229 research outputs found
New Trends in Quantum Computing
Classical and quantum information are very different. Together they can
perform feats that neither could achieve alone, such as quantum computing,
quantum cryptography and quantum teleportation. Some of the applications range
from helping to preventing spies from reading private communications. Among the
tools that will facilitate their implementation, we note quantum purification
and quantum error correction. Although some of these ideas are still beyond the
grasp of current technology, quantum cryptography has been implemented and the
prospects are encouraging for small-scale prototypes of quantum computation
devices before the end of the millennium.Comment: 8 pages. Presented at the 13th Symposium on Theoretical Aspects of
Computer Science, Grenoble, 22 February 1996. Will appear in the proceedings,
Lecture Notes in Computer Science, Springer-Verlag. Standard LaTeX. Requires
llncs.sty (included
Brief History of Quantum Cryptography: A Personal Perspective
Quantum cryptography is the only approach to privacy ever proposed that
allows two parties (who do not share a long secret key ahead of time) to
communicate with provably perfect secrecy under the nose of an eavesdropper
endowed with unlimited computational power and whose technology is limited by
nothing but the fundamental laws of nature. This essay provides a personal
historical perspective on the field. For the sake of liveliness, the style is
purposely that of a spontaneous after-dinner speech.Comment: 14 pages, no figure
On The Power of Exact Quantum Polynomial Time
We investigate the power of quantum computers when they are required to
return an answer that is guaranteed correct after a time that is upper-bounded
by a polynomial in the worst case. In an oracle setting, it is shown that such
machines can solve problems that would take exponential time on any classical
bounded-error probabilistic computer.Comment: 10 pages, LaTeX2e, no figure
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
We investigate the power of quantum computers when they are required to
return an answer that is guaranteed to be correct after a time that is
upper-bounded by a polynomial in the worst case. We show that a natural
generalization of Simon's problem can be solved in this way, whereas previous
algorithms required quantum polynomial time in the expected sense only, without
upper bounds on the worst-case running time. This is achieved by generalizing
both Simon's and Grover's algorithms and combining them in a novel way. It
follows that there is a decision problem that can be solved in exact quantum
polynomial time, which would require expected exponential time on any classical
bounded-error probabilistic computer if the data is supplied as a black box.Comment: 12 pages, LaTeX2e, no figures. To appear in Proceedings of the Fifth
Israeli Symposium on Theory of Computing and Systems (ISTCS'97
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