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Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…

Quantum Physics · Physics 2007-05-23 David Collins

Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a…

Statistical Finance · Quantitative Finance 2024-12-05 Stijn De Backer , Luis E. C. Rocha , Jan Ryckebusch , Koen Schoors

We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…

Quantum Physics · Physics 2008-10-08 E. Agliari , A. Blumen , O. Muelken

A discrete-time method for solving problems in optimal quantum control is presented. Controlling the time discretized markovian dynamics of a quantum system can be reduced to a Markov-decision process. We demonstrate this method in this…

Quantum Physics · Physics 2012-06-05 Jon R. Grice , David A. Meyer

In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…

Quantum Physics · Physics 2016-10-20 Krišjānis Prūsis , Jevgēnijs Vihrovs , Thomas G. Wong

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

Quantum Physics · Physics 2024-07-17 Boxuan Ai

In this paper, the aim is to develop a quantum counterpart to classical Markov decision processes (MDPs). Firstly, we provide a very general formulation of quantum MDPs with state and action spaces in the quantum domain, quantum…

Quantum Physics · Physics 2024-09-19 Naci Saldi , Sina Sanjari , Serdar Yuksel

Distributed computing seems to be a natural approach to overcome size limitations of quantum computers in terms of number of qubits. But one lacks an efficient distribution approach to deal systematically with potential algorithms. This…

Quantum Physics · Physics 2012-08-21 Iaakov Exman , Efrat Levy

Quantum walks are a promising framework that can be used to both understand and implement quantum information processing tasks. The quantum stochastic walk is a recently developed framework that combines the concept of a quantum walk with…

Quantum Physics · Physics 2018-12-07 Bruno G. Taketani , Luke C. G. Govia , Frank K. Wilhelm

We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover's database search algorithm. Some…

Quantum Physics · Physics 2007-05-23 H. De Raedt , A. H. Hams , K. Michielsen , S. Miyashita , K. Saito

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…

Quantum Physics · Physics 2020-04-06 Václav Potoček

We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…

Mathematical Physics · Physics 2019-01-08 Carlos F. Lardizabal

Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for…

Quantum Physics · Physics 2016-02-04 C. Vlachou , J. Rodrigues , P. Mateus , N. Paunković , A. Souto

Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…

Quantum Physics · Physics 2021-05-26 Peter K. Schuhmacher , Luke C. G. Govia , Bruno G. Taketani , Frank K. Wilhelm

The problem of reducing a Hidden Markov Model (HMM) to one of smaller dimension that exactly reproduces the same marginals is tackled by using a system-theoretic approach. Realization theory tools are extended to HMMs by leveraging suitable…

Machine Learning · Computer Science 2024-06-24 Tommaso Grigoletto , Francesco Ticozzi

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…

Quantum Physics · Physics 2018-01-17 Antonio Sciarretta

Quantum walks contribute significantly to developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the $d$-dimensional quantum domain, where $d>2$, and show its…

Quantum Physics · Physics 2024-10-04 Amit Saha , Debasri Saha , Amlan Chakrabarti

This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…

High Energy Physics - Phenomenology · Physics 2007-05-23 Carl M. Bender , Lawrence R. Mead , Kimball A. Milton

We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reductions. In addition, we give a procedure for constructing a…

Combinatorics · Mathematics 2022-12-02 Mark Kempton , John Tolbert

The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are…

Quantum Physics · Physics 2009-11-07 David Collins