Quantum Algorithms with Fixed Points: The Case of Database Search

Details Quantum Algorithms with Fixed Points: The Case of Database Search Quantum Algorithms with Fixed Points: The Case of Database Search

2006-03-15

arxiv.org/abs/quant-ph/0603132v1

Physics

Quantum Physics

12 pages, 4 figures. Invited lecture by LKG at the Workshop on Quantum Information, Computation and Communication (QICC-2005),

Scientific paper

The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which get around this limitation. The first replaces selective inversions in the algorithm by selective phase shifts of $\frac{\pi}{3}$. The second controls the selective inversion operations using two ancilla qubits, and irreversible measurement operations on the ancilla qubits drive the starting state towards the target state. Using $q$ oracle queries, these variations reduce the probability of finding a non-target state from $\epsilon$ to $\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead to robust quantum algorithms, and provide conceptually new schemes for error correction.

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