The resilience of quantum random access memory to generic noise

Quantum random access memory (qRAM)—a memory which stores classical data but allows queries to be performed in superposition—is required for the implementation of numerous quantum algorithms. While naive implementations of qRAM are highly susceptible to decoherence and thus not scalable, it has been argued that the bucket brigade qRAM scheme [Phys. Rev. Lett. 100 160501 (2008)] possesses a remarkable resilience to noise. In this scheme, the infidelity of a memory call scales only logarithmically with the size of the memory. In prior analyses of the scheme, however, this favorable scaling followed directly from the use of restricted noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage. We prove that, quite surprisingly, the favorable scaling holds for general noise models (including depolarization) and hence should be achievable in realistically noisy devices. As a corollary, we show that the benefits of the bucket-brigade scheme persist even when quantum error correction is used, in which case the scheme offers improved resilience to logical errors and better hardware efficiency.