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Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…
Present quantum computers are constrained by limited qubit capacity and restricted physical connectivity, leading to challenges in large-scale quantum computations. Distributing quantum computations across a network of quantum computers is…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero stationary distributions (localization), thus distinguishing themselves…
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…
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…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
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…
Mainstream machine-learning techniques such as deep learning and probabilistic programming rely heavily on sampling from generally intractable probability distributions. There is increasing interest in the potential advantages of using…
Quantum walks are expected to serve important modelling and algorithmic applications in many areas of science and mathematics. Although quantum walks have been successfully implemented physically in recent times, no major efforts have been…
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
In this paper, we investigate the simulation of continuous-time quantum walks on specific classes of graphs, for which it is possible to fast-forward the time-evolution operator to achieve constant-time simulation complexity and to perform…