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Frontiers in Optics

Photonic Architecture of Entanglement Assisted Binary Quantum Tensor Product Codes

Priya J. Nadkarni, Shayan Srinivasa Garani

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We propose an architecture of an error correction scheme for a quantum communication system using integrated optics. Our scheme corrects burst errors using entanglement assisted binary quantum tensor product codes with an interleaver. © OSA 2019. The Author(s).
DOI
10.1364/fio.2019.jtu4a.99

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Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help correct quantum errors on noisy qubits, which can be too severe an assumption. We prove that a more relaxed and realistic assumption is sufficient by presenting encoding and decoding operations assisted by qubits on which quantum errors of one particular kind may occur. As in entanglement assistance, our scheme can import any binary or quaternary linear codes. If the auxiliary qubits are noiseless, our codes become entanglement-assisted codes, and saturate the quantum Singleton bound when the underlying classical codes are maximum distance separable.
Quantum communication channels benefit from nonbinary entanglement-assisted stabilizer codes using preshared entangled states for achieving better error correction capability compared to those that do not use preshared entanglement, making them indispensable for realizing large-scale quantum computing and communication systems over qudits. We provide a previously unreported design architecture of the syndrome computation unit for qudit stabilizer codes based on classical additive codes using discrete Fourier transform gates, ADD\mathrm{ADD}ADD gates, and multiplication gates. The proposed syndrome computation circuit architectures are necessary toward the implementable realization of such entanglement-assisted and -unassisted qudit stabilizer codes within the quantum transceiver system. We further provide an equivalent design architecture of the syndrome computation unit that decomposes into two syndrome computation units based on X errors and Z errors separately for entanglement-assisted and -unassisted qudit CSS codes. The proposed quantum error correction architectures are useful for building high-density coded quantum memories for archival quantum storage.
Abstract: This study investigates a topological quantum error-correction framework for scalable photonic quantum-computing architectures in which fusion-based entangling primitives are combined with tensor-network optimization. The central problem addressed is the gap between high-fidelity photonic components and the stringent logical-error rates required for fault-tolerant quantum computation. Photonic platforms offer room-temperature operation, manufacturable silicon-photonic process flows, high-bandwidth optical interconnects and natural compatibility with measurement-based computation; however, photon loss, probabilistic fusion and decoder latency impose architectural constraints that cannot be resolved by hardware fidelity alone. The proposed framework therefore treats hardware metrics, code geometry and decoding as a coupled optimization problem rather than as separate engineering layers. The manuscript develops a mathematically grounded model of surface-code and cluster-state error correction under photonic loss and fusion noise, then evaluates tensor-network contraction as a decoder and resource-allocation method. The data section explicitly uses published real-data-based benchmark inputs from contemporary photonic and quantum-error-correction literature, supplemented by transparent, domain-plausible projections where complete open photonic logical-QEC datasets are not yet available. Results show that tensor-network optimization improves the logical-error index relative to matching-based baselines in the modelled photonic regime, while the feasibility boundary remains dominated by loss, fusion infidelity and real-time decoding latency. The contribution is a reproducible evaluation framework that links topological protection, photonic architecture constraints and decoder design for future scalable fault-tolerant systems. Keywords: topological quantum error correction; surface code; photonic quantum computing; fusion-based quantum computation; tensor-network decoding; loss tolerance; scalable quantum architecture; measurement-based quantum computing; fault tolerance; silicon photonics.
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat such error patterns in the quantum regime. Our contributions are as follows. Firstly, we derive an upper bound for the correctable burst errors of QBECCs, the quantum Reiger bound (QRB). Secondly, we propose two constructions of QBECCs: one by heuristic computer search and the other by concatenating two quantum tensor product codes (QTPCs). We obtain several new QBECCs with better parameters than existing codes with the same coding length. Moreover, some of the constructed codes can saturate the quantum Reiger bounds. Finally, we perform numerical experiments for our constructed codes over Markovian correlated depolarizing quantum memory channels, and show that QBECCs indeed outperform standard QECCs in this scenario.