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IEEE International Conference on Quantum Computing and Engineering (QCE)

Topology- and Locality-Guided Pre-Processing for Measurement Error Mitigation with Crosstalk Effects

Tatsuhiko Shirai

Published Aug 30, 2025• 0 citations
Publisher

Abstract

This study proposes a scalable pre-processing method that incorporates crosstalk effects in quantum devices, with a focus on mitigating measurement errors. Measurement errors are modeled as a transition probability matrix between ideal and noisy distributions. However, the size of this matrix grows exponentially with the number of qubits, posing a major challenge for large systems. To overcome this, we exploit two empirical observations obtained from experiments on an 8-qubit superconducting quantum device: (i) error correlations are strongly influenced by the topology of the qubit connectivity, and (ii) the mitigated observable exhibits locality, with dominant contributions from low-order terms. Based on these features, we introduce an approximation scheme that restricts attention to observables with limited locality and to qubits within a bounded distance on a device graph. Transition probabilities are efficiently estimated using parallel measurements based on a perfect hash family, reducing the required number of measurements from polynomial to quasi-linear in system size. We validate our approach on a 32-qubit device and demonstrate that it achieves a 50 % reduction in error compared to unmitigated data and a 10 % improvement over a conventional method that neglects crosstalk. Our results highlight the potential of topology-aware, locality-preserving error mitigation for enhancing quantum computations on near-term devices.

DOI
10.1109/qce65121.2025.10357

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This study proposes a scalable pre-processing method that incorporates crosstalk effects in quantum devices, with a focus on mitigating measurement errors. Measurement errors are modeled as a transition probability matrix between ideal and noisy distributions. However, the size of this matrix grows exponentially with the number of qubits, posing a major challenge for large systems. To overcome this, we exploit two empirical observations obtained from experiments on an 8-qubit superconducting quantum device: (i) error correlations are strongly influenced by the topology of the qubit connectivity, and (ii) the mitigated observable exhibits locality, with dominant contributions from low-order terms. Based on these features, we introduce an approximation scheme that restricts attention to observables with limited locality and to qubits within a bounded distance on a device graph. Transition probabilities are efficiently estimated using parallel measurements based on a perfect hash family, reducing the required number of measurements from polynomial to quasi-linear in system size. We validate our approach on a 32-qubit device and demonstrate that it achieves a 50 % reduction in error compared to unmitigated data and a 10 % improvement over a conventional method that neglects crosstalk. Our results highlight the potential of topology-aware, locality-preserving error mitigation for enhancing quantum computations on near-term devices.
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Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using Diagonal Detector Overlapping Tomography – a generalization of the recently introduced Quantum Overlapping Tomography to the problem of reconstruction of readout noise with restricted locality. The procedure allows to characterize k -local measurement cross-talk on N -qubit device using O(k2klog(N)) circuits containing random combinations of X and identity gates. We perform experiments on 15 (23) qubits using IBM's (Rigetti's) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor >22 ( >5.5 ) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.
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 T1T_1T1​, T2T_2T2​, 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.
Accurate and efficient implementation of parallel quantum gates is crucial for scalable quantum information processing. However, the unavoidable crosstalk between qubits in current noisy processors impedes the achievement of high gate fidelities and renders full Hilbert-space control optimization prohibitively difficult. Here, we overcome this challenge by reducing the full-system optimization to crosstalk-robust control over constant-sized subsystems, which dramatically reduces the computational cost. Our method effectively eliminates the leading-order gate operation deviations induced by crosstalk, thereby suppressing error rates. Within this framework, we construct analytical pulse solutions for parallel single-qubit gates and numerical pulses for parallel multi-qubit operations. We validate the proposed approach numerically across multiple platforms, including coupled nitrogen-vacancy centers, a nuclear-spin processor, and superconducting-qubit arrays with up to 200 qubits. As a result, the noise scaling is reduced from exponential to linear for parallel single-qubit gates, and an order-of-magnitude reduction is achieved for parallel multi-qubit gates. Moreover, our method does not require precise knowledge of crosstalk strengths and makes no assumption about the underlying qubit connectivity or lattice geometry, thereby establishing a scalable framework for parallel quantum control in large-scale quantum architectures.
Reducing measurement errors in multiqubit quantum devices is critical for performing any quantum algorithm. Here we show how to mitigate measurement errors by a classical postprocessing of the measured outcomes. Our techniques apply to any experiment where measurement outcomes are used for computing expected values of observables. Two error-mitigation schemes are presented based on tensor product and correlated Markovian noise models. Error rates parametrizing these noise models can be extracted from the measurement calibration data using a simple formula. Error mitigation is achieved by applying the inverse noise matrix to a probability vector that represents the outcomes of a noisy measurement. The error-mitigation overhead, including the number of measurements and the cost of the classical postprocessing, is exponential in $\ensuremath{\epsilon}n$, where $\ensuremath{\epsilon}$ is the maximum error rate and nnn is the number of qubits. We report experimental demonstration of our error-mitigation methods on IBM Quantum devices using stabilizer measurements for graph states with $n\ensuremath{\le}12$ qubits and entangled 20-qubit states generated by low-depth random Clifford 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+12^{n+1}2n+1 calibration circuits on the quantum hardware, where nnn 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.