An improved method for quantum matrix multiplication. (English) Zbl 1542.68068
Summary: Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), A. M. Childs et al. [SIAM J. Comput. 46, No. 6, 1920–1950 (2017; Zbl 1383.68034)] provided an approach to solve a linear system of equations with exponentially improved dependence on precision. In this note, we aim to complement such a result for applying a matrix to some quantum state, based upon their Chebyshev polynomial approach. A few examples that motivate this application are included, and we further discuss an application of this improved matrix application algorithm explicitly with an efficient quantum procedure.
MSC:
| 68Q12 | Quantum algorithms and complexity in the theory of computing |
| 65F05 | Direct numerical methods for linear systems and matrix inversion |
| 65Y10 | Numerical algorithms for specific classes of architectures |
| 81P68 | Quantum computation |
Citations:
Zbl 1383.68034References:
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