Machine learning in quantum spaces

Esma Aı̈meur, Gilles Brassard A, Sébastien Gambs

Jincheng Zhang

Probability Space Quantum Machine Learning (PSML) represents a paradigm shift in machine learning, extending beyond traditional static models to leverage the inherent properties of quantum probability spaces. This research explores the potential of PSML to significantly enhance machine learning model performance, particularly through the optimization of models based on quantum feature spaces. The core claim of this work is that PSML not only facilitates quantum machine learning but actively refines models to improve generalization. This is achieved through the utilization of quantum probability spaces, offering a novel approach to optimization.

Siddharth Sharma

Machine learning and quantum computing are two technologies that are causing a paradigm shift in the performance and behavior of certain algorithms, achieving previously unattainable results. Machine learning (kernel classification) has become ubiquitous as the forefront method for pattern recognition and has been shown to have numerous societal applications. While not yet fault-tolerant, Quantum computing is an entirely new method of computation due to its exploitation of quantum phenomena such as superposition and entanglement. While current machine learning classifiers like the Support Vector Machine are seeing gradual improvements in performance, there are still severe limitations on the efficiency and scalability of such algorithms due to a limited feature space which makes the kernel functions computationally expensive to estimate. By integrating quantum circuits into traditional ML, we may solve this problem through the use of quantum feature space, a technique that improves existing Machine Learning algorithms through the use of parallelization and the reduction of the storage space from exponential to linear. This research expands on this concept of the Hilbert space and applies it for classical machine learning by implementing the quantum-enhanced version of the K nearest neighbors algorithm. This paper first understands the mathematical intuition for the implementation of quantum feature space and successfully simulates quantum properties and algorithms like Fidelity and Grover's Algorithm via the Qiskit python library and the IBM Quantum Experience platform. The primary experiment of this research is to build a noisy variational quantum circuit KNN (QKNN) which mimics the classification methods of a traditional KNN classifier. The QKNN utilizes the distance metric of Hamming Distance and is able to outperform the existing KNN on a 10-dimensional Breast Cancer dataset.

Michael Brooks

Naoko Koide‐Majima, Kei Majima

The application of near-term quantum devices to machine learning (ML) has attracted much attention. Recently, Mitarai et al. [Phys. Rev. A 98, 032309 (2018)] proposed a framework to use a quantum circuit for ML tasks, called quantum circuit learning (QCL). Due to the use of a quantum circuit, QCL employs an exponentially high-dimensional Hilbert space as its feature space. However, its efficiency compared to classical algorithms remains unexplored. Here, we present a classical ML algorithm that uses the same Hilbert space. In numerical simulations, our algorithm demonstrates similar performance to QCL for several ML tasks, providing a perspective for the computational and memory efficiency of quantum ML algorithms.

A. S. Wilson