Non-unitary extension of Grover's search algorithm

• URL: http://arxiv.org/abs/2604.23382v1
• Date: Sat, 25 Apr 2026 17:13:50 GMT
• Title: Non-unitary extension of Grover's search algorithm
• Abstract summary: We develop a non-unitary extension of Grover's search algorithm.<n>Our algorithm finds the solution for search problem by performing a unique bigger rotation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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