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IEEE International Conference on Quantum Computing and Engineering (QCE)

Learning Spatiotemporally Correlated Noise in Multi-Qubit Systems with Neural Networks

Abhiram Nallamalli, Shantanu Misra, Gregory Quiroz

Published Sep 15, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qce60285.2024.10365

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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.
Spatiotemporally correlated errors are widespread in quantum devices and are particularly adversarial to error correcting schemes. To characterize these errors, we propose and validate a nonparametric quantum noise spectroscopy (QNS) protocol to estimate both spectra and static errors associated with spatiotemporally correlated dephasing noise and fluctuating quantum crosstalk on two qubits. Our scheme reconstructs the real and imaginary components of the two-qubit cross-spectrum by using fixed total time pulse sequences and single qubit and joint two-qubit measurements to separately resolve spatially correlated noise processes. We benchmark our protocol by reconstructing the spectra of spatiotemporally correlated noise processes engineered via the Schrödinger Wave Autoregressive Moving Average technique, emulating dephasing errors. Furthermore, we show that the protocol can outperform existing comb-based QNS protocols. Our results demonstrate the utility of our protocol in characterizing spatiotemporally correlated noise and quantum crosstalk in a multi-qubit device for potential use in noise-adapted control or error protection schemes.
Abstract The undesired interaction of a quantum system with its environment generally leads to a coherence decay of superposition states in time. A precise knowledge of the spectral content of the noise induced by the environment is crucial to protect qubit coherence and optimize its employment in quantum device applications. We experimentally show that the use of neural networks (NNs) can highly increase the accuracy of noise spectroscopy, by reconstructing the power spectral density that characterizes an ensemble of carbon impurities around a nitrogen-vacancy (NV) center in diamond. NNs are trained over spin coherence functions of the NV center subjected to different Carr–Purcell sequences, typically used for dynamical decoupling (DD). As a result, we determine that deep learning models can be more accurate than standard DD noise-spectroscopy techniques, by requiring at the same time a much smaller number of DD sequences.
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.
Precise qubit control in the presence of spatiotemporally correlated noise is pivotal for transitioning to fault-tolerant quantum computing. Generically, such noise can also have non-Gaussian statistics, which hampers existing non-Markovian noise spectroscopy protocols. By utilizing frame-based characterization and a control-based symmetry analysis, we show how to achieve higher-order spectral estimation for noise-optimized circuit design. Remarkably, we find that the digitally driven qubit dynamics can be solely determined by the complexity of the applied control rather than the nonperturbative nature of the non-Gaussian environment. This enables us to address certain nonperturbative qubit dynamics more simply. We delineate several complexity bounds for learning such high-complexity noise and demonstrate our single- and two-qubit digital characterization and control using a series of numerical simulations. Our results not only provide insights into the exact solvability of (small-size) open quantum dynamics but also highlight a resource-efficient approach for optimal control and possible error-reduction techniques for current qubit devices.
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.
Qubit noise spectroscopy (QNS) is a valuable tool for both the characterization of a qubit's environment and as a precursor to more effective qubit control to improve qubit fidelities. Existing approaches to QNS are what the classical spectrum estimation literature would call "non-parametric" approaches, in that a series of probe sequences are used to estimate noise power at a set of points or bands. In contrast, model-based approaches to spectrum estimation assume additional structure in the form of the spectrum and leverage this for improved statistical accuracy or other capabilities, such as superresolution. Here, we derive model-based QNS approaches using inspiration from classical signal processing, primarily though the recently developed Schrodinger wave autoregressive moving-average (SchWARMA) formalism for modeling correlated noise. We show, through both simulation and experimental data, how these model-based QNS approaches maintain the statistical and computational benefits of their classical counterparts, resulting in powerful new estimation approaches. Beyond the direct application of these approaches to QNS and quantum sensing, we anticipate that the flexibility of the underlying models will find utility in adaptive feedback control for quantum systems, in analogy with their role in classical adaptive signal processing and control.