Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization

TL;DR

This paper demonstrates the use of Tensor Processing Units (TPUs) for large-scale, high-fidelity simulations of quantum many-body dynamics, specifically Floquet prethermalization, achieving significant speedups and efficiency over traditional hardware.

Contribution

The authors develop methods to leverage TPUs for simulating quantum dynamics on long timescales, enabling simulations of up to 40 qubits with high efficiency and demonstrating advantages over GPUs and CPUs.

Findings

Achieved 230x speedup over CPU and 15x over GPU for 30-qubit simulations.

Simulated 34 qubits for over 10^5 Floquet periods, involving millions of gates.

TPU clusters are more energy and cost-efficient than large GPU setups.

Abstract

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.