Grover's Algorithm and Many-Valued Quantum Logic

Abstract

As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model, in which the information and transformations can be expressed in any arity, and analyse the structural and behavioural properties while preserving the semantics; namely, searching for the unique preimage to an output a function. We conclude by demonstrating that the generalised procedure retains $O(\sqrt{N})$ time complexity.

References in corpus (5)

• High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments
• High-dimensional optical quantum logic in large operational spaces
• Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits
• Hybrid quantum computing with ancillas
• Generalization of the Deutsch algorithm using two qudits

Cited by in corpus (1)

• Circuit Design for $k$-coloring Problem and Its Implementation in Any Dimensional Quantum System