Emulators of Quantum Computers on Qubits and on Qudits

Quantum computing is still a developing, but an extremely promising area. The article lays out the main ideas behind quantum computing in simple terms. The topic of quantum computers based on qudits - multidimensional analogues of qubits, which have recently received much attention due to their efficiency, is also covered The fundamentals of quantum mechanics, which are necessary for understanding the principles of operation of a quantum computer, such concepts as qubits and qudits, linear operators, the measurement process, etc are introduced. As an example of quantum computing, the principle of operation of the Deutsch-Jozsa algorithm, one of the first quantum algorithms to demonstrate their advantages, and its generalization to qudits, are analyzed in detail. The process of writing the simplest quantum computer emulator in the Python programming language is described step by step. The emulator operates with an arbitrary number of qubits and allows you to apply arbitrary operators to them and carry out multiple measurements of the final state of the qubit. A generalization of this emulator for working with qudits is given after that. To demonstrate the emulator we have written, we present programs that implement the Deutsch-Jozsa algorithm and its generalizations on it, and test them.