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Artificial Intelligence Revolutions (AIR)

Variational Quantum Regression on NISQ Hardware with Error Mitigation

Eider Garate, Paul San Sebastian, Guillermo Valverde, Alejandra Ruiz, Meritxell Gómez-Omella

Published Oct 30, 2024• 1 citation
Publisher

Abstract

At the intersection of two promising technologies, Machine Learning (ML) and Quantum Computing (QC), Quantum Machine Learning (QML) emerges. However, while QC is still in an early stage of development, QML is even more so. In this study, the Auto-MPG dataset was selected for its dimension, making it suitable for QML tasks within the current limitations of quantum hardware, especially regarding qubit requirements. Unlike classification problems that dominate the literature, regression problems have only been explored theoretically. This study aims to bridge that gap by applying QML techniques to a practical regression task. To this end, a preliminary analysis was conducted using a classical model as a reference point for subsequent evaluation. The quantum experimentation was performed in two phases: first, the model was trained in an ideal simulator to determine the model's best hyperparameters. Then, these best models were run in a noisy simulator using quantum error mitigation techniques. The results show how the Variational Quantum Algorithms (VQA) outperforms classical Extreme Gradient Boosting and the methods used to mitigate errors in quantum hardware are effective, as they achieve comparable results between the noisy simulator and the perfect simulator. This brings closer the possible applications in NISQ current devices.

