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arXiv:1510.05655 · Physical Review A

Characterization of decohering quantum systems: Machine learning approach

Markku P. V. Stenberg, Oliver Köhn, Frank K. Wilhelm

Published Jan 26, 2016• 22 citations
arXivHTMLPDF

Abstract

Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make adaptive characterization difficult. As an example, we consider two coupled discrete quantum systems. When one of the systems can be controlled and measured, the standard method to characterize another, with an unknown frequency ${\ensuremath{\omega}}_{\mathrm{r}}$, is swap spectroscopy. Here, adapting measurements can provide estimates whose error decreases exponentially in the number of measurement shots rather than as a power law in conventional swap spectroscopy. However, when the decoherence time is so short that an excitation oscillating between the two systems can only undergo less than a few tens of vacuum Rabi oscillations, this approach can be marred by a severe limit on accuracy unless carefully designed. We adopt machine learning techniques to search for efficient policies for the characterization of decohering quantum systems. We find, for instance, that when the system undergoes more than 2 Rabi oscillations during its relaxation time ${T}_{1}, O({10}^{3})$ measurement shots are sufficient to reduce the squared error of the Bayesian initial prior of the unknown frequency ${\ensuremath{\omega}}_{\mathrm{r}}$ by a factor $O({10}^{4})$ or larger. We also develop policies optimized for extreme initial parameter uncertainty and for the presence of imperfections in the readout.

DOI
10.1103/physreva.93.012122

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Adaptive data collection and analysis, where data are being fed back to update the measurement settings, can greatly increase speed, precision, and reliability of the characterization of quantum systems. However, decoherence tends to make adaptive characterization difficult. As an example, we consider two coupled discrete quantum systems. When one of the systems can be controlled and measured, the standard method to characterize another, with an unknown frequency \ensuremathωr{\ensuremath{\omega}}_{\mathrm{r}}\ensuremathωr​, is swap spectroscopy. Here, adapting measurements can provide estimates whose error decreases exponentially in the number of measurement shots rather than as a power law in conventional swap spectroscopy. However, when the decoherence time is so short that an excitation oscillating between the two systems can only undergo less than a few tens of vacuum Rabi oscillations, this approach can be marred by a severe limit on accuracy unless carefully designed. We adopt machine learning techniques to search for efficient policies for the characterization of decohering quantum systems. We find, for instance, that when the system undergoes more than 2 Rabi oscillations during its relaxation time T1,O(103){T}_{1}, O({10}^{3})T1​,O(103) measurement shots are sufficient to reduce the squared error of the Bayesian initial prior of the unknown frequency \ensuremathωr{\ensuremath{\omega}}_{\mathrm{r}}\ensuremathωr​ by a factor O(104)O({10}^{4})O(104) or larger. We also develop policies optimized for extreme initial parameter uncertainty and for the presence of imperfections in the readout.
The recent advances in Machine Learning hold great promises for the field of quantum sensing and metrology. With the help of reinforcement learning, we can tame the complexity of quantum systems and solve the problem of optimal experimental design. Reinforcement learning is a powerful model-free technique that allows an agent, which is typically a neural network, to learn the best strategy to reach a certain goal in a completely a priori unknown environment. However, in general, we know something about the quantum system the agent is interacting with, at least that it follows the rules of quantum mechanics. In quantum metrology, we typically have a model for the system and only some parameters of the evolution or of the initial state are unknown. We present here a general Machine Learning technique that can optimize the precision of quantum sensors, and in doing so it exploits the knowledge we have on the system. We have developed a Python package to automate a broad class of optimizations that can be found in the tasks of quantum parameter estimation, quantum metrology and quantum hypothesis testing. What the agent is learning here is an optimal adaptive strategy, that, on the basis of the previous outcomes, decides the next measurements to perform. It works both for Bayesian estimation and for frequentist estimation. The user is required to implement the physics of the system to be studied and state which parameters in the experiment are controllable and which are unknowns. The functions of the library allow then to easily train a neural network agent for optimizing the precision of the sensor, by simulating the experiment. We have explored some applications of this technique to magnetometry on NV centers (both DC and AC), to state discrimination in quantum optics and to phase estimation. So far, we were able to certify better results than the current state-of-the-art controls for many examples. The Machine Learning technique developed here can be applied in all those scenarios where the quantum system is well characterized and relatively simple and small. In these cases, we can squeeze every last bit of information from a quantum sensor by controlling it with a neural network appropriately trained.
In characterization of quantum systems, adapting measurement settings based on data while it is collected can generally outperform in efficiency conventional measurements that are carried out independently of data. The existing methods for choosing measurement settings adaptively assume that the model, or the number of unknown parameters, is known. We introduce simultaneous adaptive model selection and parameter estimation. We apply our technique for characterization of a superconducting qubit and a bath of incoherent two-level systems, a leading decoherence mechanism in the state-of-the-art superconducting qubits.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
We present methods for efficient characterization of an optical coherent state $|\ensuremath{\alpha}\ensuremath{\rangle}$. We choose measurement settings adaptively and stochastically, based on data while it is collected. Our algorithm divides the estimation into two distinct steps: (i) before the first detection of a vacuum state, the probability of choosing a measurement setting is proportional to detecting vacuum with the setting, which makes using too similar measurement settings twice unlikely; and (ii) after the first detection of vacuum, we focus measurements in the region where vacuum is most likely to be detected. In step (i) [(ii)] the detection of vacuum (a photon) has a significantly larger effect on the shape of the posterior probability distribution of $\ensuremath{\alpha}$. Compared to nonadaptive schemes, our method makes the number of measurement shots required to achieve a certain level of accuracy smaller approximately by a factor proportional to the area describing the initial uncertainty of $\ensuremath{\alpha}$ in phase space. While this algorithm is not directly robust against readout errors, we make it such by introducing repeated measurements in step (i).
Two-level systems (TLS) in superconducting quantum devices are a dominant source of decoherence, noise, and device variability, ultimately limiting qubit performance and scalability. Efficient and reliable extraction of TLS parameters from spectroscopy measurements is therefore essential for both device characterization and materials optimization. In this thesis, machine learning methods are developed to accelerate and enhance TLS characterization from superconducting qubit spectroscopy data. The approach combines physics-based simulation of driven qubit–TLS dynamics with supervised learning models trained on synthetic datasets to infer underlying physical parameters from two-dimensional spectroscopy maps. Particular emphasis is placed on understanding how different parameters are encoded in observable features, and on evaluating the extent to which the inverse problem is well-posed. The results demonstrate that machine-learning-assisted inference can significantly reduce the computational cost of parameter estimation compared to conventional fitting-based approaches, while maintaining high accuracy for spectrally encoded parameters such as TLS frequency and coupling strength. In contrast, decoherence parameters are shown to be intrinsically more challenging to extract from short-time spectroscopy data, highlighting fundamental limitations of the measurement protocol rather than the learning model. Overall, this work establishes a data-driven framework for scalable TLS characterization and provides insight into the interplay between physical observability and machine learning-based inference in quantum systems.
Combating decoherence---the randomization of qubit values in a physical system---is a key challenge in quantum computing. Control theory provides a powerful set of tools to stabilize classical systems, but much work remains to bring its full weight to the quantum domain. Aiming to track and predict qubit-state evolution under various forms of decoherence, the authors employ machine-learning algorithms to optimize qubit-state forecasting, and adapt classical algorithms to work directly with discrete, single-shot qubit measurements. These results suggest that exciting opportunities exist for implementing real-time feedback using purely classical, hardware-agnostic techniques.