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International Journal of Quantum Information

QUANTUM ERROR CORRECTION DRIVEN ENTANGLEMENT DYNAMICS IN THE PRESENCE OF CORRELATED NOISE

Gabriele De Chiara, Rosario Fazio, Chiara Macchiavello, G. Massimo Palma

Published Dec 16, 2004• 2 citations
Publisher

Abstract

The effects of quantum error correction (QEC) on the dynamics of entanglement between logical qubits in the presence of a dephasing interaction with a correlated environment is investigated. Such a correlated reservoir introduces entanglement between physical qubits which, for short times, is interpreted as error and suppressed by the QEC routine. However for longer times, although QEC is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.

DOI
10.1142/s0219749905000761

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The effects of quantum error correction (QEC) on the dynamics of entanglement between logical qubits in the presence of a dephasing interaction with a correlated environment is investigated. Such a correlated reservoir introduces entanglement between physical qubits which, for short times, is interpreted as error and suppressed by the QEC routine. However for longer times, although QEC is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.
We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between physical qubits. We show that for short times the quantum error correction interprets such entanglement as errors and suppresses it. However, for longer time, although quantum error correction is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.
Quantum error correction (QEC) faces a significant challenge in realistic noisy intermediate-scale quantum (NISQ) devices: correlated decoherence. Building upon the foundational QEC-C protocol, we introduce QEC-C II, a scalable framework that delivers robust fault tolerance against spatially and temporally correlated noise. By integrating decoherence-free subspace (DFS) principles and correlation-aware adaptive feedback, QEC-C II achieves exponential error suppression in simulation under correlated noise models, with fewer physical qubits than typical topological baselines for the same target error in our benchmarks. The protocol leverages an enhanced scaling law, β(n) = 0.788 e 0.360n , and efficiently suppresses noise with minimal computational overhead. We validate QEC-C II on 28-qubit GHZ states, extend it to 56-qubit subspaces, and conduct 84-qubit stress-test simulations under correlated noise models. The results demonstrate sustained fidelities exceeding 99.99 % in simulations under realistic dephasing, amplitude-damping, burst-error, and correlated decoherence scenarios, with rapid convergence (typically ≤ 2 iterations in our simulations). QEC-C II significantly reduces both resource and control complexity, simplifying hardware integration and improving performance with increasing system size. This work provides a practical pathway toward resource-efficient fault tolerance in quantum processors operating in real-world correlated environments.
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation, however, are limited by decoherence, in which the effect of an external environment causes random errors in the quantum calculation. To combat this problem, quantum error correction schemes have been proposed, in which a single quantum bit (qubit) is ``encoded'' as a state of some larger number of qubits, chosen to resist particular types of errors. Most such schemes are vulnerable, however, to errors in the encoding and decoding itself. We examine two such schemes, in which a single qubit is encoded in a state of nnn qubits while subject to dephasing or to arbitrary isotropic noise. Using both analytical and numerical calculations, we argue that error correction remains beneficial in the presence of weak noise, and that there is an optimal time between error correction steps, determined by the strength of the interaction with the environment and the parameters set by the encoding.
Abstract Quantum entanglement is a fundamental resource for quantum computing, quantum communication, and quantum cryptography. In realistic quantum channels, however, entanglement is highly susceptible to noise and decoherence. Entanglement purification(EP) and quantum error correction (QEC) offer distinct approaches to protecting entanglement against noisy quantum channels. In this work, we propose a hybrid scheme that integrates these two approaches to enhance the protection of entanglement between logical qubits. The scheme exploits both the error-correcting capability of encoded logical qubits and the distillation power of entanglement purification, assuming recovery to the logical codespace after each QEC cycle. This combined approach enables improved entanglement preservation under noisy conditions. The resulting robust logical entanglement is well-suited for applications in quantum communication and quantum cryptography and offers a promising route toward more reliable distributed quantum information processing.
We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.