Quantum Algorithms with Fixed Points: The Case of Database Search

Abstract

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.

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

References in corpus (1)

• Quantum error correction of systematic errors using a quantum search framework