, Los Alamos National Laboratory

Pages: p. 26

In a conventional computer, information is represented by quantities that obey the laws of classical physics, such as the voltage levels in a logic circuit. But as the size of microelectronics shrinks, quantum physics becomes increasingly important.

In the early 1980s, this observation led Paul Benioff and later Richard Feynman to consider how to compute with information represented by quantum mechanical quantities. For example, an atomic electron has certain quantum states of motion with energies that are *discrete* or quantized. An electron could be used to represent a binary 0 when it is in one of these states and to represent a binary 1 when it is in a second state. The representation of a single bit of information by such a two-state quantum system has come to be known as a *qubit*. (Other examples of qubits include the two distinct polarizations of a photon and the orientation of the intrinsic angular momentum or spin of an atomic nucleus, which can be parallel or antiparallel to an applied magnetic field.)

With two or more qubits, we can consider quantum logical "gate" operations in which the state of one qubit changes in a way that is contingent upon the state of another. These gate operations are the building blocks of a quantum computer. However, because of the quantum mechanical superposition principle, qubits are not restricted to the binary 0 or 1 values only. This would let a quantum computer perform much more general quantum gate operations than ordinary computers can using conventional Boolean operations.

In 1994, Peter Shor showed that this new freedom would let a quantum computer find the prime factors of composite integers much more efficiently than any conventional computer. Subsequently, Lov Grover showed that a quantum computer could also search an unstructured database more efficiently than any classical computer. Because integer factorization and related problems that are computationally intractable with conventional computers are the basis for the security of modern public key cryptosystems, Shor's result has turned quantum computation into a very active research field. Likewise, researchers are devoting considerable effort to determining the classes of problems that are amenable to a "quantum speedup."

In this special issue, we have three articles highlighting the status of these algorithmic investigations. George Cybenko's article provides an introduction to quantum algorithms, Richard Josza then casts quantum factoring into a bigger class of problems, and Colin Williams surveys the status of quantum search algorithms.

- R.P. Feynman,
*Feynman Lectures on Computation*, Addison-Wesley, Reading, Mass., 1996. - A.J.G. Hey, ed., Feynman and Computation: Exploring the Limits of Computers, Perseus, Reading, Mass., 1999.
- L.K. Grover, "A Fast Quantum Mechanical Algorithm for Database Search,"
*Proc. 28th Ann. ACM Symp. Theory of Computing*, ACM Press, New York, 1996. - P.W. Shor, "Algorithms for Quantum Computation: Discrete Logarithm and Factoring,"
*Proc. 35th Ann. Symp. Foundations of Computer Science*, IEEE CS Press, Los Alamitos, Calif., 1994, p.124.

Richard Hughes is a laboratory fellow and quantum information science team leader in the Physics Division at Los Alamos National Laboratory. He is principal investigator of several projects in quantum computation and quantum cryptography. He obtained his PhD in theoretical elementary particle physics from the University of Liverpool, England, and has held research positions at Oxford University and the Queen's College, Oxford; the California Institute of Technology; and CERN, Geneva, Switzerland. In 1996 and 1998 he was awarded the Los Alamos Distinguished Performance Award for his quantum cryptography research, and in 1997 he received the Los Alamos Fellows' Prize for his work on quantum information science. He became a fellow of the American Physical Society in 1999. In his spare time, he competes in ultra running events in excess of 100 km. Contact him at hughes@lanl.gov.