Preparation of matrix product states with log-depth quantum circuits

• URL: http://arxiv.org/abs/2307.01696v2
• Date: Thu, 25 Jan 2024 08:23:19 GMT
• Title: Preparation of matrix product states with log-depth quantum circuits
• Authors: Daniel Malz, Georgios Styliaris, Zhi-Yuan Wei, J. Ignacio Cirac
• Abstract summary: 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.
• Score: 0.3277163122167433
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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