Related papers: Szegedy Walk Unitaries for Quantum Maps
The development of universal quantum computers has achieved remarkable success in recent years, culminating with the quantum supremacy reported by Google. Now is possible to implement short-depth quantum circuits with dozens of qubits and…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Quantum magic, which accounts for the non-stabilizer content of a state, is essential for universal quantum computation beyond classically simulable resources. We investigate the generation and evolution of quantum magic in discrete-time…
Quantum walks have emerged as a transformative paradigm in quantum information processing and can be applied to various graph problems. This study explores discrete-time quantum walks on simplicial complexes, a higher-order generalization…
This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states,…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
We define the quaternionic quantum walk on a finite graph and investigate its properties. This walk can be considered as a natural quaternionic extension of the Grover walk on a graph. We explain the way to obtain all the right eigenvalues…
A new model maps a quantum random walk described by a Hadamard operator to a particular case of a birth and death process. The model is represented by a 2D Markov chain with a stochastic matrix, i.e., all the transition rates are positive,…
We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…
A scheme that successfully employs quantum mechanics in the design of autonomous learning agents has recently been reported in the context of the projective simulation (PS) model for artificial intelligence. In that approach, the key…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain…
The quantization of the PageRank algorithm is a promising tool for a future quantum internet. Here we present a modification of the quantum PageRank introducing arbitrary phase rotations (APR) in the underlying Szegedy's quantum walk. We…
Computational advantages gained by quantum algorithms rely largely on the coherence of quantum devices and are generally compromised by decoherence. As an exception, we present a quantum algorithm for graph isomorphism testing whose…
Based on studies on four specific networks, we conjecture a general relation between the walk dimensions $d_{w}$ of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that $d_{w}$ of the…
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification.…
Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the…
The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. The circuit model usually implements a desired unitary…