Tensor Train Multiplication (TTM)

Alexios A Michailidis, Christian Fenton, Martin Kiffner. We present the Tensor Train Multiplication (TTM) algorithm for the elementwise multiplication of two tensor trains with bond dimension χ. The computational complexity and memory requirements of the TTM algorithm scale as χ3 and χ2, respectively. This represents a significant improvement compared with the conventional approach, where the computational complexity scales as χ4 and memory requirements scale as χ3.We benchmark…
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The QCFD (Quantum Computational Fluid Dynamics) project is funded under the European Union’s Horizon Programme (HORIZON-CL4-2021-DIGITAL-EMERGING-02-10), Grant Agreement 101080085 QCFD.