###### Abstract
In one paper [38], using a one-dimensional quantum walk, an array of quantum dots was studied, where the authors paid particular attention to how noise and inaccuracies in their circuit gates affect the quantum walk. In [PERSON] et al. [39], they presented a detailed theoretical study of the impact of different types of errors on the quantum walk on line when the coin has different symmetries. It is also discussed how different types of errors affect the QRW implementation in nuclear magnetic resonance quantum information processor and for atoms in an optical lattice. Due to the importance of knowing the type and magnitude of noise in a quantum system to assess its negative impact, a method that can be used to sense different types of noise in one- and two-dimensional quantum walks was studied [40]. A comparison of how noise affects [PERSON]'s search and discrete QRWS algorithm was made [41]. Their numerical calculations suggest that QRWS is more robust against white noise. How continuous time QRWS on different topologies is affected by the noise is studied in the work by [PERSON] and [PERSON][42]. The authors also investigated the relation of certain quantum parameters and algorithm's robustness. The continuous time quantum search algorithm on hypercube with noise was studied [43]. The discrete time quantum walk search algorithm with systematic phase error in the walk coin was investigated [44]. The authors use as a coin only Generalized HR, and show that the algorithm has very low robustness in this case. They investigated the algorithm's stability against phase errors in the HR. Currently, machine learning (ML) is a diverse and modern topic that is used for a variety of tasks that include speech recognition [45], image and video generation [46; 47], and medical diagnostics [48]. The quantum analog of the classical ML is an object of high scientific interest too [49; 50]. In our previous work [51], we discussed discrete time QRWS on a hypercube algorithm with a walk coin constructed by one generalized HR and a phase multiplier. Numerical simulations for some particular cases (coins consisting of 1, 2, and 3 qubits) and particular configuration of the parameters showed high robustness of the algorithm to inaccuracies in those parameters. In the current work, we investigate the stability of the modified QRWS algorithm (constructed as in [51]) in the case of qudit coins with a size from 2 to 12. Linear and nonlinear functional dependencies between walk coin parameters are studied, and we show that some of those relations lead to high robustness of QRWS on hypercube. Here, we make a detailed analysis of the quantum algorithm's robustness to simultaneous variations in both the generalized Householder phase and an additional parameter introduced by the nonlinear functions mentioned above. We show that there is a two-dimensional region in the combined space spanned by those parameters that gives very high robustness to the algorithm. Next, we point out that the modified algorithm becomes more stable than the one with coin built by just HR (as in [44]). Most of the results here are based on numerical methods, such as Monte Carlo simulations and ML, in addition to various numerical statistical techniques used to analyze the modified algorithm's robustness for larger set of coin register size. This paper is organized as follows: In Section 2, a particular modification of the QRWS algorithm has been described. First, in Section 2.1, a brief description of QRWS algorithm and its quantum circuit is given. Next, in Section 2.2, we show the definition of the HR and its use in the construction of the walk coin. The simulation's results of the QRWS algorithm's walk coin with arbitrary dimension using HR and an additional phase are explained in Section 3. In Section 3.1, our Monte Carlo method for studying QRWS algorithm is explained and a few examples with a qudit coin are given.