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arXiv:0710.1717 · Physical Review Letters

Error Correction in Ensemble Registers for Quantum Repeaters and Quantum Computers

E. Brion, Line Hjortshøj Pedersen, Mark E. Saffman, Klaus Mølmer

Published Mar 21, 2008• 50 citations
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Abstract

We propose to use a collective excitation blockade mechanism to identify errors that occur due to disturbances of single atoms in ensemble quantum registers where qubits are stored in the collective population of different internal atomic states. A simple error correction procedure and a simple decoherence-free encoding of ensemble qubits in the hyperfine states of alkali-metal atoms are presented.

DOI
10.1103/physrevlett.100.110506

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Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information and the coherent conversion of quantum information between atomic and optical degrees of freedom. We describe a scheme for full-scale quantum computing with atomic ensembles, in which qubits are encoded in symmetric collective excitations of many atoms. We consider the most important sources of error—imperfect exciton–photon coupling and photon losses—and demonstrate that the scheme is extremely robust against these processes: the required photon emission and collection efficiency threshold is ≳86%. Our scheme uses similar methods to those already demonstrated experimentally in the context of quantum repeater schemes and yet has information processing capabilities far beyond those proposals.
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We demonstrate a new approach for fast preparation, manipulation, and collective readout of an atomic Rydberg-state qubit. By making use of Rydberg blockade inside a small atomic ensemble, we prepare a single qubit within $3\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$ with a success probability of ${F}_{p}=0.93\ifmmode\pm\else\textpm\fi{}0.02$, rotate it, and read out its state in $6\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$ with a single-shot fidelity of ${F}_{d}=0.92\ifmmode\pm\else\textpm\fi{}0.04$. The ensemble-assisted detection is 103{10}^{3}103 times faster than imaging of a single atom with the same optical resolution, and enables fast repeated nondestructive measurement. We observe qubit coherence times of $15\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$, much longer than the $\ensuremath{\pi}$ rotation time of 90 ns. Potential applications ranging from faster quantum information processing in atom arrays to efficient implementation of quantum error correction are discussed.
Spin ensembles are promising quantum technological platforms, but their utility relies on the ability to perform quantum error correction (QEC) for the specific decoherence in these systems. Typical QEC for ensembles requires addressing individually resolved qubits, but this is practically challenging in most realistic architectures. Here, we propose QEC schemes for unresolvable spin ensembles. By using degenerate superpositions of excited states, which are fundamentally mixed, we find codes that can protect against both individual and collective errors, including dephasing, decay, and pumping. We show how information recovery can be achieved with only collective measurement and control, and illustrate its applications in extending memory lifetime and loss-tolerant sensing.