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Collective qubits and hybrid schemes for quantum computing

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In conventional registers for quantum information processing, quantum bits are associated with individual two-level quantum systems. Separate addressing and interaction with these systems permit one-bit gates, while an interaction between systems is needed to accomplish two-bit gates. I will review a recent proposal to implement quantum computing in collective excitation degrees of freedom in ensembles of identical quantum systems. In this proposal one does not need to address individual particles, but one needs an interaction between all particles in the system. Such interactions exist in hybrid systems where large spin-ensembles are coupled to superconducting qubit elements via a resonant single mode of the quantized radiation field. We will review the main ideas of ensemble encoding and we will discuss recent results on the effects of unwanted interactions and inhomogeneities in such systems

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