- 01.Introduction
- 02.Network Operations and Communication Service Fault Diagnosis System
- 03.Quantum Kernel Learning Algorithm and Proposed Method
- 04.Error Suppression in Quantum Computers
- 05.Simulation Experiment for Proposed Method Using Quantum Computers
- 06.System Demonstration Experiment Using IBM Quantum Computer Hardware
- 07.Conclusion

Blogs

- Aug 30, 2024
- Blog
- Network, Computing, Service

## Demonstration Experiment of a Communication Service Fault Diagnosis System Using Quantum Machine Learning

#Quantum Technology

## 1．Introduction

SoftBank Corp. (hereinafter "SoftBank"), The University of Electro-Communications (hereinafter "UEC"), and Keio University (hereinafter "Keio") have successfully conducted a demonstration experiment of a communication service fault diagnosis system using quantum machine learning.

In recent years, with the advancement of corporate DX (Digital Transformation) and the widespread adoption of remote work, along with the expectation that Beyond 5G/6G will realize a data-driven society through the combination of ultra-high-speed, large-capacity transmission technology and edge computing technology, the quality of communication networks supporting these developments has become a crucial indicator.

As the demand for such networks expands, the configuration of communication equipment for service providers has become large-scale and complex. The automation of network operations using advanced computing technologies powered by artificial intelligence (AI), known as MLOps, is under consideration [1] - [4]. However, realizing MLOps with classical computers and their algorithms presents challenges in terms of energy consumption, computational complexity, and vulnerabilities. Therefore, there are high expectations for quantum computers to enhance and speed up these processes.

Currently, most quantum computers available are NISQ (Noisy Intermediate-Scale Quantum) devices [5], which are mid-sized systems with around 100 qubits. To achieve practical performance with these devices, it is crucial to improve algorithms and develop error suppression and correction technologies. Research on quantum computer algorithms is primarily advancing in the fields of quantum chemistry, mathematical optimization, and machine learning, with performance validation using hardware like IBM's superconducting gate-based quantum computers becoming increasingly active [6][7][8].

In light of these developments, SoftBank, UEC, and Keio have conducted a demonstration experiment using IBM's superconducting gate-based quantum computer and Q-CTRL's error suppression system to implement a quantum machine learning-based communication service fault diagnosis system.

## 2. Network Operations and Communication Service Fault Diagnosis System

The commercial service network that forms the foundation for telecommunication services provided to customers consists of a core network connecting major cities nationwide like arteries, an area network configured at the regional level, and an access network connecting customer sites and mobile base stations. At the top level, these connect to international communication networks such as submarine cables via IX (Internet Exchange) points.

Network operations by telecommunications providers primarily focus on maintaining uninterrupted communication services for customers. This involves 24/7 service monitoring, fault isolation, and recovery, as well as maintenance work. Operators use operational systems to perform these tasks (Figure 2). Fault isolation, in particular, involves identifying the equipment hosting the affected service and determining the cause of the fault using a vast array of equipment commands (Figure 3).

In this study, we conducted a proof-of-concept experiment for a communication service fault diagnosis system using quantum machine learning. We used a dataset extracted from logs of systems operating in commercial networks. The dataset (Figure 4) has command types on the horizontal axis and fault patterns on the vertical axis. The plots correspond to 1 if the command execution result is abnormal, and 0 if normal. The colors of each plot correspond to seven types of fault causes. We use the 0-1 sequence on the horizontal axis as a feature vector. Machine learning is performed using the fault cause for each feature vector as training data, and the constructed model is used for fault diagnosis.

The communication service fault diagnosis system (Figure 5) operates by performing offline training using the dataset, and during online processing, it estimates the cause of faults for unknown feature vectors. The system is divided into parts processed by classical computers and quantum computers. In the offline training process, the dataset is first dimensionally reduced to match the number of qubits used in calculations and then normalized. For cross-validation, the dataset is split into learning and test sets, used to evaluate the machine learning model's performance. In this study, a 50% split ratio was used. Then, parameterization processing for qubits is performed to generate quantum circuits. In this study, the dataset was split with a ratio of 50%. Then, the data is parameterized for qubits, and a quantum circuit is generated. Up to this point, all processing is done on a classical computer. Following this, a quantum computer is used to generate a Gram matrix by performing exhaustive inner product calculations for the number of fault patterns in the training data. This Gram matrix is used as a kernel in a Support Vector Machine (SVM) machine learning model to estimate the fault causes.

Currently, for each fault diagnosis, all commands corresponding to the dimensions of the feature vector are executed. However, in our previous research [1], we developed a technology using deep reinforcement learning, which assigns a reward based on the confidence level of class convergence, to explore and execute only the commands necessary for identifying the fault cause.

## 3. Quantum Kernel Learning Algorithm and Proposed Method

Quantum kernel learning is expected to provide superior analytical performance compared to classical computers due to the rich expressiveness of qubits and the complexity in ultra-high-dimensional spaces of quantum entanglement.

