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arXiv:2401.06535

Simulating open quantum systems using noise models and NISQ devices with error mitigation

M. Roy, Jessica John Britto, Ryan Hill, Victor Onofre

Published Jan 12, 2024• 0 citations
arXivHTMLPDF

Abstract

In this work, we present simulations of two Open Quantum System models, Collisional and Markovian Reservoir, with noise simulations, the IBM devices ($\textit{ibm_kyoto}$, $\textit{ibm_osaka}$) and the OQC device Lucy. Extending the results of García-Pérez, et al. [npj Quantum Information 6.1 (2020): 1]. Using the Mitiq toolkit, we apply Zero-Noise extrapolation (ZNE), an error mitigation technique, and analyze their deviation from the theoretical results for the models under study. For both models, by applying ZNE, we were able to reduce the error and overlap it with the theoretical results. All our simulations and experiments were done in the qBraid environment.

DOI
10.48550/arxiv.2401.06535

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In this work, we present simulations of two Open Quantum System models, Collisional and Markovian Reservoir, with noise simulations, the IBM devices (\textit{ibm_kyoto}, \textit{ibm_osaka}) and the OQC device Lucy. Extending the results of García-Pérez, et al. [npj Quantum Information 6.1 (2020): 1]. Using the Mitiq toolkit, we apply Zero-Noise extrapolation (ZNE), an error mitigation technique, and analyze their deviation from the theoretical results for the models under study. For both models, by applying ZNE, we were able to reduce the error and overlap it with the theoretical results. All our simulations and experiments were done in the qBraid environment.
In quantum computing, noisy intermediate-scale quantum (NISQ) devices offer unprecedented computational capabilities but are vulnerable to errors, notably measurement inaccuracies that impact computation accuracy. This study explores the efficacy of error mitigation techniques in improving quantum circuit performance on NISQ devices. Techniques such as dynamic decoupling (DD), twirled readout error extraction (T-REx) and zero-noise extrapolation (ZNE) are examined through extensive experimentation on an ideal simulator, IBM Kyoto, and IBM Osaka quantum computers. Results reveal significant performance discrepancies across scenarios, with error mitigation techniques notably enhancing both estimator result and variance values, aligning more closely with ideal simulator outcomes. The comparison results with ideal simulator (having expected result value 0.8284) shows that T-Rex has improved results on IBM Kyoto and enhanced average expected result value from 0.09 to 0.35. Similarly, DD has improved average expected result values from 0.2492 to 0.3788 on IBM Osaka. These findings underscore the critical role of error mitigation in bolstering quantum computation reliability. The results suggest that selection of mitigation technique depends upon quantum circuit and its depth, type of hardware and operations to be performed.
Abstract The practical application of Noisy Intermediate-Scale Quantum (NISQ) hardware is fundamentally limited by gate-level noise, which corrupts computational results. This research addresses this challenge through the development and validation of a modular software framework for Quantum Error Mitigation (QEM). We implement and compare two leading QEM strategies: Zero-Noise Extrapolation (ZNE) and Probabilistic Error Cancellation (PEC). The framework is built using the Qiskit library and is validated using a realistic, hardware-calibrated noisy simulator that mimics the error characteristics of a real IBM Quantum device. Our methodology focuses on a robust implementation of ZNE via unitary folding and a proof-of-concept demonstration of the PEC algorithm. The framework's effectiveness is demonstrated on a simulated noisy backend where, for a 3-qubit Greenberger-Horne-Zeilinger (GHZ) state, the baseline state fidelity was increased from 93.5% to 97.3% via ZNE, corresponding to a 59% reduction in the state's infidelity. This work provides a practical demonstration of how software-based error mitigation can enhance the reliability of quantum computations on current noisy hardware.
Quantum Neural Networks (QNNs) represent a promising direction within Quantum Machine Learning (QML), yet their realization on noisy intermediate-scale quantum (NISQ) devices remains constrained by decoherence, gate imperfections, crosstalk, and readout errors. This study provides a systematic evaluation of noise effects and mitigation strategies in hybrid quantum neural networks (HQNNs). Zero-Noise Extrapolation (ZNE), Digital Dynamical Decoupling (DDD), and Layerwise Richardson Extrapolation (LRE) are incorporated into end-to-end QNN training pipelines developed with PennyLane, simulated using Qiskit Aer noise models, and integrated with the Mitiq framework, while Probabilistic Error Cancellation (PEC) is evaluated separately under depolarizing noise due to its computational cost. Experiments conducted on the Iris dataset with five representative noise channels show that the impact of noise and the effect of mitigation are strongly dependent on the noise model and its strength. The model maintains comparatively strong performance under phase-flip and phase-damping noise, while substantial degradation is observed under high depolarizing and amplitude-damping noise. Across the evaluated mitigation methods, the observed benefits remain limited and noise-dependent: ZNE, DDD, and LRE generally follow the same degradation trends as the unmitigated baseline, while PEC shows limited gains only in the low-noise depolarizing regime. These findings highlight the need for context-specific mitigation strategies to improve the robustness of QNNs in practical NISQ settings.
Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm's sensitivity to these errors without increasing the number of required qubits. Here we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH+{\text{HeH}}^{+}HeH+ molecule at 0.8A˚0.8\phantom{\rule{3.33333pt}{0ex}}\text{\AA{}}0.8A˚ in the presence of experimental noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time stretching the two-qubit gates, scaling the sideband detuning parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find that time stretching and sideband detuning scaling fail to scale the noise on our particular hardware in a way that can be extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve error suppression of 96.896.8%96.8, resulting in an energy estimate within $\ensuremath{-}0.004\ifmmode\pm\else\textpm\fi{}0.04$ hartree of the ground state energy. This is an improvement, but still outside the chemical accuracy threshold of 0.0016 hartree. Our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.
Performance Optimization of Noise-Mitigated Quantum-Classical Hybrid Classifiers via Zero-Noise Extrapolation in NISQ Environments Overview Near-Term Intermediate-Scale Quantum (NISQ) hardware remains heavily constrained by physical noise, gate infidelities, and decoherence, which severely degrade the performance of Variational Quantum Classifiers (VQCs). This research presents an end-to-end, noise-mitigated hybrid quantum-classical machine learning pipeline that integrates PyTorch classical layers with PennyLane parameterized quantum circuits (PQCs) and applies Zero-Noise Extrapolation (ZNE) via Mitiq to counteract hardware noise. Key Highlights & Contributions Modular Hybrid Architecture: Combines classical feature mapping and post-processing in PyTorch with parameterized quantum variational circuits built in PennyLane. Digital Error Mitigation: Evaluates global gate folding (G→GG†GG \to G G^\dagger GG→GG†G) across varying scale factors (λ∈{1,3,5}\lambda \in \{1, 3, 5\}λ∈{1,3,5}) to extrapolate expectation values back to the zero-noise limit. Accuracy Recovery: Demonstrates that ZNE recovers classification accuracy near ideal noiseless performance (98.5%98.5\%98.5%) under low-to-moderate depolarizing noise levels (p < 0.01), outperforming unmitigated noisy executions by up to 11.3%. Model Benchmarking: Directly compares linear and second-order polynomial extrapolation models, analyzing variance trade-offs under finite shot noise constraints. Repository & Code Contents This deposit includes the full PDF manuscript alongside the accompanying code archive: Noise_Mitigated_Quantum_Classical_Hybrid_Classifier_with_Zero_Noise_Extrapolation.pdf — Full IEEE-formatted research paper. Noise-MitigatedQuantum-ClassicalHybridClassifierwithZero-NoiseExtrapolation.ipynb — Executable Jupyter Notebook containing the full PyTorch–PennyLane–Mitiq benchmarking pipeline. requirements.txt & README — Environment setup and reproduction instructions. How to Cite If you find this work or codebase helpful for your research in Quantum Machine Learning (QML) or Quantum Error Mitigation (QEM), please cite this preprint using the Zenodo DOI provided above.
The advent of noisy intermediate-scale quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics.NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe.Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems.Here, we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum systems theory.During the last decade an increasing number of experiments have successfully tackled the task of simulating open quantum systems in different platforms, from linear optics to trapped ions, from nuclear magnetic resonance (NMR) to cavity quantum electrodynamics.Generally, each individual experiment demonstrates a specific open quantum system model, or at most a specific class.Our main result is to prove the great versatility of the IBM Q Experience processors.Indeed, we experimentally implement one and two-qubit open quantum systems, both unital and non-unital dynamics, Markovian and non-Markovian evolutions.Moreover, we realise proof-of-principle reservoir engineering for entangled state generation, demonstrate collisional models, and verify revivals of quantum channel capacity and extractable work, caused by memory effects.All these results are obtained using IBM Q Experience processors publicly available and remotely accessible online.