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arXiv:quant-ph/0510139

Scheme for implementing the Deutsch-Jozsa algorithm via atomic ensembles

Ping Dong, Zheng‐Yuan Xue, Ming Yang, Zhuo‐Liang Cao

Published Oct 18, 2005• 0 citations
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Abstract

We propose a physical scheme for implementing the Deutsch-Jozsa algorithm using atomic ensembles and optical devices. The scheme has inherent fault tolerance to the realistic noise and efficient scaling with the number of ensembles for some entangled states within the reach of current technology. It would be an important step toward more complex quantum computation via atomic ensembles.

DOI
10.48550/arxiv.quant-ph/0510139

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We propose a physical scheme for implementing the Deutsch-Jozsa algorithm using atomic ensembles and optical devices. The scheme has inherent fault tolerance to the realistic noise and efficient scaling with the number of ensembles for some entangled states within the reach of current technology. It would be an important step toward more complex quantum computation via atomic ensembles.
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We propose a scheme of implementing the Deutsch–Jozsa algorithm based on superconducing charge qubits, which would be a key step to scale more complex quantum algorithms and very important for constructing a real quantum computer via superconducting charge qubits. The present scheme is simple but fairly efficient, and easily manipulated because arbitrary two-qubit can be selectively and effectively coupled by a common inductance. More manipulations can be carried out before decoherence sets in. The proposed scheme is in line with current technology.
The first optical proposal for the realization of the two-bit version of the Deutsch-Jozsa algorithm [D. Deutsch and R. Jozsa, Proc. R. Soc. London A {\bf 493}, 553 (1992)] is presented. The proposal uses Stark shifts in an ensemble of atoms and degenerate sources of photons. The photons interact dispersively with an atomic ensemble, leading to an effective Hamiltonian in atom-field basis, which is useful for performing the required two-qubit operations. Combining these with a set of one-qubit operations, the algorithm can be implemented. A discussion of the experimental feasibility of the proposal is given.
We show that one can implement the Deutsch-Josza algorithm, one of the first and simplest quantum algorithms, in a fault-tolerant manner using the smallest quantum error-detecting code -- the [[4,2,2]][[4,2,2]][[4,2,2]] code -- without any ancillae. We implemented the algorithm on a trapped-ion quantum computer with and without fault-tolerant encoding and compared the results. With approximately 99%99 \%99% confidence, we found that the fault-tolerant implementation provided a noise reduction for all oracles. Averaged across all oracles, the reduction in error rate was nearly 90%90 \%90%.