Quantum Measurement Classification with Qudits

Quantum computing has gained a lot of attention in recent years due to its potential to solve complex problems which would take exponential time in classical computers. Most of the research efforts have been focused on constructing quantum computers based on qubits [1]. However, there has been a growing interest in building quantum computers based on qudits, i.e. machines that simulate and operate d-dimensional quantum states, with d > 2. Various physical implementations of high-dimensional quantum states have been proposed, such as photonic states integrated in chips [2, 3], photonic modes encoded in the orbital angular momentum (OAM) [4], ion traps [5], ququarts implemented on a quadrupolar nuclear magnetic resonance (NMR) [6], and molecular quantum magnets [7]. Two of the main advantages of highdimensional quantum computers compared to their qubit-based counterparts are their larger information storage [8], and their higher resilience to noise [9]. One closely related field of quantum computing is quantum machine learning (QML). This field aims to develop novel quantum-inspired machine learning (ML) methods that may run on classical or quantum computers and to implement the existing ML algorithms on quantum computers. For instance, some classical machine learning algorithms like support vector machines and restricted Boltzmann machines can be implemented on qubit-based quantum computers [10, 11], and many of the ML methods have been reformulated in the language of quantum physics like quantum decision trees [12], quantum neural networks [13, 14], and quantum generative adversarial networks [15]. In contrast with QML methods built on qubits, less research has been done on QML based on qudits, i.e. algorithms that run in high-dimensional quantum computers. Some of these methods include protocols with qudits for reinforcement learning [16], and for training quantum neural networks [17, 18, 19].