Filip Rozpedek

We propose a novel strategy of using the Gottesman-Kitaev-Preskill (GKP) code in a two-way repeater architecture with multiplexing. The crucial feature of the GKP code that we make use of, is the fact that GKP qubits easily admit deterministic two-qubit gates, hence allowing for deterministic entanglement swapping. Furthermore, thanks to the availability of the analog information generated during the measurement of the GKP qubits, we can design better entanglement swapping procedures between the multiplexed elementary links. To boost the loss-resilience of our encoded qubits, we consider a concatenation of the GKP code with the discrete variable [[7,1,3]] code which has already proven effective in the context of quantum repeater schemes. We find that our architecture allows for high-rate near-deterministic end-to-end entanglement generation with much larger repeater spacing than for the previously considered error-correction based repeater schemes.

We propose a novel architecture of quantum-error-correction-based quantum repeaters that combines the techniques used in discrete and continuous variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous variable GKP code which encodes the qubit in a single bosonic mode. On the second level we use a small discrete variable code, encoding a logical qubit in as few as seven physical qubits. Such an architecture introduces two major novelties which allow us to make efficient use of resources. Firstly, our architecture makes use of two types of quantum repeaters: the simpler GKP repeaters that need to only be able to store and correct errors on a single GKP qubit and more powerful but more costly multi-qubit repeaters that additionally can correct errors on the higher level. We find that the combination of using the two types of repeaters enables us to achieve performance needed in practical scenarios with a significantly reduced cost with respect to an architecture based solely on multiqubit repeaters. Secondly the use of continuous variable GKP code on the lower level has the advantage of providing us with the information about the success probability of the specific GKP correction round. This analog information, unique to bosonic codes, provides significant boost in performance when used to correct second level errors in the multi-qubit repeaters.