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

Grover, Lov K and Patel, Apoorva and Tulsi, Tathagat (2006) Quantum Algorithms with Fixed Points: The Case of Database Search. In: Workshop on Quantum Information, Computation and Communication QICC-2005, February 2005, IIT Kharagpur, India.

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Official URL: http://arxiv.org/abs/quant-ph/0603132

## 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.

Item Type: Conference Paper Publisher Copyright of this article belongs to Allied Publishers. Division of Physical & Mathematical Sciences > Centre for High Energy Physics 24 Nov 2011 07:04 24 Nov 2011 07:04 http://eprints.iisc.ernet.in/id/eprint/42149