Hilbert space Archives - IEEE Transactions on Quantum Engineering

One-Dimensional Lazy Quantum Walk in Ternary System

Quantum walks play an important role for developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional lazy quantum walk in the ternary quantum domain and show its equivalence for circuit realization in ternary quantum logic. Using an appropriate logical mapping of the position space on which a walker evolves […]

Finding Small and Large k-Clique Instances on a Quantum Computer

December 18, 2020Sara Ayman Metwalli; François Le Gall; Rodney Van MeterOpen Access, Quantum Computer Architecture, Quantum InformationComputers, Hamming weight, Hilbert space, Logic gates, Quantum computing, Qubit, Time complexity

Algorithms for triangle finding, the smallest nontrivial instance of the k -clique problem, have been proposed for quantum computers. Still, those algorithms assume the use of fixed access time quantum RAM. In this article, we present a practical gate-based approach to both the triangle-finding problem and its NP-hard k -clique generalization. We examine both constant factors for near-term implementation […]