Generally, kernel methods (Figure 6) refer to techniques that make data that cannot be linearly separated linearly separable by mapping it to a higher-dimensional feature space (kernel space). Quantum kernel learning, however, uses the quantum state space of quantum computers as the feature space. Figure 7 illustrates how classical data, mapped to the quantum state space, is separated based on its amplitude direction within the phase range of 0 to 2π.

In this study, we devised a proprietary quantum entanglement control circuit (patent pending) for kernel generation in quantum kernel learning, successfully enhancing the performance of quantum computers to accommodate more generalized data. By parameterizing the feature vectors of the input data into each qubit and adjusting the entanglement strength between adjacent qubits, we were able to control the mapping into quantum states that correspond to the characteristics of the input data. This enabled the implementation of a computational method that efficiently utilizes the quantum state space across the entire quantum circuit.

For kernel generation, the quantum computer performs exhaustive inner product calculations for combinations of the input data feature vectors x_{l}, x_{m}(Equation 1). For each Φ(x) in the gate operator U_{Φ(x)}, the elements of each vector are mapped into the unitary space of n qubits, and a quantum circuit is generated (Equation 2).

We defined the conventional method using a quantum circuit where the feature vector to be computed is simply parameterized into X rotation gates, as shown in Figure 8. We then compared this with our proposed method, which is explained below.

In our proposed method, we control the mapping to quantum states according to input data characteristics by adjusting the entanglement strength between adjacent qubits (Figure 9). This realizes a computational method that efficiently utilizes the quantum state space across the entire quantum circuit (Figure 10).

In the quantum entanglement generation circuit of the gate operator U_{Φ(x)} in the proposed method (Equation 3), the phase parameters Φ_{p,q}(x) of the Z-rotation gate (Equation 4) are influenced by parameterized values that act on adjacent qubits with respect to the quantum entanglement strength. By defining a coefficient α for this, we made it possible to efficiently adjust the quantum entanglement effect.

The kernel can be obtained by calculating the Gram matrix 𝐾 using a quantum computer for each parameterized quantum circuit (Equation 5).

This study, as explained above, investigates how the proposed method of quantum entanglement control affects the classification performance in quantum kernel learning.

## 4. Error Suppression in Quantum Computers

Errors in quantum computers are caused by various factors such as decoherence, gate errors, readout errors, crosstalk, quantum phase errors, and thermal noise. While error suppression is relatively manageable when the physical model is well understood, it becomes increasingly difficult as the system scales up.

In this study, we successfully reduced quantum noise in NISQ machines significantly by using Q-CTRL's error suppression system, “Fire Opal”.

Fire Opal is a software package designed to achieve AI-based error suppression and improve quantum algorithm performance on quantum hardware. It achieves a deterministic approach to error reduction without requiring additional execution overhead such as sampling or randomization.

Using deep reinforcement learning, the hardware model is effectively learned, encapsulating environmental information from the quantum computer as reward information in terms of fidelity. The agent is operated by mapping this reward to actions related to control pulses and other environmental changes. For piecewise constant control waveforms, the optimal Hamiltonian is explored by repeating episodes concerning state observation cycles, with learning and calibration continuing until the optimal value is reached. This use of deep reinforcement learning enables effective quantum computer error suppression without prior knowledge of the error's physical model [11][12].

## 5. Simulation Experiment for Proposed Method Using Quantum Computers

We evaluated the proposed method using a tensor network simulator. For the 120-dimensional command sequence in the dataset, we performed dimensionality reduction to 10-50 dimensions to match the number of qubits being evaluated. We then assessed the distribution of classification estimation accuracy using 50% cross-validation across 100 split patterns.

The proposed method showed superior performance compared to SVM using conventional quantum kernel learning and SVM using classical kernel learning. Comparing the average of evaluation results across all qubit numbers, conventional quantum kernel learning achieved 77%, our proposed quantum kernel learning achieved 81%, and classical kernel learning achieved 78%.

The following evaluation was conducted using a single split sample data for each number of qubits. The classification accuracy for each classical method ranged from 85% to 89%.

Figure 13 evaluates the relationship between the 𝛼 parameter, which controls the quantum entanglement strength, and the estimation accuracy in the proposed method. This shows that there are optimal settings for the quantum entanglement strength and the number of qubits with respect to the training data.

In this study, we used a common α parameter for all qubit pairs. However, we anticipate that setting independent parameters for each qubit pair could yield learning performance that's more sensitive to detailed data features. For learning, we conducted parameter searches using pre-evaluation through simulation. While current state vector simulators can only handle calculations up to about 30 qubits, tensor network simulators can simulate larger qubit numbers, albeit with some approximation errors. As we move to even larger qubit numbers that simulations can't handle, evaluating ideal values becomes impossible. In such cases, we can consider models that operate while directly tuning parameters on quantum computer hardware.

## 6. System Demonstration Experiment Using IBM Quantum Computer Hardware

We evaluated the proposed method using IBM's gate-based quantum computer (IBM Quantum System One: IBM-Kawasaki 127 qubits), employing the optimal settings confirmed through simulation.

