One-Dimensional Lazy Quantum walk in Ternary System

TL;DR

This paper introduces a one-dimensional three-state lazy quantum walk, demonstrating its circuit implementation in ternary quantum logic and addressing scalability with multi-qutrit systems.

Contribution

It presents the first circuit realization of lazy quantum walks in ternary quantum systems with logical mapping and scalability analysis.

Findings

Efficient quantum circuits for lazy quantum walks in ternary systems

Logical mapping of position space onto multi-qutrit states

Scalability analysis for n-qutrit systems

Abstract

Quantum walks play an important role for developing quantum algorithms and quantum simulations. Here we present one dimensional three-state quantum walk(lazy quantum walk) and show its equivalence for circuit realization in ternary quantum logic for the first of its kind. Using an appropriate logical mapping of the position space on which a walker evolves onto the multi-qutrit states, we present efficient quantum circuits considering the nearest neighbour position space for the implementation of lazy quantum walks in one-dimensional position space in ternary quantum system. We also address scalability in terms of $n$-qutrit ternary system with example circuits for a three qutrit state space.