Abstract
The HHL algorithm for matrix inversion is a landmark algorithm in quantum computation. Its ability to produce a state |x> that is the solution of Ax=b, given the input state |b>, is envisaged to have diverse applications. In this paper, we substantially simplify the algorithm, originally formed of a complex sequence of phase estimations, amplitude amplifications and Hamiltonian simulations, by replacing the phase estimations with a continuous time quantum walk. The key technique is the use of weak couplings to access the matrix inversion embedded in perturbation theory.
| Original language | English |
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| Number of pages | 7 |
| Publication status | Submitted - 8 Aug 2025 |