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arXiv · 2512.15100

Exponential convergence dynamics in Grover's search algorithm

Samuel Cogan·Jonathan Raghoonanan·Tim Byrnes
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Abstract

Grover's search algorithm is the cornerstone of many applications of quantum computing, providing a quadratic speed-up over classical methods. One limitation of the algorithm is that it requires knowledge of the number of solutions to obtain an optimal success probability, due to the oscillatory dynamics between the initial and solution states (the ``souffl{\'e} problem''). While various methods have been proposed to solve this problem, each has its drawbacks in terms of inefficiency or sensitivity to control errors. Here, we modify Grover's algorithm so that, for suitably chosen parameters, the usual oscillatory dynamics are replaced by an approximately exponential convergence into the solution subspace. The basic idea is to couple the solution states to an engineered ancilla reservoir such that the initial state is nonreflectively absorbed. Trotterizing the continuous algorithm yields a quantum circuit that gives equivalent performance, while preserving the same quadratic quantum speedup as the original algorithm.

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Samuel Cogan, Jonathan Raghoonanan, Tim Byrnes. 2025-12-17. Exponential convergence dynamics in Grover's search algorithm. https://doi.org/10.1088/2058-9565%2Fae8df3

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