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arXiv · 2307.01696

Preparation of matrix product states with log-depth quantum circuits

Daniel Malz·Georgios Styliaris·Zhi-Yuan Wei·J. Ignacio Cirac
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Abstract

We consider the preparation of matrix product states (MPS) on quantum devices via quantum circuits of local gates. We first prove that faithfully preparing translation-invariant normal MPS of $N$ sites requires a circuit depth $T=\Omega(\log N)$. We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error $\epsilon$ in depth $T=O(\log (N/\epsilon))$, which is optimal. We also show that measurement and feedback leads to an exponential speedup of the algorithm, to $T=O(\log\log (N/\epsilon))$. Measurements also allow one to prepare arbitrary translation-invariant MPS, including long-range non-normal ones, in the same depth. Finally, the algorithm naturally extends to inhomogeneous MPS.

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Daniel Malz, Georgios Styliaris, Zhi-Yuan Wei, J. Ignacio Cirac. 2023-07-04. Preparation of matrix product states with log-depth quantum circuits. https://doi.org/10.1103/physrevlett.132.040404

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