2026/06/30 by Eugene Dumitrescu
Physics and Astronomy · #quant-ph
8 pages, 3 figures, comments welcome
arxiv created 2026/07/31 · arxiv updated 2026/08/03
We develop a block-encoding compiler that treats matrix product operators as compressed, virtual-path linear combination of unitaries programs. The compiler constructs conditional PREP and local SELECT stages directly from a parent matrix product operator, establishing tensor networks as structured quantum intermediate representations that can be efficiently compiled to block-encoded circuits. We apply the construction to real-time evolution in the Heisenberg chain and two perturbed Heisenberg-family models. Across the regimes studied, the compressed, approximately unitary propagator MPOs retain mild bond dimension and LCU normalization. Relative to an LCU that explicitly lists the \(O(NK)\) Pauli-product branches of an order-\(K\) truncated Taylor polynomial, our virtual-transition implementation replaces combinatorial branch enumeration by a circuit complexity scaling as \(O(α\rm MPONχ2)\), approaching \(O(Nχ2)\) when \(α\rm MPO\) remains mild. We numerically characterize how truncation order, bond-dimension budget, and system size affect approximation error, normalization, and compiler cost. These results demonstrate how classically compressed tensor-network representations can serve as quantum compiler intermediate representations for block encoding and opens new avenues to accelerate quantum algorithms.