Determining the parity of a permutation using an experimental NMR qutrit

Abstract

We present the NMR implementation of a recently proposed quantum algorithm to find the parity of a permutation. In the usual qubit model of quantum computation, speedup requires the presence of entanglement and thus cannot be achieved by a single qubit. On the other hand, a qutrit is qualitatively more quantum than a qubit because of the existence of quantum contextuality and a single qutrit can be used for computing. We use the deuterium nucleus oriented in a liquid crystal as the experimental qutrit. This is the first experimental exploitation of a single qutrit to carry out a computational task.

6 pages 4 figures revtex

References in corpus (10)

• Quantum Computing
• State-independent experimental test of quantum contextuality
• Experimental non-classicality of an indivisible quantum system
• State-independent experimental tests of quantum contextuality in a three dimensional system
• Entanglement sudden death in qubit-qutrit systems
• Proposed experiments of qutrit state-independent contextuality and two-qutrit contextuality-based nonlocality
• Geometric quantum computation using fictitious spin- 1/2 subspaces of strongly dipolar coupled nuclear spins
• Projective measurement in nuclear magnetic resonance
• Discrimination of unitary transformations in the Deutsch-Jozsa algorithm
• An experimental test of the non-classicality of quantum mechanics using an unmovable and indivisible system

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