DOI
10.1109/air63653.2024.00016

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At the intersection of two promising technologies, Machine Learning (ML) and Quantum Computing (QC), Quantum Machine Learning (QML) emerges. However, while QC is still in an early stage of development, QML is even more so. In this study, the Auto-MPG dataset was selected for its dimension, making it suitable for QML tasks within the current limitations of quantum hardware, especially regarding qubit requirements. Unlike classification problems that dominate the literature, regression problems have only been explored theoretically. This study aims to bridge that gap by applying QML techniques to a practical regression task. To this end, a preliminary analysis was conducted using a classical model as a reference point for subsequent evaluation. The quantum experimentation was performed in two phases: first, the model was trained in an ideal simulator to determine the model's best hyperparameters. Then, these best models were run in a noisy simulator using quantum error mitigation techniques. The results show how the Variational Quantum Algorithms (VQA) outperforms classical Extreme Gradient Boosting and the methods used to mitigate errors in quantum hardware are effective, as they achieve comparable results between the noisy simulator and the perfect simulator. This brings closer the possible applications in NISQ current devices.
Quantum computing has emerged as a transformative paradigm capable of addressing computational challenges beyond the reach of classical systems.In the current era of Noisy Intermediate-Scale Quantum (NISQ) devices, practical quantum hardware is characterized by limited qubit counts, short coherence times, gate errors, and the absence of full error correction.Despite these constraints, significant progress has been made in developing quantum machine learning (QML) techniques tailored to operate on near-term quantum processors.This paper presents a comprehensive review of Quantum Machine Learning in the context of NISQ computing.We first outline the fundamental principles of quantum computing, including qubits, superposition, entanglement, and quantum parallelism, followed by a detailed discussion of the NISQ computing model and its hardware limitations.The review then examines hybrid quantum-classical learning frameworks, variational quantum algorithms, quantum data encoding strategies, and noise mitigation techniques that enable practical implementation on existing platforms.Emerging applications across healthcare, finance, cybersecurity, climate modeling, and materials science are also surveyed to highlight the real-world potential of QML.Furthermore, key challenges such as scalability, trainability issues, and algorithmic robustness are analyzed, along with current research efforts aimed at overcoming these barriers.The paper concludes by identifying promising future directions for advancing QML toward quantum advantage.This review aims to provide researchers and practitioners with a structured understanding of the capabilities, limitations, and opportunities of quantum machine learning in the NISQ era .
The rapid advancement of quantum computing hardware and software has ushered in a new era for computational science, promising to tackle problems that are intractable for classical computers. Parallelly, machine learning (ML) has revolutionized data analysis and artificial intelligence. The confluence of these two fields, known as Quantum Machine Learning (QML), aims to harness the principles of quantum mechanics-such as superposition, entanglement, and interference-to enhance and redefine classical machine learning algorithms. This survey provides a comprehensive overview of the burgeoning field of QML. We begin by elucidating the fundamental quantum concepts that underpin QML approaches. We then present a detailed taxonomy and analysis of prominent QML algorithms, categorizing them into quantum-enhanced classical models and fully quantum models. Key families of algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNNs), and Quantum Generative Adversarial Networks (QGANs). For each, we explain the theoretical quantum advantage, the circuit implementation, and the current limitations. Furthermore, we delve into the critical challenges facing the practical realization of QML, including the pervasive issue of noise in Noisy Intermediate-Scale Quantum (NISQ) devices, the problem of barren plateaus in training quantum circuits, and the complexities of efficient data encoding (quantum feature maps). We also present a small-scale experimental simulation of a variational quantum classifier on a standardized dataset, demonstrating its principle and comparing its performance with a classical counterpart. Finally, the paper discusses the future trajectory of QML, highlighting the importance of error mitigation, hybrid quantum-classical architectures, and the development of quantum-specific learning inductive biases. We conclude that while fault-tolerant quantum computers remain on the horizon, QML represents a paradigm shift with the potential to deliver profound computational advantages in the coming decades.
Machine Learning-based quantum error mitigation (ML-QEM) has emerged as a promising approach for improving the performance of noisy quantum algorithms. However, existing ML-QEM methods often have restricted applicability to variational circuits and rely on inaccessible noiseless training data. In this work, we propose a practical ML-QEM protocol tailored to variational quantum algorithms, which generates training data by simulating (near-)Clifford circuits. This data is used for model selection and training, producing a mitigation model that can correct variational circuits with arbitrary parameters and transfer across different target Hamiltonians of similar structure. We benchmark the proposed method on the Variational Quantum Eigensolver (VQE) task for the Sherrington-Kirkpatrick Hamiltonian of up to n=12n=12n=12 qubits under various noise models, analyzing its effect on trainability and comparing its performance against standard Zero-Noise Extrapolation (ZNE). The results demonstrate consistent several-fold error suppression across all tested settings and superior performance over ZNE in the high-noise regime, providing evidence for the applicability of the proposed protocol to present-day NISQ processors.
Quantum machine learning (QML) is an emerging field that synergistically combines quantum computing principles with classical ML techniques. With quantum principles like superposition and entanglement, QML has the potential of offering speedups for real-time optimization, classification, and generative modeling. While still in its infancy, QML has seen progress especially in hybrid quantum-classical algorithms, variational quantum circuits, and quantum kernel methods. Leading tech companies (IBM, Google, Xanadu) and startups are actively developing QML tools like Qiskit, TensorFlow Quantum, and PennyLane, enabling experiments on both simulators and early-stage quantum hardware. Recent breakthroughs include quantum advantage demonstrations in specific tasks, such as quantum-enhanced feature spaces and optimization problems. However, challenges remain due to noise in near-term quantum devices (NISQ era), limited qubit coherence, and significant error rates. Some researchers are exploring error-mitigation techniques and hybrid models that leverage classical ML to compensate for quantum hardware limitations. Key applications of QML that have shown promise include drug discovery and materials science (e.g., quantum chemistry simulations), finance (e.g., portfolio optimization and decision support), AI acceleration (e.g., quantum neural networks). While fault-tolerant and error-resistant quantum computers are still under development, QML is advancing through classical-quantum hybrid algorithms, making it a promising but rapidly evolving field. Investment from academia, industry, and governments suggests QML could play a transformative role in AI's future when hardware matures. This paper provides a primer on quantum principles as they relate to QML and takes a snapshot of the current status of QML development with an emphasis on quantum neural networks (QNNs) and highlights recent advances in automated QML (AutoQML).
Quantum Machine Learning (QML) is a newly emerging research area at the intersection of classical machine learning (CML) and quantum computing (QC). Data is becoming voluminous rapidly, so it is challenging for classical computers to train Machine Learning (ML) models over massive datasets. The hope is that quantum physics' intrinsic features, such as entanglement, superposition, and interference, could be exploited as resources for training ML models on big datasets that would otherwise be relatively impossible for classical computers. It is theoretically proven that quantum computers have an exponential-time advantage over their classical counterparts in solving several problems, e.g., complex large dimensional matrix multiplication, factorization problem, unstructured database search, etc. QML models attempt to find a quantum advantage over their classical counterparts. Variational Quantum Classifiers (VQC) are hybrid quantum neural networks to perform the task of classification using QML models. VQC models in the present NISQ (Noisy Intermediate Scale Quantum — 50 to 100 qubits) era can produce comparable and even better results than Classical models. In this article, we examined the performance of a VQC while performing a simple binary classification task. In this article, we use a VQC to evaluate this method's performance empirically. We constructed a VQC to predict the label of fresh input for the typical Iris dataset comprising pairings of target outputs and training inputs. Our quantum classifier can reasonably predict species labels using only four qubits. These levels are fairly good compared to the accuracy levels attained by classical classifiers.
An interesting approach to using noisy intermediate-scale quantum (NISQ) devices is hybrid classical-quantum machine learning (QML). In these methods, classical processors handle optimisation and large-scale computation, while quantum hardware is devoted to tasks like feature mapping, nonlinear transformations, or kernel evaluation. Practical near-term demonstrations are made possible by this division of labour, which also mitigates existing hardware restrictions. In specialised fields like molecular modelling, materials discovery, and small-sample learning issues, recent advancements in variational quantum circuits, hybrid neural networks, and quantum kernel techniques have produced promising outcomes. However, scalability and wider applicability are still hampered by enduring issues including noise, barren plateaus, and the expense of repeated measurements. Long-term developments will require fault tolerance, logical qubits, and established software infrastructures, whereas near-term success depends on noise-aware algorithm design, repeatable experimental benchmarks, and enhanced error-mitigation strategies. When taken as a whole, these advancements show a viable path to achieving quantum advantage in machine learning. Quanta 2026; 15: 1–12.