Abstract
The quantum search algorithm is a technique for searching N possibilities in only O(√N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schrödinger’s equation. This paper also provides a self contained introduction to quantum computing algorithms from a new perspective.
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References
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For an N-state system, in order for the terms in each row to sum to unity, the diagonal terms of D should be (1 − i(N − 1)ε). However, for simplicity, we write this as (1 − iNε). For N large, the error due to this is negligible
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A preliminary version of this paper was presented in the Winter Institute of Foundations of Quantum Theory in January 2000. A modified version of this has been accepted for publication in the American Journal of Physics and will appear sometime in the period July–September 2000.
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Grover, L.K. From Schrödinger’s equation to the quantum search algorithm. Pramana - J Phys 56, 333–348 (2001). https://doi.org/10.1007/s12043-001-0128-3
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DOI: https://doi.org/10.1007/s12043-001-0128-3