. Lidar, Prospects for quantum enhancement with diabatic quantum annealing, Nature Reviews Physics 3(7), 466 (2021), 10.1038/s42254-021-00313-6.
  20. J. E. Avron and A. Elgart, Adiabatic theorem without a gap condition, Communications in mathematical physics 203, 445 (1999), 10.1007/s002200050620.
  21. S. Teufel, A note on the adiabatic theorem without gap condition, Letters in Mathematical Physics 58, 261 (2001), 10.1023/A:1014556511004.
  22. M. Demirplak and S. A. Rice, Adiabatic population transfer with control fields, J. Phys. Chem. A 107(46), 9937 (2003), 10.1021/jp030708a.
  23. M. Demirplak and S. A. Rice, Assisted adiabatic passage revisited, The Journal of Physical Chemistry B 109(14), 6838 (2005), 10.1021/jp040647w.
  24. M. V. Berry, Transitionless quantum driving, Journal of Physics A: Mathematical and Theoretical 42(36), 365303 (2009), 10.1088/1751-8113/42/36/365303.
  25. D. Sels and A. Polkovnikov, Minimizing irreversible losses in quantum systems by local counterdiabatic driving, PNAS 114(20), E3909 (2017), 10.1073/pnas.1619826114.
  26. Geometry and non-adiabatic response in quantum and classical systems, Physics Reports 697, 1 (2017), https://doi.org/10.1016/j.physrep.2017.07.001, Geometry and non-adiabatic response in quantum and classical systems.
  27. Frictionless atom cooling in harmonic traps: A time-optimal approach, Phys. Rev. A 82, 063422 (2010), 10.1103/PhysRevA.82.063422.
  28. D. Stefanatos and E. Paspalakis, A shortcut tour of quantum control methods for modern quantum technologies, EPL 132(6), 60001 (2021), 10.1209/0295-5075/132/60001.
  29. Q. Zhang, X. Chen and D. Guéry-Odelin, Connection between inverse engineering and optimal control in shortcuts to adiabaticity, Entropy 23(1), 84 (2021), 10.3390/e23010084.
  30. Counterdiabatic optimized local driving, PRX Quantum 4, 010312 (2023), 10.1103/PRXQuantum.4.010312.
  31. 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), 10.1103/PhysRevX.11.031070.
  32. Perspectives of quantum annealing: Methods and implementations, Reports on Progress in Physics 83(5), 054401 (2020), 10.1088/1361-6633/ab85b8.
  33. Two-parameter counter-diabatic driving in quantum annealing, Phys. Rev. Res. 3, 013227 (2021), 10.1103/PhysRevResearch.3.013227.
  34. Counterdiabatic driving in the quantum annealing of the p𝑝pitalic_p-spin model: A variational approach, Phys. Rev. Res. 2, 013283 (2020), 10.1103/PhysRevResearch.2.013283.
  35. G. Passarelli and P. Lucignano, Counterdiabatic reverse annealing, Phys. Rev. A 107, 022607 (2023), 10.1103/PhysRevA.107.022607.
  36. S. Kumar, S. Sharma and V. Tripathi, Counterdiabatic route for preparation of state with long-range topological order, Phys. Rev. B 104, 245113 (2021), 10.1103/PhysRevB.104.245113.
  37. Q. Xie, K. Seki and S. Yunoki, Variational counterdiabatic driving of the hubbard model for ground-state preparation, Phys. Rev. B 106, 155153 (2022), 10.1103/PhysRevB.106.155153.
  38. Experimental realization of shortcuts to adiabaticity in a nonintegrable spin chain by local counterdiabatic driving, Phys. Rev. Appl. 13, 044059 (2020), 10.1103/PhysRevApplied.13.044059.
  39. Counterdiabatic control of transport in a synthetic tight-binding lattice, Phys. Rev. Res. 2, 043201 (2020), 10.1103/PhysRevResearch.2.043201.
  40. T. Hatomura and K. Takahashi, Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential, Phys. Rev. A 103, 012220 (2021), 10.1103/PhysRevA.103.012220.
  41. Scrambling and quantum chaos indicators from long-time properties of operator distributions, Phys. Rev. A 107, 032418 (2023), 10.1103/PhysRevA.107.032418.
  42. Adiabatic eigenstate deformations as a sensitive probe for quantum chaos, Phys. Rev. X 10, 041017 (2020), 10.1103/PhysRevX.10.041017.
