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• W2513011489 abstract "Solving the Toeplitz systems, which is to find the vector $x$ such that $T_nx = b$ given a $ntimes n$ Toeplitz matrix $T_n$ and a vector $b$, has a variety of applications in mathematics and engineering. In this paper, we present a quantum algorithm for solving the Toeplitz systems, in which a quantum state encoding the solution with error $epsilon$ is generated. It is shown that our algorithm's complexity is nearly linear in the condition number, and polylog in the dimensions $n$ and in the inverse error $epsilon^{-1}$. This implies our algorithm is exponentially faster than the best classical algorithm for the same problem if the condition number of $T_n$ is $O(textrm{poly}(textrm{log},n))$. Since no assumption on the sparseness of $T_n$ is demanded in our algorithm, the algorithm can serve as an example of quantum algorithms for solving non-sparse linear systems." @default.
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• W2513011489 date "2016-08-07" @default.
• W2513011489 modified "2023-09-27" @default.
• W2513011489 title "Quantum Algorithm for the Toeplitz Systems" @default.
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