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.
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Entry modified 17 December 2004.
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Paul E. Black, "Deutsch-Jozsa algorithm", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 17 December 2004. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/deutschJozsaAlgo.html