(algorithm)

**Definition:**
A quantum algorithm to determine whether a function is *constant* or balanced, that is, returns 1 for half the *domain* and 0 for the other half. For a function taking n input qubits, first, do Hadamards on n 0's, forming all possible inputs, and a single 1, which will be the answer qubit. Next, run the function once; this *exclusive or*'s the result with the answer qubit. Finally, do Hadamards on the n inputs again, and measure the answer qubit. If it is 0, the function is constant, otherwise the function is balanced.

**See also**
*quantum computation*.

*Note:
The algorithm needs only one (quantum) evaluation of the function. A classical algorithm to answer the same question is to examine one more than half the domain in the worst case. *

* See Arthur O. Pittenger, "An Introduction to Quantum Computing Algorithms", page 41, or Michael A. Nielsen and Isaac L. Chuang, "Quantum Computation and Quantum Information", pages 34-36.*

Author: PEB

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Entry modified 17 December 2004.

HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:

Paul E. Black, "Deutsch-Jozsa algorithm", in
*Dictionary of Algorithms and Data
Structures* [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/deutschJozsaAlgo.html