Quantum Computation via Entangled State Teleportation

Abstract

This paper investigates the feasibility and potential benefits of utilizing quantum entanglement and the principle of quantum state teleportation for distributed computing. The core idea is to decompose complex computational tasks into smaller sub-tasks, which are then executed concurrently across a network of interconnected quantum nodes. Quantum state teleportation is employed to transfer intermediate results and perform logical operations between these nodes. We propose a framework for designing such a system, analyzing its computational complexity, and discussing the challenges associated with scalability and error correction. The potential advantages of this approach include increased computational speed, enhanced security through inherent quantum properties, and the possibility of tackling problems intractable for classical computers. This research explores the theoretical foundations and identifies key areas for future investigation within this emerging field. The central equation demonstrating the teleportation process is: $|\psi_A\rangle \rightarrow |\psi_B\rangle$ where $|\psi_A\rangle$ is the initial quantum state at Alice's location, $|\psi_B\rangle$ is the reconstructed quantum state at Bob's location, and the process relies on pre-shared entanglement ($|E\rangle$) between Alice and Bob. Furthermore, the following equations represent the key steps: $|\psi_A\rangle \otimes |E\rangle \rightarrow \frac{1}{\sqrt{2}}(|\psi_A\rangle |E\rangle + E^*| \psi_A\rangle)$ Bell Measurement: The Bell measurement is defined as: $M = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)$ where |00⟩ and |11⟩ are the two possible outcomes of the measurement. Projector: The projector operator is defined as: $P_x = \frac{1}{\sqrt{2}}(|0\rangle|0\rangle + |1\rangle|1\rangle)$ The density matrix evolution equation is: $\rho_B(t) = \frac{1}{2^n} \sum_{i=0}^{2^n-1} \rho_A(t, i) \Pi_i$ where $\rho_A(t, i)$ is the density matrix at Alice's location at time *t* and index *i*, and $\Pi_i$ is the projector operator corresponding to the *i*-th state.