Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer

Abstract

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch–Jozsa algorithm1,2) requires just one examination step. The Deutsch–Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques3,4, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises3 motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate6, the entanglement of four ions7, quantum state engineering8 and entanglement-enhanced phase estimation9. Here we exploit techniques10,11 developed for nuclear magnetic resonance to implement the Deutsch–Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.

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Figure 1: Quantum circuit for implementing the Deutsch–Jozsa algorithm with basic quantum operations.
Figure 2: Quantum mechanical energy levels relevant for the ion-trap quantum computer.
Figure 3: Time evolution of |〈1a〉|2.

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Acknowledgements

We gratefully acknowledge support by the European Commission (QSTRUCT, QI, QUEST and QUBITS networks), by the Austrian Science Fund (FWF), and by the Institut für Quanteninformation GmbH.

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Correspondence to Ferdinand Schmidt-Kaler.

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Gulde, S., Riebe, M., Lancaster, G. et al. Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003). https://doi.org/10.1038/nature01336

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