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Chinese Physics Review

Divided-Qubit Noise-Tolerant Strategy for Bell State Preparation in Qiskit

Independent Researcher, Yang Daniel Ou, Wenming SUN

Published Dec 28, 2025• 0 citations
Publisher

Abstract

This study focuses on achieving high-fidelity preparation of Bell states in depolarization noise environments. Based on Qiskit simulations, we propose a quantum-bit-by-quantum-bit noise-resistant strategy: applying dynamic decoupling to control qubits and implementing quantum error correction for target qubits. Experimental results demonstrate that this strategy maintains fidelity at 1. 0000 while significantly reducing the error rate from approximately 24% to 0. 4%, requiring only four additional quantum gate operations. The method achieves high-fidelity quantum entanglement with low complexity, showcasing significant practical value. As the standard form. of two-qubit maximum entanglement state, the Bell states are widely applied in critical tasks such as quantum teleportation, superdense coding, and quantum key distribution. However, real quantum systems inevitably interact with their environment, leading to quantum state decoherence and a significant decrease in the fidelity of the Bell state. Existing anti-jamming schemes mainly fall into two categories: dynamic decoupling through periodic pulse application to cancel noise, and quantum error correction through redundant encoding to fix errors. However, dynamic decoupling requires extremely high synchronization for multi-qubit systems, while quantum error correction necessitates additional auxiliary qubits, resulting in an exponential growth in circuit complexity.

DOI
10.48014/cpr.20251029002

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Decoherence is a primary barrier to practical quantum computation, causing quantum states to degrade through phase randomization and irreversible energy relaxation. This study presents a simulation-based evaluation of echo-based dynamical decoupling (DD) pulse sequences as a software-level mitigation strategy in single-qubit systems. Using the Qiskit Aer density matrix simulator, four strategies—baseline, Hahn Echo, Carr-Purcell-Meiboom-Gill (CPMG), and Mixed Synchronization—were evaluated across low-frequency phase noise, high-frequency phase noise, and combined T₁ + T₂ noise regimes. Hahn Echo restored mean fidelity to 100.00% under low-frequency noise (baseline: 57.90%), while CPMG achieved 97.62% under high-frequency noise (baseline: 2.45%). Under combined noise, all strategies showed limited improvement, with Mixed-Sync reaching 65.34% versus 60.95%. Coefficient of variation (CV) analysis across 500 Monte Carlo trials showed that CPMG reduced purity-decay variance threefold under high-frequency noise, with bootstrap confidence intervals confirming statistical significance. Time-resolved analysis showed that CPMG suppressed variance growth throughout evolution, reducing variance growth from +267% (baseline) to +89%, while baseline and Hahn Echo exhibited progressive amplification of variance. These results show that dynamical decoupling influences the temporal structure of noise, not just mean fidelity. In T₂-dominated regimes, pulse sequences constrain variability; in mixed regimes, they partially shape it; and in T₁-dominated regimes, both mean performance and variability converge to hardware-limited behavior. DD effectively corrects reversible phase errors but cannot overcome irreversible T₁ loss, with implications for NISQ circuit design.
Quantum error correction (QEC) codes are necessary to fault-tolerantly operate quantum computers. However, every such code is inherently limited by its inability to detect logical errors. Here, we propose and implement a method that leverages dynamical decoupling (DD) to drastically suppress logical errors. The key to achieving this is to use the normalizer elements of the QEC code as DD pulses, which we refer to as normalizer dynamical decoupling (NDD). The resulting hybrid QEC-NDD strategy is in principle capable of handling arbitrary weight errors. We test an error detecting version of this strategy using IBM transmon devices and the [[4, 2, 2]] code, demonstrating performance that significantly exceeds the capabilities of using either this code or DD in isolation. We present a method that allows for the detection of logical errors affecting logically encoded Bell states, which, in this case, arise primarily from crosstalk among physical qubits. Building on this, we experimentally demonstrate high-fidelity entangled logical qubits. The fidelities we achieve are beyond-breakeven, i.e., they significantly exceed the corresponding fidelities of unprotected entangled qubits in the same setting. Quantum error correction codes are hindered by the inability to detect logical errors. Here the authors demonstrate a method that integrates quantum error correction with logical level dynamical decoupling to suppress these errors and achieve high fidelity entangled logical qubits.
Dynamic quantum circuits integrate unitary evolution with mid-circuit measurement and feedforward, enabling conditional operations essential for efficient quantum algorithms and foundational for fault-tolerant quantum computation. However, such operations introduce measurement-induced errors and control constraints that are not addressed by conventional error-suppression techniques. Here, we introduce an empirical learning framework that optimizes dynamical decoupling (DD) sequences for dynamic circuits at the level of circuit subintervals and qubit subregisters. Applying empirically learned DD sequences, we achieve a three-fold reduction in average dynamic circuit error rates as measured via randomized benchmarking. We apply the learned strategies to the dynamic circuit implementation of the quantum Fourier transform with measurement (QFT+M), demonstrating nontrivial process fidelity on connected chains of up to 20 qubits. Applying the resulting enhancement, we perform a high signal-to-noise QFT immediately following the preparation of a 10-qubit entangled state. Our results demonstrate that empirically optimized DD systematically outperforms theoretically derived sequences for dynamic circuits, establishing it as an efficient approach for error suppression in dynamic quantum circuits, with direct relevance to applications requiring measurement and feedback such as quantum error correction.
In order to improve the anti-noise performance of quantum teleportation, this paper proposes a novel dynamic quantum anti-noise scheme based on the quantum teleportation which transmits single qubit state using Bell state. Considering that quantum noise only acts on the transmitted qubit, i.e., the entangled state that Alice and Bob share in advance is affected by the noise, thus affecting the final transmission result. In this paper, a method for dynamically adjusting the shared entangled state according to the noise environment is proposed. By calculating the maximum fidelity of the output state to determine the shared entangled state, which makes the quantum teleportation be affected by the noise as little as possible. This paper calculates the fidelity of teleportation under four kinds of channel noise (amplitude damping, phase damping, bit flip and depolarizing noise). The results show that the scheme has a suppression effect on phase damping, bit flip and depolarizing noise under certain conditions. When the noise intensity is larger, the optimized efficiency is better.