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1. The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver

   https://doi.org/10.22331/q-2025-10-20-1887  

   Costa, Pedro CS; An, Dong; Babbush, Ryan; Berry, Dominic (October 2025, Quantum)

   The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $\kappa$and the allowable error $ϵ$\cite{CostaAnYuvalEtAl2022}. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,200 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is about an order of magnitude more efficient than using a randomised approach from \cite{jennings2023efficient} that claimed to be more efficient. 

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2. Fast forward to the classical adiabatic invariant

   https://doi.org/10.1103/PhysRevE.95.032122  

   Jarzynski, Christopher; Deffner, Sebastian; Patra, Ayoti; Subaşı, Yiğit (March 2017, Physical Review E)
3. Non-adiabatic Matsubara dynamics and non-adiabatic ring-polymer molecular dynamics

   https://doi.org/10.1063/5.0042136  

   Chowdhury, Sutirtha N.; Huo, Pengfei (March 2021, The Journal of Chemical Physics)
4. On adiabatic subtraction in an inflating Universe

   https://doi.org/10.1088/1475-7516/2023/07/005  

   Corbà, Sofia P.; Sorbo, Lorenzo (July 2023, Journal of Cosmology and Astroparticle Physics)

   Abstract Adiabatic subtraction is a popular method of renormalization of observables in quantum field theories on a curved spacetime. When applied to the computation of the power spectra of light ( m ≪ H ) fields on de Sitter space with flat Friedmann-Lemaître-Robertson-Walker slices, the standard prescriptions of adiabatic subtraction, traceable back to [1,2], lead to results that are significantly different from the standard expectations not only in the ultraviolet ( k ≫ aH ) but also at intermediate ( m ≪ k / a ≲ H ) wavelengths. In this paper we review those results and we contrast them with the power spectra obtained using an alternative prescription for adiabatic subtraction applied to quantum field theoretical systems by Dabrowski and Dunne [3,4]. This prescription eliminates the intermediate-wavelength effects of renormalization that are found when using the standard one. 

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5. Freeze-in dark matter perturbations are adiabatic

   https://doi.org/10.1088/1475-7516/2023/01/020  

   Racco, D.; Riotto, A. (January 2023, Journal of Cosmology and Astroparticle Physics)

   Abstract We show that the large-scale perturbations in the dark matter generated by the freeze-in mechanism are only of adiabatic nature. The freeze-in mechanism is not at odds with the current stringent constraints on isocurvature perturbations. 

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