Shortcuts to Adiabaticity in Krylov Space

Takahashi, Kazutaka; del Campo, Adolfo

doi:10.1103/physrevx.14.011032

Cited by 7 publications

(3 citation statements)

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“…As mentioned in section 1, we use a condition for the counterdiabatic Hamiltonian [24] as a cost function and optimize a trial counterdiabatic Hamiltonian by minimizing it. Recently, direct approaches to the condition for the counterdiabatic Hamiltonian [65][66][67] and detailed analysis of the variational approach [68] were considered. These results give a set of linear equations…”

Section: Approximate Construction Of Counterdiabatic Drivingmentioning

confidence: 99%

“…Recently, application of the Lanczos algorithm to construction of the counterdiabatic Hamiltonian was proposed [66,67]. In this approach, we solve equation ( 54) using the Krylov basis instead of the basis operators.…”

Section: Then We Can Express a Trial Counterdiabatic Hamiltonian Asmentioning

confidence: 99%

“…multiple Pauli matrices with an odd number of the Pauli-Y in multi-qubits systems consisting of the Pauli-X and the Pauli-Z. The Krylov approach [66,67] is advantageous because the matrix B is the tri-diagonal matrix and the set of linear equations (51) can effectively be solved, but the generation of the Krylov basis and determination of the coefficients may be complicated in some cases. We can use appropriate ones depending on given situations.…”

Section: Unified Viewpointmentioning

confidence: 99%

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Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations

Hatomura

2024

J. Phys. B: At. Mol. Opt. Phys.

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Shortcuts to adiabaticity guide given systems to final destinations of adiabatic control via fast tracks. Various methods were proposed as varieties of shortcuts to adiabaticity. Basic theory of shortcuts to adiabaticity was established in the 2010s, but it has still been developing and many fundamental findings have been reported. In this Topical Review, we give a pedagogical introduction to theory of shortcuts to adiabaticity and revisit relations between different methods. Some versatile approximations in counterdiabatic driving, which is one of the methods of shortcuts to adiabaticity, will be explained in detail. We also summarize recent progress in studies of shortcuts to adiabaticity.

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Section: Approximate Construction Of Counterdiabatic Drivingmentioning

confidence: 99%

Section: Then We Can Express a Trial Counterdiabatic Hamiltonian Asmentioning

confidence: 99%

Section: Unified Viewpointmentioning

confidence: 99%

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Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations

Hatomura

2024

J. Phys. B: At. Mol. Opt. Phys.

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Approximate constructions of counterdiabatic driving with NMR quantum systems

Zhou 周,

Dai 代,

Geng 耿

et al. 2024

Chinese Phys. B

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Counterdiabatic driving (CD) offers a fast and robust route to manipulate quantum systems, which has widespread applications in quantum technologies. However, for higher-dimensional complex systems, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form, impeding its experimental realization. Recently, many approximate methods have been proposed for designing CD passages in many-body systems. In this topical review, we focus on the CD formalism and briefly introduce several experimental constructions and applications of approximate CD driving in spin-chain models with nuclear magnetic resonance (NMR) systems.

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