  43. Defining classical and quantum chaos through adiabatic transformations, arXiv preprint arXiv:2401.01927 (2024).
  44. J. Wurtz and P. J. Love, Counterdiabaticity and the quantum approximate optimization algorithm, Quantum 6, 635 (2022), 10.22331/q-2022-01-27-635.
  45. Adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer, Phys. Rev. Res. 4, 033029 (2022), 10.1103/PhysRevResearch.4.033029.
  46. Digitized-counterdiabatic quantum approximate optimization algorithm, Phys. Rev. Res. 4, 013141 (2022), 10.1103/PhysRevResearch.4.013141.
  47. Variational schrieffer-wolff transformations for quantum many-body dynamics, Phys. Rev. B 101, 014302 (2020), 10.1103/PhysRevB.101.014302.
  48. Floquet-Engineering Counterdiabatic Protocols in Quantum Many-Body Systems, Phys. Rev. Lett. 123, 090602 (2019), 10.1103/PhysRevLett.123.090602.
  49. Ising machines as hardware solvers of combinatorial optimization problems, Nature Reviews Physics 4(6), 363 (2022), 10.1038/s42254-022-00440-8.
  50. A. Lucas, Ising formulations of many NP problems, Frontiers in Physics 2 (2014), 10.3389/fphy.2014.00005, ArXiv:1302.5843 [cond-mat, physics:quant-ph].
  51. Quantum optimization of maximum independent set using rydberg atom arrays, Science 376(6598), 1209 (2022), 10.1126/science.abo6587.
  52. Validity of the adiabatic approximation in quantum mechanics, Phys. Rev. A 76, 044102 (2007), 10.1103/PhysRevA.76.044102.
  53. A. del Campo, Shortcuts to adiabaticity by counterdiabatic driving, Phys. Rev. Lett. 111, 100502 (2013), 10.1103/PhysRevLett.111.100502.
  54. 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), 10.1103/PhysRevLett.109.115703.
  55. B. Damski, Counterdiabatic driving of the quantum ising model, Journal of Statistical Mechanics: Theory and Experiment 2014(12), P12019 (2014), 10.1088/1742-5468/2014/12/P12019.
  56. Quantum annealing for industry applications: Introduction and review, Reports on Progress in Physics (2022), 10.1088/1361-6633/ac8c54.
  57. Quantum annealing: An overview, Philosophical Transactions of the Royal Society A 381(2241), 20210417 (2023), 10.1098/rsta.2021.0417.
  58. Quantum annealing with manufactured spins, Nature 473(7346), 194 (2011), 10.1038/nature10012.
  59. Defining and detecting quantum speedup, science 345(6195), 420 (2014).
  60. T. Albash and D. A. Lidar, Demonstration of a scaling advantage for a quantum annealer over simulated annealing, Phys. Rev. X 8, 031016 (2018), 10.1103/PhysRevX.8.031016.
  61. Probing entanglement in adiabatic quantum optimization with trapped ions, Frontiers in Physics 3, 21 (2015), 10.3389/fphy.2015.00021.
  62. Quantum annealing for the number-partitioning problem using a tunable spin glass of ions, Nature communications 7(1), 11524 (2016), 10.1038/ncomms11524.
  63. Semiclassical approach to finite-temperature quantum annealing with trapped ions, Phys. Rev. A 97, 052310 (2018), 10.1103/PhysRevA.97.052310.
  64. A coherent quantum annealer with rydberg atoms, Nature communications 8(1), 15813 (2017), 10.1038/ncomms15813.
  65. P. Erdős and A. Rényi, Asymmetric graphs, Acta Math. Hung. 14(3-4), 295 (1963).
  66. Validity of many-body approximation methods for a solvable model:(i). exact solutions and perturbation theory, Nuclear Physics 62(2), 188 (1965), 10.1016/0029-5582(65)90862-X.
  67. K. Takahashi and A. del Campo, Shortcuts to adiabaticity in krylov space, arXiv (2023), 2302.05460.
  68. On the self-dual normal bases and their distribution, Linear Algebra and its Applications 457, 179 (2014), https://doi.org/10.1016/j.laa.2014.05.025.
  69. Quantum error correction via codes over gf(4), IEEE Transactions on Information Theory 44(4), 1369 (1998), 10.1109/18.681315.
  70. Analytical inversion of symmetric tridiagonal matrices, Journal of Physics A: Mathematical and General 29(7), 1511 (1996), 10.1088/0305-4470/29/7/020.
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