Resonance-Invariant Structures in Quantum Error Suppression A Conceptual Framework for Topological Protection in Noisy Intermediate-Scale Quantum Devices

Р С Лукин

Published Mar 6, 2026• 0 citations

Abstract

Abstract Current quantum computing architectures rely on probabilistic error correction codes that scale exponentially with the number of logical qubits. This work proposes a conceptual shift toward resonance-invariant structures, where protection against certain classes of noise arises from global topological properties of the multi-qubit Hamiltonian rather than from local redundancy alone. The central object is a dimensionless sensitivity parameter Ψ = ρ / A, where ρ is the effective growth rate of perturbations and A is a measure of the local stability basin in the many-body Hilbert space. When Ψ remains below a critical threshold, specific decoherence channels are topologically suppressed. The framework is purely theoretical and does not claim hardware feasibility at present. It is offered as a starting point for discussion within the quantum error-correction and topological quantum computing communities.

DOI: 10.5281/zenodo.18894300

Related papers

Resonance_Invariant_Structures_in_Quantum_Error_Suppression A_Conceptual_Framework_for_Topological_Protection_in_Noisy _Intermediate_Scale_Quantum_Devices

Р С Лукин

Abstract Current quantum computing architectures rely on probabilistic error correction codes that require exponential overhead in physical qubits per logical qubit. This conceptual preprint explores an alternative theoretical direction: resonance-invariant structures, where protection against certain classes of noise emerges from global symmetries in the multi-qubit Hamiltonian rather than from local redundancy alone.

Mar 7, 20260 citations

Topological Quantum Error Correction Realization via Topological Quantum Computers

Jincheng Zhang

This paper investigates the potential of utilizing topological quantum computers to achieve robust quantum error correction. The core claim centers on leveraging the unique physical properties of topological quantum computers – specifically, their inherent topological protection – to implement topological quantum error correction schemes. The proposed mechanism involves designing a quantum error-correcting code based on the interactions between entangled topological qubits within a physical topological structure. This approach allows for distributed error detection and correction, theoretically offering superior error correction rates and reduced resource requirements compared to traditional, single-qubit-based methods. The work explores the fundamental principles and theoretical framework for achieving topological quantum error correction, outlining key considerations for code design, qubit connectivity, and error mitigation strategies. The central focus is on demonstrating the feasibility of a topologically protected quantum code, contributing to the advancement of fault-tolerant quantum computing.

Aug 31, 20260 citations

Topological Protection of Quantum Error Correction

Jincheng Zhang

This paper investigates the application of topological protection to enhance quantum error correction, ultimately aiming for increased reliability in quantum information transmission and storage. The core concept revolves around encoding quantum bits (qubits) within topological defects, specifically leveraging the robust protection offered by these defects against local disturbances. We explore theoretical frameworks where topological protection fundamentally alters the error correction landscape, moving beyond traditional approaches reliant on local control and measurement. The study details how the inherent symmetries and conserved quantities associated with topological defects create a resilient environment for qubits, effectively mitigating the detrimental effects of decoherence and noise. Mathematical models are presented to illustrate the principles of topological error correction, including the concept of topological codes and their ability to detect and correct errors without directly measuring the qubits themselves. The paper concludes with a discussion on the challenges and future directions in realizing practical topological quantum computers, emphasizing the need for controlled manipulation and characterization of topological defects.

Aug 31, 20260 citations

Topological Quantum States-Based Entanglement Preservation for Quantum Error Correction

Jincheng Zhang

This paper proposes a novel quantum error correction code leveraging the inherent entanglement preservation properties of topological quantum states. Traditional quantum error correction schemes rely on creating and maintaining fragile quantum entanglement, which is highly susceptible to environmental noise. Our approach utilizes the topologically protected nature of certain quantum states to provide a robust mechanism for error detection and correction. We formulate a code based on the controlled-Z operation within a topological qubit architecture, demonstrating a significant improvement in error correction capabilities compared to conventional approaches. Specifically, we define the code parameters, including the code rate, minimum distance, and the required number of physical qubits. We analyze the code's performance under various noise models, highlighting the enhanced resilience due to topological protection. The key innovation lies in harnessing the natural, robust entanglement provided by topological states, offering a pathway to more practical and reliable quantum computation. The theoretical framework presented here provides a foundation for future research and development in topological quantum error correction.

Aug 29, 20260 citations

Topological Noise Suppression via Entangled Topology: A Novel Approach to Quantum Decoherence

Jincheng Zhang

Quantum decoherence poses a significant challenge to the development of practical quantum computers. The inherent sensitivity of quantum states to environmental interactions leads to rapid loss of quantum information. This work proposes a novel strategy for mitigating decoherence effects by leveraging topological protection. Specifically, we investigate the construction of quantum device arrays utilizing topologically protected states, combined with non-Abelian entanglement, to create a robust barrier against external noise. The core concept relies on isolating quantum bits (qubits) from environmental interactions through the unique properties of topological insulators and engineered topological structures. This approach aims to dramatically improve the fidelity and stability of quantum computations. Mathematical formulations detail the theoretical framework, demonstrating the potential of this method to achieve significantly reduced decoherence rates and enhanced quantum coherence times. The proposed architecture offers a pathway toward building more reliable and scalable quantum computing platforms.

Aug 28, 20260 citations

Quantum Error Correction: Surface And Topological Codes

N Raji

Quantum error correction (QEC) represents a critical enabler for fault-tolerant quantum computing, protecting fragile quantum states from decoherence and operational errors. This paper provides a comprehensive analysis of leading quantum error correction schemes, focusing on surface codes and topological codes within the context of Noisy Intermediate-Scale Quantum (NISQ) era processors. We examine the theoretical foundations of stabilizer codes, compare surface code implementations with code distances ranging from d=3 to d=17, and analyze topological codes including toric codes and color codes. Our investigation encompasses syndrome extraction circuits, logical qubit encoding strategies, and threshold analysis for contemporary quantum hardware platforms. Performance metrics reveal that surface codes achieve error thresholds of approximately 1% with realistic noise models, while topological codes offer architectural advantages for specific qubit connectivity constraints. We discuss implementation challenges on current NISQ processors including IBM Quantum, Google Sycamore, and IonQ systems, addressing qubit overhead, gate fidelity requirements, and decoding algorithms. This analysis provides insights for selecting appropriate error correction schemes based on application requirements and hardware capabilities.

Mar 12, 20260 citations