Algorithms for Embedding Quantum-Dot Cellular Automata Networks onto a Quantum Annealing Processor

TL;DR

This paper explores methods to embed quantum-dot cellular automata networks onto a quantum annealing processor, enabling quantum simulations of QCA beyond classical limits.

Contribution

It introduces and compares two embedding algorithms for QCA networks onto flux-qubit processors, addressing a key challenge in quantum simulation.

Findings

The dense placement algorithm performs well with high flux-qubit yields.

The heuristic method offers flexible embedding options.

Benchmark results demonstrate the effectiveness of both algorithms.

Abstract

Advancements in computing based on qubit networks, and in particular the flux-qubit processor architecture developed by D-Wave System's Inc., have enabled the physical simulation of quantum-dot cellular automata (QCA) networks beyond the limit of classical methods. However, the embedding of QCA networks onto the available processor architecture is a key challenge in preparing such simulations. In this work, two approaches to embedding QCA circuits are characterized: a dense placement algorithm that uses a routing method based on negotiated congestion; and a heuristic method implemented in D-Wave's Solver API package. A set of benchmark QCA networks is used to characterise the algorithms and a stochastic circuit generator is employed to investigate the performance for different processor sizes and active flux-qubit yields.