Volume 141, Number 5, March 2023
|Number of page(s)||5|
|Published online||22 February 2023|
Phase matching in quantum search algorithm
Beam Technology Development Group, Bhabha Atomic Research Centre - Mumbai-400085, India
(a) E-mail: firstname.lastname@example.org (corresponding author)
Received: 11 November 2022
Accepted: 8 February 2023
We systematically generalize the Grover algorithm in a density matrix formalism by exploiting the underlying two-dimensional subspace of the problem. Using this, we derive analytic expressions for the success probability after arbitrary iterations of the generalized Grover operator with two generic phase angles . We show for the phase matching condition with three iterations, success probability can be achieved only with knowledge about the lower bound , where λ is the ratio of marked to total number of states in the database. This result will improve the quantum search algorithm when applied to databases with unknown number of marked states in the specified regime of λ, at the cost of decreased efficiency in the smaller λ region.
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