Fundamental causal bounds of quantum random access memories
Yunfei Wang Yuri Alexeev Liang Jiang Frederic T. Chong Junyu Liu
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.