A new time-series model based on quantum walk

Abstract

The quantum walk (QW) was introduced as a quantum counterpart of the classical random walk. A number of non-classical properties of the QW have been shown, e.g., ballistic spreading, anti-bellshaped limit density, localization. Since around 2000, extensive research has been conducted in both theoretical aspects as well as the practical application of QWs. However, the application of a QW to the time-series analysis is not known. On the other hand, it is well known that the ARMA or GARCH models have been widely used in economics and finance. These models are studied under some suitable stationarity conditions. In this paper, we propose a new time-series model based on the QW, which does not assume such a stationarity. Therefore, our method would be applicable to the non-stationary time series.Abbr. title: A new time-series model based on quantum walk

Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk

“…In fundamental fields, there have been many attempts to analyze these evolution models mathematically [ 6 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ] due to varying behavior of QWs depending on the conditions or settings of time and space. In applied fields, their unique behavior is useful for implementing quantum structures or quantum analogs of existing models; therefore, various QW-based models have been considered for subjects such as time-series analysis [ 23 ], topological insulators [ 24 , 25 ], radioactive waste reduction [ 26 , 27 ], and optics [ 28 , 29 ]. In addition, the contribution to quantum information technology is becoming more prominent these days.…”

Directivity of Quantum Walk via Its Random Walk Replica

“…Indeed, quantum walks exhibit versatile behavior depending on conditions or settings of time and space, so there are many studies about their mathematical analysis [6][7][8][9][10][11][12][13]. In addition, their unique behavior is useful for implementing quantum structures or quantum analogs of existing models; therefore, the application is considered in fields such as quantum teleportation [14,15], time series analysis [16], topological insulators [17,18], radioactive waste reduction [19,20], and optics [21]. Moreover, properties of quantum walks have also been simulated numerically [22] or experimentally via the interference of classical light waves [23][24][25].…”

A time-Series Model Based on Quanntum Walk in terms of Quantum Bernoulli Noise

“…On the other hand, time-series models such as the ARMA or GARCH play an important role in the research of eco-nomics and finance [2]. Recently, by using quantum walks with finite number degrees of freedom, Konno [4] has introduced a new time-series model and shown its interesting properties.…”

“…In this paper, motivated by the recent work of Konno [4], we would like to construct a time-series model in terms of the QBN-based walk and illustrate its basic properties.Throughout this paper, Z always denotes thesetof all integers, while N means the Set of all nonnegative integers. We denote by Γ the finite power set of N, namely Γ = { σ | σ ⊂ N and # σ < ∞ }, (1.1) where #σ means the cardinality of σ.…”