Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data regression (CDR), rely on noise scaling or global regression, and their performance is constrained by the exponential growth of the system degrees of freedom. We construct a graph-enhanced mitigation (GEM) framework, which incorporates physical information into the model representation. In this work, quantum circuits are encoded as attributed graphs. Hardware-level physical information is mapped to node and edge features: local noise parameters such as calibration parameters $T_1$, $T_2$, and readout errors are encoded at nodes, while coupling-related information such as two-qubit gate errors is encoded as edge features. Graph neural networks are used to model how errors propagate along the physical coupling structure and build up into non-local correlations. This allows the model to capture local interactions and part of the resulting non-local correlations across qubits. A dual-branch affine correction is applied to maintain consistency with physical constraints. Experiments on 10-qubit and 16-qubit random circuits executed on superconducting quantum processors show that GEM provides a level of accuracy comparable to CDR at small scales, while yielding lower mean absolute error and improved stability in zero-shot transfer to larger systems. Results of the traditional QEM strategy indicate that global regression methods remain effective in low-dimensional settings but become less reliable as system degrees of freedom grow. In contrast, GEM makes use of local physical structures to show better scalability and generalization, while preserving the overall error propagation patterns. This work provides a practical scalable approach to QEM for NISQ devices.
Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data regression (CDR), rely on noise scaling or global regression, and their performance is constrained by the exponential growth of the system degrees of freedom. We construct a graph-enhanced mitigation (GEM) framework, which incorporates physical information into the model representation. In this work, quantum circuits are encoded as attributed graphs. Hardware-level physical information is mapped to node and edge features: local noise parameters such as calibration parameters T1, T2, and readout errors are encoded at nodes, while coupling-related information such as two-qubit gate errors is encoded as edge features. Graph neural networks are used to model how errors propagate along the physical coupling structure and build up into non-local correlations. This allows the model to capture local interactions and part of the resulting non-local correlations across qubits. A dual-branch affine correction is applied to maintain consistency with physical constraints. Experiments on 10-qubit and 16-qubit random circuits executed on superconducting quantum processors show that GEM provides a level of accuracy comparable to CDR at small scales, while yielding lower mean absolute error and improved stability in zero-shot transfer to larger systems. Results of the traditional QEM strategy indicate that global regression methods remain effective in low-dimensional settings but become less reliable as system degrees of freedom grow. In contrast, GEM makes use of local physical structures to show better scalability and generalization, while preserving the overall error propagation patterns. This work provides a practical scalable approach to QEM for NISQ devices.
Abstract Noisy Intermediate-Scale Quantum (NISQ) computing is fundamentally constrained by hardware noise that is not only large but also temporally drifting and structurally complex. Traditional quantum error mitigation (QEM) techniques, such as Zero-Noise Extrapolation (ZNE), often rely on simplified noise assumptions that degrade under coherent errors and deep circuit structures. Conversely, existing machine learning-based QEM approaches typically treat device noise as a static background, leading to poor generalization when hardware calibration shifts. In this work, we propose \textbf{Calib-GNN}, a novel framework that explicitly integrates real-time hardware calibration data into a Graph Neural Network (GNN) architecture. By embedding gate-specific error rates directly into the graph representation, our model learns a dynamic mapping from noisy measurements to ideal expectation values. Through extensive simulations based on real noise profiles from the IBM Quantum \texttt{ibm\_fez} backend, we demonstrate that Calib-GNN significantly outperforms standard baselines. Specifically, it reduces the Root Mean Square Error (RMSE) by approximately 14\% compared to ZNE on random circuits and exhibits superior robustness against severe noise drift where traditional models fail. Furthermore, we show that Calib-GNN effectively scales to deeper circuits and recovers the ground state energy of the H2 molecule in Variational Quantum Eigensolver (VQE) tasks with high fidelity, overcoming the limitations of ZNE in the presence of coherent noise.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.
