Use of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance

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 logic gates by 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 errors. 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 these geometric phase gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.

References in corpus (3)

• An experimental observation of geometric phases for mixed states using NMR interferometry
• Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule
• Spectral implementation of some quantum algorithms by one- and two-dimensional nuclear magnetic resonance

Cited by in corpus (10)

• Quantum Computing with NMR
• Composite pulses in NMR as non-adiabatic geometric quantum gates
• Nonadiabatic dynamics and geometric phase of an ultrafast rotating electron spin
• Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases
• Geometric Phase in Entangled Systems: A Single-Neutron Interferometer Experiment
• Geometric quantum computation using fictitious spin- 1/2 subspaces of strongly dipolar coupled nuclear spins
• Implementation of controlled phase shift gates and Collins version of Deutsch-Jozsa algorithm on a quadrupolar spin-7/2 nucleus using non-adiabatic geometric phases
• Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like Effect
• Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model
• Application of Geometric Phase in Quantum Computations