Heterogeneously error-corrected QRAMs

Quantum Random Access Memories (QRAM) could prove essential for scalable quantum computing, for everything from accessing classical databases for unordered search to creating arbitrary superpositions of states. However, like most applications of quantum computing, QRAMs suffer from qubit error and decoherence. Quantum Error Correction (QEC) provides a potential solution, but unfortunately, most QEC proposals that uniformly correct all qubits of the QRAM incur major overheads, making the QRAM infeasible. In this work, we propose a surface code error-corrected QRAM made of heterogeneous code distance logical qubits. Our QRAM can produce higher fidelity queries, while keeping qubit overheads smaller than the uniformly error-corrected QRAMs. Comparisons between our novel QRAM architectures and a uniformly error corrected baseline are presented, showing that our designs can achieve up to polylogarithmic reduction in query infidelity, producing constant query infidelity scaling, while simultaneously reducing qubit overhead.