ABSTRACT
Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic subroutine in many quantum algorithms and plays an important role in studying physical phenomena. Simulating quantum walk processes is computationally challenging for classical processors. With an increasing improvement in qubits fidelity and qubits number in a single register, there is a potential to improve quantum walks simulations substantially. However, efficient ways to simulate quantum walks in qubit registers still have to be explored. Here, we explore the relationship between quantum walk on graphs and quantum circuits. Firstly, we discuss ways to obtain graphs provided quantum circuit. We then explore techniques to represent quantum walk on a graph as a quantum circuit. Specifically, we study hypercube graphs and arbitrary graphs. Our approach to studying the relationship between graphs and quantum circuits paves way for the efficient implementation of quantum walks algorithms on quantum computers.
ABSTRACT
Quantum walks have been employed widely to develop new tools for quantum information processing recently. A natural quantum walk dynamics of interacting particles can be used to implement efficiently the universal quantum computation. In this work quantum walks of electrons on a graph are studied. The graph is composed of semiconductor quantum dots arranged in a circle. Electrons can tunnel between adjacent dots and interact via Coulomb repulsion, which leads to entanglement. Fermionic entanglement dynamics is obtained and evaluated.
