Enhancing the Yield of Bucket Brigade Quantum Random Access Memory using Redundancy Repair

Quantum Random Access Memory (qRAM) is an essential computing element for running oracle-based quantum algorithms. qRAM exploits quantum superposition to access all data stored in the memory cells simultaneously and guarantees the superior performance of quantum algorithms. A qRAM memory cell comprises logical qubits encoded through quantum error correction technology for successful operation against various quantum noises. In addition to quantum noise, the low-technology nodes based on silicon technology can increase the qubit density and may introduce defective qubits. As qRAM comprises many qubits, its yield will be reduced by defective qubits; these qubits must be handled using QEC scheme. However, the QEC scheme requires numerous physical qubits, which burdens resource overhead. In this paper, to resolve this overhead problem, we propose a novel quantum memory architecture that compensates for defective qubits by introducing redundant qubits. We also analyze the yield improvement offered by our proposed quantum memory architecture by varying the ideal fabrication error rate from 0.5% to 1% for different numbers of logical qubits in the qRAM. We demonstrate that for the qRAM comprising 1,024 logical qubits, eight redundant logical qubits improved the yield by 95.92% from that of qRAM not employing the redundant repair scheme.

💡 Research Summary

The paper addresses a critical bottleneck in scaling quantum random‑access memory (qRAM) for practical quantum algorithms: the combined impact of quantum noise and manufacturing defects on the yield of large‑scale qRAM devices. While prior work has shown that the bucket‑brigade architecture is more tolerant to decoherence during address routing than the fan‑out design, it largely ignores defects that may appear in the memory cells themselves. Such defects, which become increasingly likely as silicon‑based qubit densities rise, can render a substantial fraction of logical qubits unusable, dramatically lowering the overall yield of a qRAM chip.

To mitigate this problem, the authors propose a “built‑in self‑repair” (BISR) scheme that introduces a small number of spare logical qubits (redundant qubits) into the bucket‑brigade tree. When a logical qubit is found to contain a defective physical qubit (detected during fabrication testing), the spare logical qubit is swapped in to replace it. Because the spare qubits are pre‑encoded with the same quantum error‑correction (QEC) code as the regular logical qubits, the replacement does not require additional error‑correction overhead; instead, the overall degree of QEC can be reduced. Consequently, the number of physical qubits required per logical qubit (the N_PQ/N_LQ ratio) is lowered, and the total physical qubit count of the qRAM does not explode.

The paper provides a detailed background on bucket‑brigade qRAM, explaining how each node is a qutrit (states |0⟩, |1⟩, |•⟩) that routes the quantum address signal. Only O(n) qutrits are active for an n‑bit address, which already limits decoherence during routing. However, the memory cells at the leaves of the tree must still be protected against both stochastic quantum errors and static fabrication defects. The authors model fabrication defects as a per‑physical‑qubit failure probability ranging from 0.5 % to 1 %, and they define the qRAM yield as the percentage of fabricated chips that contain no defective logical qubits (Equation 2). Simulations on 1,000 chips show that yield drops sharply as the number of logical qubits grows, even when each logical qubit is encoded with 17 physical qubits (a typical surface‑code implementation).

The BISR architecture is described in both conceptual and circuit‑level terms. An automatic test equipment (ATE) flow is proposed to identify defective physical qubits during wafer testing, map the corresponding logical qubits, and activate the spare logical qubits in the bucket‑brigade network. The authors also present a quantum circuit model that incorporates the spare‑qubit selection logic, ensuring that the repair operation itself does not introduce prohibitive overhead.

Performance evaluation explores three key parameters: (1) fabrication defect rate, (2) total number of logical qubits in the qRAM (256, 512, 1,024), and (3) number of redundant logical qubits (4, 8, 12). The most striking result is that for a 1,024‑logical‑qubit qRAM with a 0.5 % defect rate, adding just eight redundant logical qubits raises the yield from roughly 30 % (with conventional QEC only) to 95.92 %. Even at a higher defect rate of 1 %, the yield improvement remains substantial. Importantly, the redundant qubits constitute only about 1 % of the total physical qubits, demonstrating that a modest resource investment can deliver a dramatic yield boost.

The discussion compares the proposed scheme with prior approaches such as the Faulty Towers architecture, which focuses on routing‑network defects, and with high‑degree QEC strategies that protect logical qubits at the cost of exponential physical‑qubit overhead. The BISR method uniquely addresses defects at the memory‑cell level while simultaneously allowing a reduction in QEC depth, thereby offering a more resource‑efficient path to fault‑tolerant qRAM. Limitations are acknowledged: the spare qubits themselves may be defective, and the control logic for managing replacements could become complex in very large trees. The authors suggest future work on optimal placement of redundant qubits, physical implementation on silicon platforms, and integration with other qRAM designs.

In conclusion, the paper demonstrates that a modest amount of redundancy, combined with a systematic self‑repair workflow, can dramatically improve the manufacturability and scalability of bucket‑brigade qRAM. By lowering the required QEC overhead and mitigating static fabrication defects, the proposed architecture moves the field closer to realizing large‑scale, high‑yield quantum memory essential for oracle‑based quantum algorithms such as Grover’s search, HHL, and many emerging quantum machine‑learning applications.