2025-09-25 東京大学
低エネルギー状態のダイナミクスを計算する量子アルゴリズムの概念図
＜関連情報
- https://www.t.u-tokyo.ac.jp/press/pr2025-09-25-002
- https://www.t.u-tokyo.ac.jp/hubfs/press-release/2025/0925/002/text.pdf
- https://journals.aps.org/prl/abstract/10.1103/q87n-5xhz
トロッター化は低エネルギー状態に対して非常に効率的である Trotterization is Substantially Efficient for Low-Energy States
Kaoru Mizuta and Tomotaka Kuwahara
Physical Review Letters Published: 23 September, 2025
DOI: https://doi.org/10.1103/q87n-5xhz
Abstract
Trotterization is one of the central approaches for simulating quantum many-body dynamics on quantum computers or tensor networks. In addition to its simple implementation, recent studies have revealed that its error and cost can be reduced if the initial state is closed in the low-energy subspace. However, the improvement by the low-energy property diminishes rapidly as the Trotter order grows in the previous studies, and thus, it is mysterious whether there exists a genuine advantage of low-energy initial states. In this Letter, we resolve this problem by proving the optimal error bound and cost of Trotterization for low-energy initial states. For generic local Hamiltonians composed of positive-semidefinite terms, we show that the Trotter error is at most linear in the initial state energy Δ and polylogarithmic in the system size . As a result, the computational cost becomes substantially small for low-energy states with Δ ∈o(Ng) compared to the one for arbitrary initial states, where denotes the energy per site and Ng means the whole-system energy. Our error bound and cost of Trotterization achieve the theoretically best scaling in the initial state energy Δ. In addition, they can be partially extended to weakly correlated initial states having low-energy expectation values, which are not necessarily closed in the low-energy subspace. Our results will pave the way for fast and accurate simulations of low-energy states, which are one of the central targets in condensed matter physics and quantum chemistry.
