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arXiv:2210.09275 · Scientific Reports

The power of one clean qubit in supervised machine learning

Mahsa Karimi, Ali Javadi-Abhari, Christoph Simon, Roohollah Ghobadi

Published Nov 15, 2023• 10 citations
arXivHTMLPDF

Abstract

This paper explores the potential benefits of quantum coherence and quantum discord in the non-universal quantum computing model called deterministic quantum computing with one qubit (DQC1) in supervised machine learning. We show that the DQC1 model can be leveraged to develop an efficient method for estimating complex kernel functions. We demonstrate a simple relationship between coherence consumption and the kernel function, a crucial element in machine learning. The paper presents an implementation of a binary classification problem on IBM hardware using the DQC1 model and analyzes the impact of quantum coherence and hardware noise. The advantage of our proposal lies in its utilization of quantum discord, which is more resilient to noise than entanglement.

DOI
10.1038/s41598-023-46497-y

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This paper explores the potential benefits of quantum coherence and quantum discord in the non-universal quantum computing model called deterministic quantum computing with one qubit (DQC1) in supervised machine learning. We show that the DQC1 model can be leveraged to develop an efficient method for estimating complex kernel functions. We demonstrate a simple relationship between coherence consumption and the kernel function, a crucial element in machine learning. The paper presents an implementation of a binary classification problem on IBM hardware using the DQC1 model and analyzes the impact of quantum coherence and hardware noise. The advantage of our proposal lies in its utilization of quantum discord, which is more resilient to noise than entanglement.
Deterministic quantum computation with one qubit (DQC1) is of significant theoretical and practical interest due to its computational advantages in certain problems, despite its subuniversality with limited quantum resources. In this work, we introduce parametrized DQC1 as a quantum machine learning model. We demonstrate that the gradient of the measurement outcome of a DQC1 circuit with respect to its gate parameters can be computed directly using the DQC1 protocol. This allows for gradient-based optimization of DQC1 circuits, positioning DQC1 as a quantum protocol for both training and inference. We then analyze the expressivity of the parametrized DQC1 circuits characterizing the set of learnable functions, and show that DQC1-based machine learning (ML) is as powerful as quantum neural networks based on universal computation. Our findings highlight the potential of DQC1 as a practical and versatile platform for ML, capable of rivaling more complex quantum computing models while utilizing simpler quantum resources.
Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the model to approximate complex functions, has a significant influence on its performance in these tasks. One approach to enhancing the expressivity of kernel machines is to combine multiple individual kernels to arrive at a more expressive combined kernel. This approach is referred to as multiple kernel learning (MKL). In this work, we propose an MKL method we refer to as quantum MKL, which combines multiple quantum kernels. Our method leverages the power of deterministic quantum computing with one qubit (DQC1) to estimate the combined kernel for a set of classically intractable individual quantum kernels. The combined kernel estimation is achieved without explicitly computing each individual kernel, while still allowing for the tuning of individual kernels in order to achieve better expressivity. Our simulations on two binary classification problems---one performed on a synthetic dataset and the other on a German credit dataset---demonstrate the superiority of the quantum MKL method over single quantum kernel machines.
Kernel methods are used extensively in classical machine learning, especially in the field of pattern analysis. In this paper, we propose a kernel-based quantum machine learning algorithm that can be implemented on a near-term, intermediate scale quantum device. Our proposal is based on estimating classically intractable kernel functions, using a restricted quantum model known as deterministic quantum computing with one qubit. Our method provides a framework for studying the role of quantum correlations other than quantum entanglement for machine learning applications.
This work focuses on quantum machine learning and analyzes the power of one single qubit to solve classical machine learning problems. We explore possible strategies to address traditional supervised, unsupervised, and reinforcement learning tasks. In particular, we study binary and multinomial classification, regression problems, time series forecasting, clustering, and quantum reinforcement learning. Our results suggest that the same methodology could be used to address all three types of learning with different measurement strategies and, despite the strong limitation of reduced data dimensionality of the candidate problems, a single qubit can achieve similar or even improved performance with respect to state-of-the-art classic machine learning methods in many cases. As simulating the evolution of one qubit state is computationally efficient, our study enables the possibility to use the qubit model as a candidate solution to implement simple decision-making machine learning models in hardware with extremely low memory resources such as embedded systems or edge devices. The outcomes provided could be also of interest in academia and for the construction of demonstrators using low-scale contemporary quantum hardware.
Enhancing quantum computing for supervised machine learning is an innovative application in the field of smart computing. With recent advancements in quantum computing, and it is rising to coalesce with Artificial Intelligence, quantum computers can revolutionize the way to address previously untenable problems. As quantum computers can succeed in producing various intuitive patterns that are strenuous for a classical system to implement, it is reasonable to presume that these quantum machines can outperform a classical computer in various tasks. They can excel at solving problems which involve data crunching with a huge amount of inputs such as machine learning tasks, complex optimization problems, communication system analysis, etc. which require complex parallel computations for an efficient result. This paper attempts to analyze one such aspect of machine learning known as supervised classification with the help of a real Quantum hardware.
Abstract Supervised machine learning is a popular approach to the solution of many real‐life problems. This approach is characterized by the use of labeled datasets to train algorithms for classifying data or predicting outcomes accurately. The question of the extent to which quantum computation can help improve existing classical supervised learning methods is the subject of intense research in the area of quantum machine learning. The debate centers on whether an advantage can be achieved already with current noisy quantum computer prototypes or it is strictly dependent on the full power of a fault‐tolerant quantum computer. The current proposals can be classified into methods that can be suitably implemented on near‐term quantum computers but are essentially empirical, and methods that use quantum algorithms with a provable advantage over their classical counterparts but only when implemented on the still unavailable fault‐tolerant quantum computer. It turns out that, for the latter class, the benefit offered by quantum computation can be shown rigorously using quantum kernels, whereas the approach based on near‐term quantum computers is very unlikely to bring any advantage if implemented in the form of hybrid algorithms that delegate the hard part (optimization) to the far more powerful classical computers.