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  • Open Access

Constant geometric speed schedule for adiabatic state preparation

Mancheon Han1,*, Hyowon Park2,3, and Sangkook Choi1,†

  • *Contact author: mchan@kias.re.kr
  • †Contact author: sangkookchoi@kias.re.kr
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Phys. Rev. Research 8, 023233 – Published 1 June, 2026

DOI: https://doi.org/10.1103/ygs3-xgb1

Abstract

The efficiency of adiabatic quantum evolution is governed by the evolution time T, which typically scales as O(Δ−2) with the minimum energy gap Δ. However, the rigorous lower bound is O(LΔ−1), where L is the adiabatic path length. Although L is formally upper bounded by O(Δ−1), such a bound is often too loose in practice, and L can be bounded independently of Δ. This indicates the potential for a quadratic speedup through adiabatic schedule construction. Here, we introduce the constant geometric speed (CGS) schedule, which traverses the adiabatic path at a uniform rate. We show that this approach reduces the scaling of the evolution time by a factor of Δ−1, provided L remains bounded independently of Δ. We propose a segmented CGS protocol where path segment lengths are computed from eigenstate overlaps on the fly, reducing the prior spectral-knowledge requirement from the full gap function Δ(s) to just a global lower bound on the energy gap. Numerical tests on adiabatic unstructured search, N2, and a [2Fe-2S] cluster demonstrate the optimal Δ−1 scaling, confirming a quadratic speedup over the standard linear schedule.

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Phys. Rev. Research 8, 023233– Published 1 June, 2026
  • Received 29 October 2025
  • Revised 3 February 2026
  • Accepted 9 May 2026
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