Physics – Quantum Physics
Scientific paper
2005-10-20
Phys. Rev. A 73, 022314 (2006)
Physics
Quantum Physics
13 pages of latex; research done at http://www.quantware.ups-tlse.fr/
Scientific paper
10.1103/PhysRevA.73.022314
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.
Braun Daniel
Georgeot Bertrand
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