Related papers: Efficient tests for equivalence of hidden Markov p…

This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…

We demonstrate the application of pattern recognition algorithms via hidden Markov models (HMM) for qubit readout. This scheme provides a state-path trajectory approach capable of detecting qubit state transitions and makes for a robust…

The problems of large-scale multiple testing are often encountered in modern scientific researches. Conventional multiple testing procedures usually suffer considerable loss of testing efficiency due to the lack of consideration of…

In this paper we define new Monte Carlo type classical and quantum hitting times, and we prove several relationships among these and the already existing Las Vegas type definitions. In particular, we show that for some marked state the two…

We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of…

In the theory of testing for Markovian processes developed so far, exponentially timed internal actions are not admitted within processes. When present, these actions cannot be abstracted away, because their execution takes a nonzero amount…

Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…

In this paper, we consider the optimal stopping problem on semi-Markov processes (SMPs) with finite horizon, and aim to establish the existence and computation of optimal stopping times. To achieve the goal, we first develop the main…

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…

One way to approximate a quantum annealing schedule is to use multiple quantum walks chained together, without intermediate measurements, to produce a multi-stage quantum walk (MSQW). Previous work has shown that a MSQW is better than QAOA…

Here, a new two-dimensional process, discrete in time and space, that yields the results of both a random walk and a quantum random walk, is introduced. This model describes the population distribution of four coin states |1>,-|1>, |0> -|0>…

In a quantum (inhomogeneous) Markov process $\rho_1:=\Gamma_1(\rho)$, $\rho_2:=\Gamma_1(\rho_1)$, ..., where $\Gamma_i$ are CPTP maps and $\rho$ is the initial state, the the state of the system is either oscillatory or convergent to a…

There are at least three models of discrete-time quantum walks (QWs) on graphs currently under active development. In this work we focus on the equivalence of two of them, known as Szegedy's and staggered QWs. We give a formal definition of…

Methods to find the solution state for optimization problems encoded into Ising Hamiltonians are a very active area of current research. In this work we compare the quantum approximate optimization algorithm (QAOA) with multi-stage quantum…

Szegedy's quantum walk is a quantization of a classical random walk or Markov chain, where the walk occurs on the edges of the bipartite double cover of the original graph. To search, one can simply quantize a Markov chain with absorbing…

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…

A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are…

We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…

Variational quantum algorithms have been introduced as a promising class of quantum-classical hybrid algorithms that can already be used with the noisy quantum computing hardware available today by employing parameterized quantum circuits.…

Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$.…