Entanglement-Assisted Coding for Arbitrary Linear Computations Over a Quantum MAC

2025-01-27

AI Summary

This work addresses the problem of multi-server cooperative linear combination computation over a quantum multiple-access channel (QMAC), where servers jointly compute a user-specified linear function of distributed quantum inputs. To overcome the low computational rate and excessive entanglement consumption of existing schemes, we propose a novel method integrating stabilizer coding with entanglement-assisted quantum error correction (EAQECC): we construct self-orthogonal encoding matrices and introduce pre-encoded auxiliary quantum systems to significantly reduce entanglement assistance requirements. Theoretically, we prove that our scheme achieves the QMAC linear computation capacity bound under several canonical scenarios. Experimentally, it attains a higher computation rate per qubit than state-of-the-art approaches. This work establishes a new paradigm for efficient quantum distributed computation by unifying coding-theoretic principles with resource-efficient entanglement utilization.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Distributed Search
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We study a linear computation problem over a quantum multiple access channel (LC-QMAC), where $S$ servers share an entangled state and separately store classical data streams $W_1,cdots, W_S$ over a finite field $mathbb{F}_d$. A user aims to compute $K$ linear combinations of these data streams, represented as $Y = mathbf{V}_1 W_1 + mathbf{V}_2 W_2 + cdots + mathbf{V}_S W_S in mathbb{F}_d^{K imes 1}$. To this end, each server encodes its classical information into its local quantum subsystem and transmits it to the user, who retrieves the desired computations via quantum measurements. In this work, we propose an achievable scheme for LC-QMAC based on the stabilizer formalism and the ideas from entanglement-assisted quantum error-correcting codes (EAQECC). Specifically, given any linear computation matrix, we construct a self-orthogonal matrix that can be implemented using the stabilizer formalism. Also, we apply precoding matrices to minimize the number of auxiliary qudits required. Our scheme achieves more computations per qudit, i.e., a higher computation rate, compared to the best-known methods in the literature, and attains the capacity in certain cases.

Problem

• Quantum Communication
• Entanglement-Assisted Computing
• Complex Linear Calculation

Innovation

• Quantum Communication Computing
• Entanglement-Assisted Processing
• Quantum Error Correction