A proposed protocol for simulating quantum systems across separate processors could make shared-entanglement use track the strength of interactions between them, rather than charge the same amount for every nonlocal operation. In the fixed-order product-formula setting studied, the expected cost of its repeat-until-success method grows linearly with simulated time and remains independent of the number of Trotter segments, apart from constants set by the formula. The approach targets a central problem in distributed quantum simulation: coordinating parts of a calculation held by different parties while limiting the entanglement they share.
The document is an arXiv preprint, version v1, dated 26 August 2026.
A weaker link for a weaker interaction
The model divides a quantum network into two parties, A and B. Each party carries out local dynamics, while some interaction terms cross the divide. The simulation uses a product formula, commonly called Trotterization, which breaks the evolution into repeated short segments. Increasing the number of segments reduces the duration of each step and systematically improves the approximation.
To implement a cross-party Pauli rotation, the protocol prepares a weakly entangled shared state and performs controlled-Pauli operations locally. The parties then measure parity in the Hadamard basis. An even result implements the desired rotation; an odd-parity result applies the inverse, after which the protocol tries again with the rotation angle doubled. The adaptive design is meant to match the shared entanglement to the rotation’s strength.
For any cutoff of at least one round and any rotation angle with magnitude at most 1, the paper bounds the truncated protocol’s entanglement cost by 9 times the angle’s magnitude. The appendix also states that, once the cutoff reaches a constant-angle correction scale, the proposed protocol has linear, or Θ(|θ|), scaling with the rotation angle. These are analytical bounds rather than measured estimates.
The contrast with teleportation
Standard teleportation-based implementation uses a fixed cost of 2 ebits for each nonlocal gate. In the full product-formula accounting, its cost also carries inverse-error and superlinear-time factors, written in the analysis as ε−1/q and t1+1/q. The analyzed RUS cost behaves differently: at fixed evolution time, reducing the target error leaves it constant, while teleportation cost grows as ε−1/q and diverges as the target error approaches 0.
The comparison is asymptotic, with fixed prefactors omitted. The RUS total-cost statement applies within the fixed-order product-formula model and under the angle assumptions used for the bound. The result therefore describes scaling for the analyzed construction, rather than a cost guarantee for every simulation method.
A linear-time limit, but only for some cases
The study also examines whether the linear dependence on evolution time can be improved. A communication-complexity argument supplies an Ω(t) lower bound on communication, and therefore on entanglement, for some bipartite Hamiltonian-simulation instances when the simulation has constant error and lies in the stated regime ∥H∥t ≤ n. Combined with the protocol’s linear upper bound, this gives Θ(t) time scaling for those cases. Because the lower bound is existential, it does not establish optimality for every Hamiltonian or implementation.
The unanswered network question
The construction formally extends to genuinely multipartite Pauli rotations using weak GHZ-type resources. The same angle-doubling protocol gives a success probability of 1 − 2^−K after K rounds, but the cost of preparing and distributing those resources depends on network topology and is not fully characterized. That leaves the resource burden of extending the method beyond two parties unresolved.
The analysis says exact preparation of the weak resource states is unnecessary because finite-preparation error can be absorbed into the overall simulation error budget. This addresses approximation of the resource itself, while the multipartite preparation cost remains dependent on how the network is connected.
For a K-round implementation covering M nonlocal attempts, a union-bound calculation gives circuit success probability of at least 1 − M·2^−K. The expression provides a way to control aggregate failure across the repeated protocol while keeping the result within its stated analytical setting.
Paper data and sources
Original title: Distributed Trotterization with optimal time-scaling entanglement cost
Authors: Tianfeng Feng, Jinzhao Sun, Yunlong Xiao, Qi Zhao
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text