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Human mobility prediction plays a critical role in applications such as disaster response, urban planning, and epidemic forecasting. Traditional methods often rely on designing crafted, domain-specific models, and typically focus on short-term predictions, which struggle to generalize across diverse urban environments. In this study, we introduce Llama-3-8B-Mob, a large language model fine-tuned with instruction tuning, for long-term citywide mobility prediction -- in a Q&A manner. We validate our approach using large-scale human mobility data from four metropolitan areas in Japan, focusing on predicting individual trajectories over the next 15 days. The results demonstrate that Llama-3-8B-Mob excels in modeling long-term human mobility -- surpassing the state-of-the-art on multiple prediction metrics. It also displays strong zero-shot generalization capabilities -- effectively generalizing to other cities even when fine-tuned only on limited samples from a single city. Source codes are available at this https URL.

[Note: After the first version of this manuscript was uploaded, the authors of [Berta, Brandão, Gour, Lami, Plenio, Regula, and Tomamichel, Quantum 7, 1103 (2023)] pointed out an issue about a part of the claims in the previous version of [Bluhm, Capel, Gondolf, Pérez-Hernández, IEEE Trans. Inf. Theory 69, 5869 (2023)] used in our analysis. Due to this issue, the analysis in the previous version of this manuscript can no longer be considered complete proof of the generalized quantum Stein's lemma. This version is a temporal update to add this note. We are planning to update the manuscript further to explain the issue and what conditions we will additionally need to complete the proof of the generalized quantum Stein's lemma.]

Reducing space and time overheads of fault-tolerant quantum computation (FTQC) has been receiving increasing attention as it is crucial for the development of quantum computers and also plays a fundamental role in understanding the feasibility and limitations of realizing quantum advantages. Shorter time overheads are particularly essential for demonstrating quantum computational speedups without compromising runtime advantages. However, surpassing the conventional polylogarithmic (polylog) scaling of time overheads has remained a significant challenge, since it requires addressing all potential bottlenecks, including the nonzero runtime of classical computation for decoding in practical implementations. In this work, we construct a protocol that achieves FTQC with doubly polylog time overhead while maintaining the conventional polylog space overhead. The key to our approach is the development of a highly parallelizable minimum-weight perfect matching (MWPM) decoder, which achieves a polylog parallel runtime in terms of the code size while providing theoretical guarantees on threshold existence and overhead bounds. Our protocol integrates this decoder with a topological-code protocol that incorporates single-shot decoding for efficient syndrome extraction; furthermore, we concatenate this with the concatenated Steane codes to guarantee the existence of the threshold while avoiding a backlog problem, enabling us to achieve doubly polylog time overheads even when accounting for the decoder's runtime. These results suggest the feasibility of surpassing the conventional polylog-time-overhead barrier, opening a new frontier in low-overhead FTQC.