General Machine Learning Algorithm for Quantum Teleportation

TL;DR

The paper introduces a machine-learning–driven protocol to construct optimal unitary corrections for quantum teleportation across a broad class of systems, from finite-spin to continuous-variable regimes, under non-ideal entanglement and resource constraints. It defines a general algorithm that entangles A and B, mediates AC interactions, measures commuting observables, and optimizes unitary corrections to maximize mean fidelity, with explicit forms for single-qubit cases and scalable to multi-particle spin states. Through a collective-spin physical model, it demonstrates high-fidelity teleportation for single qubits, N-particle spin coherent states, and rotated Dicke states, including scenarios with prior state distributions and unequal particle numbers, often surpassing classical benchmarks. The approach yields a flexible fidelity–cost tradeoff, robust against imperfections and fluctuations, and highlights avenues for enhancement via expanded optimization spaces and AI techniques. Overall, this work provides a general, adaptable framework for quantum teleportation applicable to a wide range of experimental platforms and state families, with clear implications for quantum networks and information processing.

Abstract

We present a general algorithm, based on machine learning, which can create optimal unitary operators to implement quantum teleportation in any system with well-defined set of measurements in a relevant entangled basis. We illustrate it with a collective spin model and demonstrate its versatility by applying it to teloportation of single and multiple qubit states, coherent and Dicke states, and for systems with prior distributions and unequal dimensions. All cases display significant regimes of quantum advantage over corresponding classical schemes with no entanglement. The algorithm offers the flexibility to choose a balance between target fidelity and computational cost.

Figures (4)

• Figure 1: Teleportation of single qubits, each point marking a specific input state. The four unitary operators are determined by optimizing: $I$. the three Euler angles with optimization of initial conditions; $II$. the three Euler angles without optimizing initial conditions; $III$. only $J_x$ and $J_y$ rotations but with partial optimization of initial conditions. The maximum classical fidelity (dashed line) is surpassed by all, with average fidelities, $I: 100\%, II: 95.7\%$ and $III: 81.1\%$.
• Figure 2: (a) Fidelity of coherent states in SU(1,1) initialization for $10$ particles in A,B,C, for uniform distribution of input state of C. Red dots represent the optimized fidelity after applying $\hat{U}_{ij}(\psi_i,\Phi_j^{AC})$; the black line is their average; the blue band comprises of points marking the fidelity on applying $\hat{\mathbf{U}}_j(\Phi_j^{AC})$. (b) Averaged fidelities as a function of the occupation numbers $\langle n\rangle$ for a von Mises-Fisher prior distribution shown for SU(2), SU(1,1) initializations of C, and for teloporting $\bar{C}$. Comparison with the classical limit shown with as dashed line shows a broad regime of quantum advantage.
• Figure 3: The fidelities when the number of atoms among the species are different. (a) $N_B = N_C = 10$, and $N_A = 9$, $10$, and $11$. (b) $N_A = N_C = 10$, and $N_B = 9$, $10$, and $11$.
• Figure 4: The fidelities of the first three Dicke states are plotted. All the states have regimes where a significant fraction of the states surpass the maximum fidelity without entanglement, shown as dashed lines.