Alena Romanova M.Sc., Universität Mainz

Alena Romanova M.Sc. Institut für Physik der Johannes Gutenberg Universität Mainz

We address the challenge of incorporating encoded quantum memories into an exact secret key rate analysis for quantum repeaters. To this end, we introduce the check matrix model and quantify the resilience of stabilizer codes of up to eleven qubits against Pauli noise, obtaining analytical expressions for effective logical error probabilities. Generally, we find that the five-qubit and Steane codes either outperform more complex, larger codes in the experimentally relevant parameter regimes or have a lower resource overhead. Subsequently, we apply our results to calculate lower bounds on the achievable secret key rate in memory-corrected quantum repeaters when using the five-qubit or Steane code on the memory qubits. We show that these codes mitigate the impact of experimental errors due to finite memory coherence times, imperfect state preparation, and faulty Bell state measurements. As a result, secret key rates are significantly enhanced, and communication dista­nces drastically extended.