Non-unitary extension of Grover's search algorithm
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918468185489408 |
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| author | Lula-Rocha, V. N. A. Trindade, M. A. S. |
| author_facet | Lula-Rocha, V. N. A. Trindade, M. A. S. |
| contents | We have developed a non-unitary extension of Grover's search algorithm by changing the hidden geometry of Hilbert space carried by diffusion operator. Our algorithm finds the solution for search problem by performing a unique bigger rotation rather than small rotations in order polynomial times in the size $N$ of search space. We analyze the complexity of implementing the non-unitary operation and we observed that the price paid by performing this rotation is due the normalization. In Kraus operator approach we need $O(N)$ repetition of the algorithm to have a chance of measuring a solution in a post-selection, this is no better than the classical solution. However, the quantum singular value transform in addition with block encoding and Chebyshev polynomial approximation, we got complexity $O(\sqrt{N})$ and reach the Grover's bound with an extra resource of one single qubit, compared with the standard Grover's algorithm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23382 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-unitary extension of Grover's search algorithm Lula-Rocha, V. N. A. Trindade, M. A. S. Quantum Physics Mathematical Physics We have developed a non-unitary extension of Grover's search algorithm by changing the hidden geometry of Hilbert space carried by diffusion operator. Our algorithm finds the solution for search problem by performing a unique bigger rotation rather than small rotations in order polynomial times in the size $N$ of search space. We analyze the complexity of implementing the non-unitary operation and we observed that the price paid by performing this rotation is due the normalization. In Kraus operator approach we need $O(N)$ repetition of the algorithm to have a chance of measuring a solution in a post-selection, this is no better than the classical solution. However, the quantum singular value transform in addition with block encoding and Chebyshev polynomial approximation, we got complexity $O(\sqrt{N})$ and reach the Grover's bound with an extra resource of one single qubit, compared with the standard Grover's algorithm. |
| title | Non-unitary extension of Grover's search algorithm |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2604.23382 |