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arXiv:2412.16092 · PRX Quantum

Sparse non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations

Yasuo Oda, Kevin Schultz, Leigh Norris, Omar Shehab, Gregory Quiroz

Published Mar 17, 2026• 2 citations
arXivHTMLPDF

Abstract

The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatiotemporally correlated noise sources. The model’s predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a sevenfold improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.

DOI
10.1103/lx8x-z29x

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The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatiotemporally correlated noise sources. The model’s predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a sevenfold improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.
The influence of noise in quantum dynamics is one of the main factors preventing current quantum processors from performing quantum computations. Errors must be addressed, which requires a thorough understanding of the nature and interplay of different sources of noise. In this work, we propose an effective error model of single-qubit operations on the IBM Quantum Platform (IBMQP), that possesses considerable predictive power. We showcase how Quantum Noise Spectroscopy (QNS) can be used alongside other error characterization techniques to obtain a more complete error model of the system. The model allows for both Markovian and spatio-temporally correlated non-Markovian environmental and control effects. Model parameters are obtained from a small set of characterization experiments. We show that simulations using this error model are capable of accurately predicting new experimental results.
Abstract There has been tremendous progress in the physical implementation of quantum protocols in recent times, bringing us closer than ever to realizing the promise of quantum computing. However, environmental noise continues to pose a crucial challenge to scaling up present‐day quantum processors. In the presence of uncontrollable noise sources, decoherence limits the qubits' ability to store information for long periods. Conventional noise spectroscopy protocols can characterize and model environmental noise but are usually resource‐intensive and lengthy. Moreover, the noise can vary in time, making the slow extraction futile as the profile cannot be harnessed to perform error mitigation or correction. Here, this challenge is addressed using a machine learning‐based methodology that outputs the noise associated with transmon qubits with minimal absolute error. The procedure involves implementing undemanding dynamical decoupling sequences to record coherence decays of the qubits and then predicting the underlying noise spectra with the help of a convolutional neural network pre‐trained on a synthetic dataset. While the protocol is virtually hardware‐agnostic, its effectiveness is validated using superconducting qubits available on the IBM Quantum platform. These rapidly obtained, yet accurate, noise spectra are further used to design bespoke dynamic decoupling sequences and perform time‐dependent noise spectroscopy.
Noisy quantum processors require precise and coherent quantum control to effectively execute quantum algorithms. Key to achieving precise control is the characterization of a quantum device to elucidate important details of environmentally-induced and systematic error sources. Quantum noise spectroscopy (QNS) is one such protocol used to characterize spatiotemporally correlated noise. QNS strives to provide estimates of noise statistical properties by using the quantum system as a dynamical probe. Despite its success, QNS can be challenging as it requires model selection prior to protocol implementation and suffers from scalability issues as system size grows. Here, we leverage machine learning to overcome model selection and assist in learning complex noise environments. In particular, we utilize physics-informed neural networks based on the “gray box” model to learn the dynamics of a two-qubit system subject to spatiotemporally correlated noise. Using training data sets based on dynamical decoupling, we show that the model is capable of learning the underlying power spectral densities for each qubit and the strength of parasitic qubit-qubit interactions. Furthermore, we show that the model can predict state-dependent behavior for multi-qubit observables. The results of this study further display the potential utility of machine learning to assist in the domain of quantum characterization and control.
Abstract In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress well into the complex multi-qubit regime, attention is turning to understanding the appearance and mitigation of correlated — or non-Markovian — noise, which poses a serious challenge to the progression of quantum technology. This error type has previously remained elusive to characterisation techniques. Here, we develop a framework for characterising non-Markovian dynamics in quantum systems and experimentally test it on multi-qubit superconducting quantum devices. Where noisy processes cannot be accounted for using standard Markovian techniques, our reconstruction predicts the behaviour of the devices with an infidelity of 10 −3 . Our results show this characterisation technique leads to superior quantum control and extension of coherence time by effective decoupling from the non-Markovian environment. This framework, validated by our results, is applicable to any controlled quantum device and offers a significant step towards optimal device operation and noise reduction.
Transmon qubits experience open-system effects that manifest as noise at a broad range of frequencies. We present a model of these effects using the Redfield master equation with a hybrid bath consisting of low- and high-frequency components. We use two-level fluctuators to simulate 1/f -like noise behavior, which is a dominant source of decoherence for superconducting qubits. By measuring quantum state fidelity under free evolution with and without dynamical decoupling (DD), we can fit the low- and high-frequency noise parameters in our model. We train and test our model using experiments on quantum devices available through IBM quantum experience. Our model accurately predicts the fidelity decay of random initial states, including the effect of DD pulse sequences. We compare our model with two simpler models and confirm the importance of including both high frequency and 1/f noise in order to accurately predict transmon behavior. Published by the American Physical Society 2024
Accurate modeling of noise is a central challenge for scaling superconducting quantum hardware. Standardapproaches typically assume stationary, memoryless and gate-local noise. On current processors with morethan one hundred qubits, these approximations break down: we observe short-term drift, history dependence,device-wide fluctuations and non-monotonic idle behavior.We introduce an operational measure of two-qubit noise, the information distance di j(t) = −lnFi j(t), defineddirectly from GHZ2 fidelities. This quantity is empirical and time dependent. Crucially, it does not followphysical distance on the hardware graph: adjacent qubits can have large di j, while multi-hop connections canhave smaller di j. The resulting “noise geometry” is induced by information flow rather than physical layout.Using more than 50 000 circuits across three IBM heavy-hex processors (Marrakesh, Fez and Torino), weobserve usage-dependent changes of 0.002–0.02 in di j, minute-scale relaxation, slower device-wide drift andnon-monotonic idle-time distinguishability. These local variations accumulate along multi-qubit paths. Onibm marrakesh, a trained seven-qubit path outperforms a baseline GHZ7 circuit in all 20 interleaved trials,with a mean fidelity gain of 1.6×10−2and reduced variance.We summarize these observations with a minimal dynamical model in which information distances evolve under usage, relaxation, local fluctuations and a global drift process. The results indicate that noise on present-daysuperconducting processors is time dependent, history dependent and structured in a way that is not captured bystatic gate-local models, and that operational information distance provides a practical geometry for describingthis structure.