###### Abstract  
In this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins that make the quantum algorithm more robust to deviations in the coin's parameters. This is achieved by introducing functional dependence between these parameters. The functions that give the best performance of the algorithm are studied in detail by numerical statistical methods. A thorough comparison between our modification and an algorithm, with coins made using only Householder reflection, shows significant advantages of the former. By applying a deep neural network, we make a prediction for the parameters of an optimal coin with an arbitrary size and estimate the algorithm's stability for such a coin. quantum algorithms; quantum random walk; quantum search; qudits; generalized household reflection; supervised machine learning; neural networks; Monte Carlo simulations 20231650.12.12. Qudits are also used in some quantum random walk-based algorithms, such as Boolean formula evaluation [9] and quantum unsupervised machine learning [10]. There are two main methods for generating arbitrary d-dimensional quantum gates used to construct algorithms with qudits--by Given's rotations [29] and by Householder reflections (HR) [30]. Decomposing quantum gates to HRs is quadratically faster and can be used for qudits with an arbitrary dimension [31]. It can be implemented effectively on various physical system such as ion traps [32] and photonic quantum computer [33]. In the case of linear ion traps cooled to very low temperature and individual addressing of the ions and construction of qudit gates, this requires some additional conditions to be met. For example, all Rabi frequencies of the ions interacting with the laser fields have to have the same time dependence. An HR can also be applied to qudits, when they are created by multiopod system [27]. All qudit states are metastable levels of the ion and transitions between them are made through the ancilla state. This technique requires precise control of the laser field's parameters [32] (such as pulse shape and detuning). Some techniques for reducing the sensitivity to such error types already exists. For example, composite pulses [34] can be very useful in many applications. However, in some cases, composite pulses alone will not be enough to reduce the error to the appropriate level for the algorithm to work properly. Studying the effects of noise in quantum information is necessary, as they have undesirable but inevitable effects on the quantum system, which leads to decoherence. The physical interactions that underlie the occurrence of noise depend on the implementation of the quantum computer. There are different types of errors that may occur, such as errors in the ion's state's population or errors in the quantum state's phase. The effect of quantum noise on the system is often studied by assuming that the quantum gates are imperfect, or by adding additional noise gates [29; 35]. The noise lowers the performance of quantum algorithms and quantum communication. For example, in [36], it was shown how noise strongly affects communication schemes based on quantum teleportation. As another example, in [PERSON]'s algorithm decoherence reduces the probability to find the solution by increasing the needed iterations. When the number of errors in the quantum register, occurring during the algorithm's implementation, passes a certain threshold--it stops working entirely [37]. The quantum walk, as in any other quantum system, interacts with the outside medium. This leads to noise that impacts its performance. That is why there is a lot of research on how the quantum walk is affected by noise. We will give a few examples.