International audienceA quantum memory at microwave frequencies, able to store the state of multiple superconducting qubits for long times, is a key element for quantum information processing. Electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above 1 s. Benefiting from these long coherence times requires one to apply the refocusing techniques used in magnetic resonance, a major challenge in the context of hybrid quantum circuits. Here, we report the first implementation of such a scheme, using ensembles of nitrogen-vacancy centers in diamond coupled to a superconducting resonator, in a setup compatible with superconducting qubit technology. We implement the active reset of the nitrogen-vacancy spins into their ground state by optical pumping and their refocusing by Hahn-echo sequences. This enables the storage of multiple microwave pulses at the picowatt level and their retrieval after up to 35 μs, a 3 orders of magnitude improvement compared to previous experiments

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Rényi entropy of a partial observation to a subsystem consisting of contiguous sites in the limit of large size. (2008)]. A striking feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size. This logarithmic behavior originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyze the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long-range pairing.

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