Our study evaluates the limitations and potentials of Quantum Random Access Memory (QRAM) within the principles of quantum physics and relativity. QRAM is crucial for advancing quantum algorithms in fields like linear algebra and machine learning, purported to efficiently manage large data sets with \({{{\mathcal{O}}}}(\log N)\) circuit depth. However, its scalability is questioned when considering the relativistic constraints on qubits interacting locally. Utilizing relativistic quantum field theory and Lieb–Robinson bounds, we delve into the causality-based limits of QRAM. Our investigation introduces a feasible QRAM model in hybrid quantum acoustic systems, capable of supporting a significant number of logical qubits across different dimensions-up to ~10⁷ in 1D, ~10¹⁵ to ~10²⁰ in 2D, and ~10²⁴ in 3D, within practical operation parameters. This analysis suggests that relativistic causality principles could universally influence quantum computing hardware, underscoring the need for innovative quantum memory solutions to navigate these foundational barriers, thereby enhancing future quantum computing endeavors in data science.

我们的研究根据量子物理和相对论原理评估了量子随机存取存储器 (QRAM) 的局限性和潜力。 QRAM 对于推进线性代数和机器学习等领域的量子算法至关重要，据称可以有效管理具有 \({{{\mathcal{O}}}}(\log N)\) 电路深度的大型数据集。然而，当考虑量子位局部交互的相对论约束时，其可扩展性受到质疑。利用相对论量子场论和 Lieb-Robinson 界限，我们深入研究了 QRAM 基于因果关系的限制。我们的研究在混合量子声学系统中引入了一种可行的 QRAM 模型，能够支持跨不同维度的大量逻辑量子位 - 一维可达约 10 ⁷ ，一维可达约 10 ¹⁵ 在实际操作参数范围内，2D 中约为 10 ²⁰ ，3D 中约为 10 ²⁴ 。该分析表明，相对论因果关系原理可能普遍影响量子计算硬件，强调需要创新的量子存储解决方案来克服这些基本障碍，从而增强未来数据科学领域的量子计算工作。