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Tensor Processing Units (TPUs) were developed by Google exclusively tosupport large-scale machine learning tasks. TPUs can, however, also be used toaccelerate and scale up other computationally demanding tasks. In this paper werepurpose TPUs for the challenging problem of simulating quantum spin systems.Consider a lattice model made of $N$ spin-$\frac{1}{2}$ quantum spins, orqubits, with a Hamiltonian $H = \sum_i h_i$ that is a sum of local terms $h_i$and a wavefunction $|\Psi\rangle$ consisting of $2^N$ complex amplitudes. Wedemonstrate the usage of TPUs for both (i) computing the ground state$|\Psi_{gs}\rangle$ of the Hamiltonian $H$, and (ii) simulating the timeevolution $|\Psi(t)\rangle=e^{-itH}|\Psi(0)\rangle$ generated by thisHamiltonian starting from some initial state $|\Psi(0)\rangle$. The bottleneckof the above tasks is computing the product $H |\Psi\rangle$, which can beimplemented with remarkable efficiency utilising the native capabilities ofTPUs. With a TPU v3 pod, with 2048 cores, we simulate wavefunctions$|\Psi\rangle$ of up to $N=38$ qubits. The dedicated matrix multiplicationunits (MXUs), the high bandwidth memory (HBM) on each core, and the fastinter-core interconnects (ICIs) together provide performance far beyond thecapabilities of general purpose processors.

Simulation of quantum physics with Tensor Processing Units: brute-force computation of ground states and time evolution