Entanglement and quantum computational speed-up

Jincheng Zhang

This paper proposes a novel approach to distributed computing leveraging the phenomenon of quantum entanglement. The core claim is that by directly connecting distributed computing nodes through entangled quantum states, we can drastically reduce data transmission latency and significantly accelerate computational processes. The proposed mechanism involves constructing a carefully designed quantum entanglement network, enabling instantaneous information exchange between nodes – effectively bypassing the limitations imposed by the speed of light. This approach shifts the paradigm from relying solely on quantum computers for classical computation to utilizing the fundamental properties of quantum mechanics as an intrinsic acceleration mechanism. We explore the theoretical underpinnings of this method, focusing on the potential for parallel computation and collaborative processing facilitated by entanglement. This research aims to establish a foundational understanding of entanglement-accelerated distributed computing, paving the way for future exploration and development in this nascent field. The central equation demonstrating the potential speed-up is: Δt = (Δs/c) + t_c, where Δt is the total computation time, Δs is the size of the data set, c is the speed of light, and t_c is the classical computation time. We demonstrate that, with perfect entanglement, Δt can be reduced substantially, approaching a speed increase of approximately 1/c, which is significantly faster than the conventional speed of data transfer.

Shengchao Ding, Zhi Hao Jin

Richard Jozsa, Noah Linden

For any quantum algorithm operating on pure states, we prove that the presence of multi‐partite entanglement, with a number of parties that increases unboundedly with input size, is necessary if the quantum algorithm is to offer an exponential speed‐up over classical computation. Furthermore, we prove that the algorithm can be efficiently simulated classically to within a prescribed tolerance η even if a suitably small amount of global entanglement is present. We explicitly identify the occurrence of increasing multi‐partite entanglement in Shor's algorithm. Our results do not apply to quantum algorithms operating on mixed states in general and we discuss the suggestion that an exponential computational speed‐up might be possible with mixed states in the total absence of entanglement. Finally, despite the essential role of entanglement for pure‐state algorithms, we argue that it is nevertheless misleading to view entanglement as a key resource for quantum‐computational power.

Arvind

F.J. Duarte

Samuel L. Braunstein, Arun Kumar Pati

Grover's algorithm on pure states naturally generates entanglement during computation. For pseudo-pure state implementations we show that not only is entanglement necessary to achieve a speed-up, but it must be present throughout the computation. Despite the non-asymptotic character of this result we find that it only unambiguously applies to ensemble implementations, such as in liquid-state NMR, for asymptotically large search spaces. This ambiguity and its implications for interpreting a claimed speed-up in existing NMR based quantum searches is discussed.