Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization
| Autor: | Morningstar, Alan, Hauru, Markus, Beall, Jackson, Ganahl, Martin, Lewis, Adam G. M., Khemani, Vedika, Vidal, Guifre |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | PRX Quantum 3, 020331 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PRXQuantum.3.020331 |
| Popis: | Tensor Processing Units (TPUs) are specialized hardware accelerators developed by Google to support large-scale machine-learning tasks, but they can also be leveraged to accelerate and scale other linear-algebra-intensive computations. In this paper we demonstrate the usage of TPUs for massively parallel, classical simulations of quantum many-body dynamics on long timescales. We apply our methods to study the phenomenon of Floquet prethermalization, i.e., exponentially slow heating in quantum spin chains subject to high-frequency periodic driving. We simulate the dynamics of L=34 qubits for over $10^5$ Floquet periods, corresponding to circuits with millions of two-qubit gates. The circuits simulated have no additional symmetries and represent a pure-state evolution in the full $2^L$-dimensional Hilbert space. This is achieved by distributing the computation over 128 TPU cores. On that size TPU cluster, we find speedups in wall-clock runtime of 230x and 15x when compared to reference CPU and single-GPU simulations, respectively, for shorter 30-qubit simulations that can be handled by all three platforms. We study the computational cost of the simulations, as a function of both the number of qubits and the number of TPU cores used, up to our maximum capacity of L=40 qubits, which requires a ``full pod" of 2048 TPU cores with tens of terabytes of memory in total. For these simulations, an 8-TPU-core machine is comparable to a single A100 GPU, and thus the full TPU pod is comparable to a machine with hundreds of GPUs. However, the TPU pod is more energy and cost efficient, and readily accessible (via Google Cloud), unlike such large many-GPU configurations. We also study the accumulation of numerical error as a function of circuit depth in very deep circuits. Our work demonstrates that TPUs can offer significant advantages for state-of-the-art simulations of quantum many-body dynamics. Comment: 12 pages, 7 figures; v2 contains substantial improvements including GPU simulations |
| Databáze: | arXiv |
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