Hamming weight Archives - IEEE Transactions on Quantum Engineering

A Divide-and-Conquer Approach to Dicke State Preparation

We present a divide-and-conquer approach to deterministically prepare Dicke states |Dnk⟩ (i.e., equal-weight superpositions of all n -qubit states with Hamming weight k ) on quantum computers. In an experimental evaluation for up to n=6 qubits on IBM Quantum Sydney and Montreal devices, we achieve significantly higher state fidelity compared to previous results. The fidelity gains are achieved through several techniques: our circuits […]

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 […]