Preparation of Matrix Product States with Log-Depth Quantum Circuits.
Phys Rev Lett
; 132(4): 040404, 2024 Jan 26.
Article
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| MEDLINE
| ID: mdl-38335337
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=Ω(logN). We then introduce an algorithm based on the renormalization-group transformation to prepare normal MPS with an error ε in depth T=O[log(N/ε)], which is optimal. We also show that measurement and feedback leads to an exponential speedup of the algorithm to T=O[loglog(N/ε)]. 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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MEDLINE
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Phys Rev Lett
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2024
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Article
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Dinamarca