title: Use of non-adiabatic geometric phase for quantum computing by NMR.
abstract: Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of error. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using the non-adiabatic geometric phase we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.
authors.affiliation: NMR Quantum Computation and Quantum Information Group, Department of Physics and NMR Research Centre, Indian Institute of Science, Bangalore 560012, India. rdas@ncifcrf.gov
authors.forename: Ranabir
authors.initials: R
authors.lastname: Das
authors.forename: S K Karthick
authors.initials: SK
authors.lastname: Kumar
authors.forename: Anil
authors.initials: A
authors.lastname: Kumar