A quantized tensor network framework reduces the cost of 5D Vlasov-Maxwell simulations from O(N) to O(poly(D)) with D=64 sufficient for N=2^36 grid points.
To do this, one simply pads the original QTT with a tensor train of identity matrices for the remaining dimensions
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Quantized tensor networks for solving the Vlasov-Maxwell equations
A quantized tensor network framework reduces the cost of 5D Vlasov-Maxwell simulations from O(N) to O(poly(D)) with D=64 sufficient for N=2^36 grid points.