Fault-tolerant logical state preparation for quantum low-density parity-check codes

Abstract:

In this talk I will outline some ongoing work where we propose a single-shot protocol for the fault-tolerant preparation of logical states of arbitrary quantum low-density parity-check codes that can be used for the generation of long-range entanglement. Following a measurement-based scheme, we give a formal analysis under logical stochastic noise and prove the existence of a threshold, thereby generalizing previous works that only consider the surface code. Moreover, we show that our protocol can be applied in a long-range quantum communication setup based on quantum repeaters and prove that the entanglement of the successfully prepared state in terms of the relative entropy of entanglement approaches the code rate asymptotically.