Quantum devices should operate in adherence to quantum physics principles. Quantum random access memory (QRAM), a fundamental component of many essential quantum algorithms for tasks such as linear algebra, data search, and machine learning, is often proposed to offer $\mathcal{O}(\log N)$ circuit depth for $\mathcal{O}(N)$ data size, given $N$ qubits. However, this claim appears to breach the principle of relativity when dealing with a large number of qubits in quantum materials interacting locally. In our study we critically explore the intrinsic bounds of rapid quantum memories based on causality, employing the relativistic quantum field theory and Lieb-Robinson bounds in quantum many-body systems. In this paper, we consider a hardware-efficient QRAM design in hybrid quantum acoustic systems. Assuming clock cycle times of approximately $10^{-3}$ seconds and a lattice spacing of about 1 micrometer, we show that QRAM can accommodate up to $\mathcal{O}(10^7)$ logical qubits in 1 dimension, $\mathcal{O}(10^{15})$ to $\mathcal{O}(10^{20})$ in various 2D architectures, and $\mathcal{O}(10^{24})$ in 3 dimensions. We contend that this causality bound broadly applies to other quantum hardware systems. Our findings highlight the impact of fundamental quantum physics constraints on the long-term performance of quantum computing applications in data science and suggest potential quantum memory designs for performance enhancement.

翻译：量子设备应遵循量子物理学原理运行。量子随机存取存储器（QRAM）作为线性代数、数据搜索和机器学习等众多核心量子算法的基础组件，常被提出能在拥有N个量子比特时，以O(log N)的电路深度处理O(N)的数据规模。然而，当处理大量局域相互作用的量子材料中的量子比特时，这一声称似乎违背了相对论原理。在本研究中，我们基于因果性严格探索快速量子存储器的内在极限，运用相对论量子场论及量子多体系统中的Lieb-Robinson界。本文考虑一种在混合量子声学系统中硬件高效的QRAM设计方案。假设时钟周期约为10^{-3}秒、晶格间距约为1微米，我们证明QRAM在1维架构下可容纳高达O(10^7)个逻辑量子比特，在各种2维架构中可容纳O(10^15)至O(10^20)个，在3维架构中可容纳O(10^24)个。我们认为这一因果边界广泛适用于其他量子硬件系统。我们的发现揭示了基础量子物理约束对数据科学中长期量子计算应用性能的影响，并提出了用于性能增强的潜在量子存储器设计方案。