The article describes how Discrete Time Quantum Walks (DTQWs) provide a useful means for recreating-quantum physical behaviour on graph structures, focusing on the effects of ballistic propagating effects and destructive interference, Methods were developed to simulate DTQWs using classical methods to visualise the changes in the probability distribution of the walker over time, specifically focusing on the Distal Path of the walker. A hybrid quantum machine learning model has been developed which combines the quantum features of quantum walk dynamics with classic technical indicators such as Relative Strength Index (RSI) and Moving Average Convergence Divergence (MACD), to enable the classification of financial trends. The classification model was trained on a synthetically balanced dataset created using Synthetic Minority Over-sampling Technique SMOTE and performance was assessed using standard metrics such as accuracy, precision and recall. The simulation results were evaluated and visualised in terms of their probability distributions. A successful model has been found which produces similar forecasting results compared with those achieved by normal benchmark methods for stock movement and portfolio construction.The article describes how Discrete Time Quantum Walks (DTQWs) provide a useful means for recreating-quantum physical behaviour on graph structures, focusing on the effects of ballistic propagating effects and destructive interference, Methods were developed to simulate DTQWs using classical methods to visualise the changes in the probability distribution of the walker over time, specifically focusing on the Distal Path of the walker. A hybrid quantum machine learning model has been developed which combines the quantum features of quantum walk dynamics with classic technical indicators such as Relative Strength Index (RSI) and Moving Average Convergence Divergence (MACD), to enable the classification of financial trends. The classification model was trained on a synthetically balanced dataset created using Synthetic Minority Over-sampling Technique SMOTE and performance was assessed using standard metrics such as accuracy, precision and recall. The simulation results were evaluated and visualised in terms of their probability distributions. A successful model has been found which produces similar forecasting results compared with those achieved by normal benchmark methods for stock movement and portfolio construction.

International Conference on Artificial Intelligence and Speech Technology (AIST)Nov 27, 20250 citations

Open quantum walks on graphs

Stéphane Attal, Francesco Petruccione, Ilya Sinayskiy

arXiv:1401.3305Physics Letters AMar 21, 201271 citations

Multiparticle quantum walks for distinguishing hard graphs

Sachin Kasture, Shaheen Acheche, Loïc Henriet +1 more

Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular we look at how we can compare multi-particle quantum walks and well known classical WL tests and how quantum walks can be used to distinguish hard graphs like CFI graphs which k-WL tests cannot distinguish. We provide theoretical proofs and empirical results to show that a k-QW with input superposition states distinguishes k-CFI graphs. In addition we also prove that a k-1 QW with localized input states distinguishes k-CFI graphs. We also prove some additional results about strongly regular graphs (SRGs).Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular we look at how we can compare multi-particle quantum walks and well known classical WL tests and how quantum walks can be used to distinguish hard graphs like CFI graphs which k-WL tests cannot distinguish. We provide theoretical proofs and empirical results to show that a k-QW with input superposition states distinguishes k-CFI graphs. In addition we also prove that a k-1 QW with localized input states distinguishes k-CFI graphs. We also prove some additional results about strongly regular graphs (SRGs).

arXiv:2501.03683Jan 7, 20250 citations

Quantum Walks on Finite Graphs

Renato Portugal

Springer eBooksJan 1, 20130 citations

Coined Quantum Walks on Graphs

Renato Portugal

Quantum science and technologyJan 1, 20181 citation

Quantum walks with a one-dimensional coin

Alessandro Bisio, Giacomo Mauro D’Ariano, Marco Erba +2 more

Quantum walks (QWs) describe particles evolving coherently on a graph. The internal degree of freedom corresponds to a Hilbert space, called a coin system. We consider QWs on Cayley graphs of some group $G$ . In the literature, investigations concerning infinite $G$ have been focused on graphs corresponding to $G={\mathbb{Z}}^{d}$ with a coin system of dimension 2, whereas for a one-dimensional coin (so-called scalar QWs) only the case of finite $G$ has been studied. Here we prove that the evolution of a scalar QW with $G$ infinite Abelian is trivial, providing a thorough classification of this kind of walks. Then we consider the infinite dihedral group ${D}_{\ensuremath{\infty}}$, that is, the unique non-Abelian group $G$ containing a subgroup $H\ensuremath{\cong}\mathbb{Z}$ with two cosets. We characterize the class of QWs on the Cayley graphs of ${D}_{\ensuremath{\infty}}$, and, via a coarse-graining technique, we show that it coincides with the class of spinorial walks on $\mathbb{Z}$ which satisfies parity symmetry. This class of QWs includes the Weyl and the Dirac QWs. Remarkably, there exist also spinorial walks that are not coarse graining of a scalar QW, such as the Hadamard walk.Quantum walks (QWs) describe particles evolving coherently on a graph. The internal degree of freedom corresponds to a Hilbert space, called a coin system. We consider QWs on Cayley graphs of some group $G$. In the literature, investigations concerning infinite $G$ have been focused on graphs corresponding to $G={\mathbb{Z}}^{d}$ with a coin system of dimension 2, whereas for a one-dimensional coin (so-called scalar QWs) only the case of finite $G$ has been studied. Here we prove that the evolution of a scalar QW with $G$ infinite Abelian is trivial, providing a thorough classification of this kind of walks. Then we consider the infinite dihedral group ${D}_{\ensuremath{\infty}}$, that is, the unique non-Abelian group $G$ containing a subgroup $H\ensuremath{\cong}\mathbb{Z}$ with two cosets. We characterize the class of QWs on the Cayley graphs of ${D}_{\ensuremath{\infty}}$, and, via a coarse-graining technique, we show that it coincides with the class of spinorial walks on $\mathbb{Z}$ which satisfies parity symmetry. This class of QWs includes the Weyl and the Dirac QWs. Remarkably, there exist also spinorial walks that are not coarse graining of a scalar QW, such as the Hadamard walk.

arXiv:1603.07666Physical Review AJun 24, 201621 citations

G

. In the literature, investigations concerning infinite

G

have been focused on graphs corresponding to

G={\mathbb{Z}}^{d}

with a coin system of dimension 2, whereas for a one-dimensional coin (so-called scalar QWs) only the case of finite

G

has been studied. Here we prove that the evolution of a scalar QW with

G

infinite Abelian is trivial, providing a thorough classification of this kind of walks. Then we consider the infinite dihedral group ${D}_{\ensuremath{\infty}}$, that is, the unique non-Abelian group

G

containing a subgroup $H\ensuremath{\cong}\mathbb{Z}$ with two cosets. We characterize the class of QWs on the Cayley graphs of ${D}_{\ensuremath{\infty}}$, and, via a coarse-graining technique, we show that it coincides with the class of spinorial walks on

\mathbb{Z}

which satisfies parity symmetry. This class of QWs includes the Weyl and the Dirac QWs. Remarkably, there exist also spinorial walks that are not coarse graining of a scalar QW, such as the Hadamard walk.