The results of the comparative evaluation of fault cause inference performance in the communication service fault diagnosis system are shown in Figure 14. We compared a state-vector simulator, a tensor-network simulator, IBM's gate-based quantum computer alone, and IBM's gate-based quantum computer with error suppression applied. By applying error suppression to the quantum computer, we achieved an inference accuracy of 82% for fault causes using 30 qubits. The number of qubits used here is currently the world record for quantum kernel learning using a real quantum device. Additionally, optimal estimation accuracy was reached at 30 qubits, beyond which a degradation trend was observed. This degradation is likely due to the effects of quantum computer noise and the depletion of data samples.

Regarding the kernel obtained from the quantum computer, a comparison of the relative values of all elements of the Gram matrix at 30 qubits against the ideal values showed that error suppression resulted in uniform performance improvement.

## 7. Conclusion

In this study, we successfully demonstrated the practical performance of quantum computers by improving the quantum kernel learning algorithm and applying error suppression, using data from systems operating in SoftBank's commercial services. This achievement significantly contributes to the advancement of computational technology using quantum computers and their implementation in society. Moving forward, we will promote research aimed at expanding the application scope and advantages of quantum algorithms, improving computational performance through enhanced quantum hardware capabilities, and achieving scalability and integration across network architectures. Through these efforts, we aim to contribute to the early practical application and social implementation of quantum computing technology.

This research outcome has been accepted as a paper for the Technical Session (QML) at the "IEEE International Conference on Quantum Computing and Engineering (QCE24)" to be held from September 15-20, 2024, where it is scheduled for presentation.

### Publication

Title: Parametrized Energy-Efficient Quantum Kernels for Network Service Fault Diagnosis

Author: Hiroshi Yamauchi, Tomah Sogabe, Rodney Van Meter

Pre-print: https://arxiv.org/abs/2405.09724

### References

[1] H Yamauchi, T Kimura, “Deep Reinforcement Learning based Command Control System for Automating Fault Diagnosis,” IEEE 19th International Conference on Network and Service Management (CNSM), November 2023, Page(s):1 - 5

[2] Mays Al-Naday, Martin Reed, Vlad Dobre, Salman Toor, Bruno Volckaert, Filip De Turck, “Service-based federated deep reinforcement learning for anomaly detection in fog ecosystems,” IEEE 26th Conference on Innovation in Clouds, Internet and Networks and Workshops (ICIN), March 2023, Page(s):121-128

[3] T. Kimura, A. Watanabe, T. Toyono, and K. Ishibashi, “Proactive failure detection learning generation patterns of large-scale network logs,”IEICE Transactions on Communications, Vol. E102.B (2019), No. 2, pp. 306-316, 2018.

[4] C. R. Kalmanek, I. Ge, S. Lee, C. Lund, D. Pei, J. Seidel, J. E. Merwe, J. Yates, “Darkstar: Using exploratory data mining to raise the bar on network reliability and performance,” Proc. DRCN, October 2009, pp.1-10.

[5] J Preskill, “Quantum computing in the NISQ era and beyond,” Quantum2, 79.

[6] Shu Kanno, Kenji Sugisaki, Hajime Nakamura, Hiroshi Yamauchi, Rei Sakuma, Takao Kobayashi, Qi Gao, Naoki Yamamoto, “Tensor-based quantum phase difference estimation for large-scale demonstration,” arXiv:2408.04946 [quant-ph].

[7] Natasha Sachdeva, Gavin S. Harnett, Smarak Maity, Samuel Marsh, Yulun Wang, Adam Winick, Ryan Dougherty, Daniel Canuto, You Quan Chong, Michael Hush, Pranav S. Mundada, Christopher D. B. Bentley, Michael J. Biercuk, Yuval Baum, “Quantum optimization using a 127-qubit gate-model IBM quantum computer can outperform quantum annealers for nontrivial binary optimization problems” arXiv: 2406.01743 [quant-ph].

[8] Zoran Krunic, Frederik F. Fl¨other, George Seegan, Nathan Earnest Noble, Omar Shehab, “Quantum Kernels for Real-World Predictions Based on Electronic Health Records,” IEEE Transactions on Quantum Engineering, 2022, Volume 3, 2500311

[9] M Schuld, N Killoran, “Quantum machine learning in feature Hilbert spaces,” Physical review letters, vol. 122, no. 4, Feb 2019.

[10] Vojtech Havlicek, Antonio D. C´orcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, Jay M. Gambetta, “Supervised learning with quantum-enhanced feature spaces,” Nature 567.7747 (Mar. 2019), pp. 209–212.

[11] Pranav S. Mundada, Aaron Barbosa, Smarak Maity, Yulun Wang, T. M. Stace, Thomas Merkh, Felicity Nielson, Andre R. R. Carvalho, Michael Hush, Michael J. Biercuk, Yuval Baum, “Experimental benchmarking of an automated deterministic error suppression workflow for quantum algorithms,” Phys. Rev. Applied, November 2023,20, 024034

[12] Yuval Baum, Mirko Amico, Sean Howell, Michael Hush, Maggie Liuzzi, Pranav Mundada, Thomas Merkh, Andre R.R. Carvalho, and Michael J. Biercuk, “Experimental Deep Reinforcement Learning for Error-Robust Gate-Set Design on a Superconducting Quantum Computer,” PRX Quantum 2, 040324