This is the second paper in a series of two. Using a multiparticle continuous-time quantum walk with two internal states, which was formulated in the first paper [R. Asaka et al., preceding paper, Phys. Rev. A 107, 022415 (2023)], we physically implement a quantum random access memory (QRAM). Data with address information are dual-rail encoded into quantum walkers. The walkers pass through perfect binary trees to access the designated memory cells and copy the data stored in the cells. A roundabout gate allocated at each node serves as a router to move the walker from the parent node to one of two child nodes, depending on the internal state of the walker. In this process, the address information is sequentially encoded into the internal states so that the walkers are adequately delivered to the target cells. The present QRAM, which processes
2nm-qubit data, is implemented in a quantum circuit of depth
O(nlog(n+m)) and requires
O(n+m) qubit resources. This is more efficient than the conventional bucket-brigade QRAM that requires
O(n2+nm) steps and
O(2n+m) qubit resources for processing. Moreover, since the walkers are not entangled with any device on the binary trees, the cost of maintaining coherence can be reduced. Notably, by simply passing quantum walkers through binary trees, data can be automatically extracted in a quantum superposition state. In other words, any time-dependent control is not required.
Quantum Random Access Memory (qRAM) is a critical component for achieving quantum advantage in algorithms ranging from database search to quantum machine learning. In a recently introduced model [arXiv:2508.02855], we proposed a resource-efficient qRAM architecture based on discrete-time quantum walkers. This article serves as a comprehensive technical follow-up, providing the full mathematical derivations, detailed protocol specifications, and in-depth resource analysis. Moreover, we extend the original proposal with novel techniques for the purpose of making the qRAM implementation more realistic. Our model resolves the primary drawbacks of leading qRAM proposals: it avoids the exponential number of active nodes
O(2n) required by the "Bucket Brigade" architecture by employing a number of quantum walkers that scales linearly with the address and message sizes,
n and
m, respectively. Simultaneously, it overcomes the spatial bottlenecks of previous quantum-walker schemes by eliminating the need for multiple parallel trees. We propose two algorithmic paradigms: the long- and the short-range approaches, which differ by the length of interaction of the main routing gates employed in the qRAM. We formalize the routing, message-copy, and walker retrieval phases for both variants and we show how, while the long-range scheme employs controlled gates having a multitude of target systems, the short-range approach decomposes these interactions into sequences of 2- and 3-body local gates, which improves the architecture's feasibility for near-term experimental implementation. Finally, our comprehensive resource analysis confirms that the short-range approach achieves the optimal
O(n+m) circuit depth. Within these two paradigms, we explore the potential of different types of quantum walkers, namely bosons, dual-rail qubits and four-level qudits.