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.

1.
L. K.
Grover
, “
Quantum Mechanics helps in searching for a needle in a haystack
,”
Phys. Rev. Lett.
78
(
2
),
325
328
(
1997
), available on my home page-http://www.bell-labs.com/user/lkgrover/.
2.
A fast quantum mechanical algorithm for database search, Proceedings of 28th Annual ACM Symposium on Theory of Computing (STOC), 1996, pp. 212–219, available on my home page-http://www.bell-labs.com/user/lkgrover/.
3.
Richard
Jozsa
, “
Searching in Grover’s Algorithm
,” http://xxx.lanl.gov/abs/quant-ph/9901021.
4.
M.
Boyer
,
G.
Brassard
,
P.
Hoyer
, and
A.
Tapp
, “
Tight bounds on quantum searching
,”
Fortsch. Phys.
46
,
493
506
(
1998
),
M.
Boyer
,
G.
Brassard
,
P.
Hoyer
, and
A.
Tapp
, http://xxx.lanl.gov/abs/quant-ph/9605034.
5.
C.
Zalka
, “
Grover’s quantum searching algorithm is optimal
,”
Phys. Rev. A
60
,
2746
2751
(
1999
),
C.
Zalka
, http://arXiv.org/abs/quant-ph/9711070.
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