One-Dimensional Lazy Quantum walk in Ternary System

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.

arXiv comment13 pages, 12 figures, and 10 tables

References in corpus (24)

• Quantum random walks - an introductory overview
• Quantum Computation and Decision Trees
• A Quantum Random Walk Search Algorithm
• Quantum walks: a comprehensive review
• Exponential algorithmic speedup by quantum walk
• On the relationship between continuous- and discrete-time quantum walk
• Multi-valued Logic Gates for Quantum Computation
• Controlling discrete quantum walks: coins and intitial states
• Quantum Information Scrambling in a Superconducting Qutrit Processor
• A random walk approach to quantum algorithms
• Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures
• Asymptotic Improvements to Quantum Circuits via Qutrits
• Grover Search with Lackadaisical Quantum Walks
• Implementation of a Walsh-Hadamard gate in a superconducting qutrit
• Synthesis of Multivalued Quantum Logic Circuits by Elementary Gates
• Experimental Implementation of Quantum Walks on IBM Quantum Computers
• Time-efficient implementation of quantum search with qudits
• Weak Limit of the 3-State Quantum Walk on the Line
• Faster Search by Lackadaisical Quantum Walk
• Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer
• Applications of Multi-Valued Quantum Algorithms
• Search on Vertex-Transitive Graphs by Lackadaisical Quantum Walk
• An efficient protocol of quantum walk in circuit QED
• One dimensional lazy quantum walks and occupancy rate

Cited by in corpus (8)

• Asymptotically Improved Circuit for $d$-ary Grover's Algorithm with Advanced Decomposition of $n$-qudit Toffoli Gate
• QuDiet: A Classical Simulation Platform for Qubit-Qudit Hybrid Quantum Systems
• Circuit Design for $k$-coloring Problem and Its Implementation in Any Dimensional Quantum System
• Nonlinear three-state quantum walks
• Localization of space-inhomogeneous three-state quantum walks
• Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits
• Universal dynamical scaling laws in three-state quantum walks
• Spectral analysis of three-state quantum walks with general coin matrices