Quantum Information Processing, Vol. 3, Nos. 1–5, October 2004 (© 2004)
Progress in Quantum Algorithms
Peter W. Shor
Received June 27, 2004; accepted July 6, 2004
We discuss the progress (or lack of it) that has been made in discovering algo-
rithms for computation on a quantum computer. Some possible reasons are given
for the paucity of quantum algorithms so far discovered, and a short survey is
given of the state of the ﬁeld.
KEY WORDS: quantum algorithms; NP-complete.
It has now been 10 years since I discovered the quantum factoring algo-
This discovery caused great excitement; although some quantum
algorithms had previously been discovered, this was the ﬁrst algorithm
that gave a substantial speedup over a classical algorithm for a well-stud-
ied and interesting problem. Many people expected a succession of other
interesting quantum algorithms to quickly follow. Lov Grover indeed dis-
covered his quantum searching algorithm shortly thereafter,
but the pro-
gress since has been disappointing, especially compared with the progress
the rest of the ﬁeld of quantum information processing has been making.
Physicists have been proposing and experimenters have been exploring pos-
sible physical implementations of quantum computers at a pace I believe is
faster than what anybody, but the most optimistic people expected; these
developments are covered in the rest of this issue. Quantum cryptography
is coming of age, with several theoretical proofs of its security recently dis-
covered, and commercial quantum cryptography systems now on the mar-
ket. The ﬁeld of quantum information theory and quantum computational
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139,
USA. E-mail: email@example.com
1570-0755/04/1000-0005/0 © 2004 Springer Science+Business Media, Inc.