Abstract
We consider the quantum linear solver for Ax = b with the circulant preconditioner C. The main technique is the singular value estimation (SVE) introduced in [Kerenidis and Prakash, Quantum recommendation system, in ITCS (2017)]. However, the SVE should be modified to solve the preconditioned linear system $C^{-1}Ax =
C^{-1}b$. Moreover, different from the preconditioned linear system considered in [Phys. Rev. Lett. 110, 250504 (2013)], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of $C$ and $C^{-1}A$, as well as the Frobenius norm $\|A\|_F$ .
C^{-1}b$. Moreover, different from the preconditioned linear system considered in [Phys. Rev. Lett. 110, 250504 (2013)], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of $C$ and $C^{-1}A$, as well as the Frobenius norm $\|A\|_F$ .
| Original language | English |
|---|---|
| Pages (from-to) | 062321 |
| Number of pages | 9 |
| Journal | Physical Review A |
| Volume | 98 |
| DOIs | |
| Publication status | Published - 18 Dec 2018 |