We present a hybrid quantum-classical framework augmented with learned error mitigation for solving the viscous Burgers equation on noisy intermediate-scale quantum (NISQ) hardware. Using the Cole-Hopf transformation, the nonlinear Burgers equation is mapped to a diffusion equation, discretized on uniform grids, and encoded into a quantum state whose time evolution is approximated via Trotterized nearest-neighbor circuits implemented in Qiskit. Quantum simulations are executed on noisy Aer backends and IBM superconducting quantum devices and are benchmarked against high-accuracy classical solutions obtained using a Krylov-based solver applied to the corresponding discretized Hamiltonian. From measured quantum amplitudes, we reconstruct the velocity field and evaluate physical and numerical diagnostics, including the L2 error, shock location, and dissipation rate, both with and without zero-noise extrapolation (ZNE). To enable data-driven error mitigation, we construct a large parametric dataset by sweeping viscosity, time step, grid resolution, and boundary conditions, producing matched tuples of noisy, ZNE-corrected, hardware, and classical solutions together with detailed circuit metadata. Leveraging this dataset, we train an attention-based graph neural network that incorporates circuit structure, light-cone information, global circuit parameters, and noisy quantum outputs to predict error-mitigated solutions. Across a wide range of parameters, the learned model consistently reduces the discrepancy between quantum and classical solutions beyond what is achieved by ZNE alone. We discuss extensions of this approach to higher-dimensional Burgers systems and more general quantum partial differential equation solvers, highlighting learned error mitigation as a promising complement to physics-based noise reduction techniques on NISQ devices.
Noise in quantum hardware is the primary obstacle to realizing the transformative potential of quantum computing. Quantum error mitigation (QEM) offers a promising pathway to enhance computational accuracy on near-term devices, yet existing methods face a difficult trade-off between performance, resource overhead, and theoretical guarantees. In this work, we introduce neighbor-informed learning (NIL), a versatile and scalable QEM framework that unifies and strengthens existing methods such as zero-noise extrapolation (ZNE) and probabilistic error cancellation (PEC), while offering improved flexibility, accuracy, efficiency, and robustness.
NIL learns to predict the ideal output of a target quantum circuit from the noisy outputs of its structurally related ``neighbor'' circuits. A key innovation is our 2-design training method, which generates training data for our machine learning model. In contrast to conventional learning-based QEM protocols that create training circuits by replacing non-Clifford gates with uniformly random Clifford gates, our approach achieves higher accuracy and efficiency, as demonstrated by both theoretical analysis and numerical simulation. Furthermore, we prove that the required size of the training set scales only \emph{logarithmically} with the total number of neighbor circuits, enabling NIL to be applied to problems involving large-scale quantum circuits. Our work establishes a theoretically grounded and practically efficient framework for QEM, paving a viable path toward achieving quantum advantage on noisy hardware.
The current advancement in quantum computers has been focusing on increasing the number of qubits and enhancing their fidelity. However, the available quantum devices, known as intermediate scale quantum (NISQ) computers, still suffer from different sources of noise that impact their reliability. Thus, practical noise modeling is of great importance in the development of quantum error mitigation approaches. In this article, we propose a machine learning (ML)-based scheme to predict the output fidelity of the quantum circuit executed on NISQ devices. We show the benefit of using graph neural network (GNN)-based models compared to traditional ML-based models in capturing the quantum circuit structure in addition to its gates’ features, which enable characterizing unpredicted quantum circuit errors. We use different metrics to measure the fidelity of the quantum circuit output. Our experimental results using different quantum algorithms executed on IBM Q Guadalupe quantum computer show the high prediction accuracy of our ML reliability models. Our results also show that our models can guide the single-qubit gate rescheduling to improve the output fidelity of the quantum circuit without the need for prior execution of dedicated calibration circuits.
In quantum computing, error mitigation is a method to improve the results of an error-prone quantum processor by post-processing them on a classical computer. In this work, we improve the General Error Mitigation (GEM) method for scalability. GEM relies on the use of a matrix to represent the device error, which requires the execution of 2n+1 calibration circuits on the quantum hardware, where n is the number of qubits. With our improved method, the number of calibration runs is independent of the number of qubits and depends only on the number of non-zero states in the output distribution. We run 1853 randomly generated circuits with widths between 2-7 qubits and depths between 10-140 gates on IBMQ superconducting devices. The experiments show that the mitigation works comparably well to GEM, while requiring a fraction of the calibration runs. Finally, an experiment to mitigate errors in a 100 qubit circuit demonstrates the scalable features of our method.