Polynomial-depth quantum algorithm for computing matrix determinant
| Autor: | Zenchuk, Alexander I., Qi, Wentao, Kumar, Asutosh, Wu, Junde |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We propose an algorithm for calculating the determinant of a square matrix, and construct the quantum circuit realizing it, using multiqubit control gates (representable in terms of Toffoli gates, CNOTs and SWAPs), Hadamard transformations and $Z$-operators. Each row of the matrix is encoded as a pure state of some quantum system. The admitted matrix is therefore arbitrary up to the normalization of quantum states of those systems. The depth of the proposed algorithm is $O(N^3\log \, N)$ for the $N\times N$ matrix. Comment: 8 pages, 3 figures, minor change in presentation |
| Databáze: | arXiv |
| Externí odkaz: |
|