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Article Dans Une Revue Physical Review A : Atomic, molecular, and optical physics [1990-2015] Année : 2006

A Quantitative Measure of Interference

Résumé

We introduce an interference measure which allows to quantify the amount of interference present in any physical process that maps an initial density matrix to a final density matrix. In particular, the interference measure enables one to monitor the amount of interference generated in each step of a quantum algorithm. We show that a Hadamard gate acting on a single qubit is a basic building block for interference generation and realizes one bit of interference, an ''i-bit''. We use the interference measure to quantify interference for various examples, including Grover's search algorithm and Shor's factorization algorithm. We distinguish between ''potentially available'' and ''actually used'' interference, and show that for both algorithms the potentially available interference is exponentially large. However, the amount of interference actually used in Grover's algorithm is only about 3 i-bits and asymptotically independent of the number of qubits, while Shor's algorithm indeed uses an exponential amount of interference.

Dates et versions

hal-00012393 , version 1 (21-10-2005)

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Daniel Braun, Bertrand Georgeot. A Quantitative Measure of Interference. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2006, 73, pp.022314. ⟨10.1103/PhysRevA.73.022314⟩. ⟨hal-00012393⟩
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