Preparation of Matrix Product States with Log-Depth Quantum| Malz, Styliaris, Wei, Cirac | TQC 2024

Описание: Preparation of Matrix Product States with Log-Depth Quantum Circuits| Daniel Malz, Georgios Styliaris, Zhi-Yuan Wei, J. Ignacio Cirac

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.

TQC 2024 | 9-13 September 2024 at OIST, Japan
http://tqc-conference.org

19th Conference on the Theory of Quantum Computation, Communication and Cryptography.

TQC is a leading annual international conference for students and researchers working in the theoretical aspects of quantum information science. The scientific objective is to bring together the theoretical quantum information science community to present and discuss the latest advances in the field.


Organisation:
OIST: Okinawa Institute for Science and Technology
Squids: Schools for Quantum Information Development



Sponsors:
JPMorganChase
Google Quantum AI
Horizon Quantum Computing
Quantinuum
Japan National Tourism Organization