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arXiv:2512.17780

Adiabatic preparation of many-body quantum states: getting the beginning and ending right

Emil T. M. Pedersen, Freek Witteveen, Klaus Mølmer, Matthias Christandl

quant-phSubmitted Dec 19, 2025• Announced Dec 22, 2025• 0 citations
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Abstract

We present numerical calculations, and simulations performed on a Rydberg atom quantum simulator, of the adiabatic evolution of many-body quantum systems around a quantum phase transition. We demonstrate that the end-to-end transfer error, for a given process duration and dissipative losses, can be suppressed by adopting smooth initial and final scheduling functions for the Hamiltonian. We consider a one-dimensional mixed-field Ising model, as well as a chain of Rydberg atoms, and compare numerical calculations and experimental results for the end-to-end transfer error with different schedule functions. We show, in particular, that if the time dependent Hamiltonian is $n$ times differentiable with vanishing $1^{st}$ to $n^{th}$ order derivatives in the beginning and in the end, the infidelity with respect to the final adiabatic eigenstate scales as $1/T^{n+1}$ when evolving for time $T$.

Comments
8 pages, 5 figures

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The adiabatic theorem of quantum mechanics states that the error between an instantaneous eigenstate of a time-dependent Hamiltonian and the state given by quantum evolution of duration $\ensuremath{\tau}$ is upper bounded by $C/\ensuremath{\tau}$ for some positive constant CCC. It has been known for decades that this error can be reduced to ${C}_{k}/{\ensuremath{\tau}}^{k+1}$ if the Hamiltonian has vanishing derivatives up to order kkk at the beginning and end of the evolution. Here we extend this result to open systems described by a time-dependent Liouvillian superoperator. We find that the same results holds provided the Liouvillian has vanishing derivatives up to order kkk only at the end of the evolution. This asymmetry is ascribable to the arrow of time inherent in open system evolution. We further investigate whether it is possible to satisfy the required assumptions by controlling only the system, as required for realistic implementations. Surprisingly, we find the answer to be affirmative. We establish this rigorously in the setting of the Davies-Lindblad adiabatic master equation, and numerically in the setting of two different time-dependent Redfield-type master equations we derive. The results are shown to be stable with respect to imperfections in the preparation. Finally, we prove that the results hold also in a fully Hamiltonian model.