Matrix Inversion by Quantum Walk
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909730606153728 |
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| author | Kay, Alastair Tamon, Christino |
| author_facet | Kay, Alastair Tamon, Christino |
| contents | The HHL algorithm for matrix inversion is a landmark algorithm in quantum computation. Its ability to produce a state $|x\rangle$ that is the solution of $Ax=b$, given the input state $|b\rangle$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix Inversion by Quantum Walk Kay, Alastair Tamon, Christino Quantum Physics The HHL algorithm for matrix inversion is a landmark algorithm in quantum computation. Its ability to produce a state $|x\rangle$ that is the solution of $Ax=b$, given the input state $|b\rangle$, 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. |
| title | Matrix Inversion by Quantum Walk |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.06611 |