Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm

TL;DR

This paper introduces a noise-aware heuristic qubit-assignment algorithm for NISQ devices, analyzing its performance, scalability, and dependence on topological graph properties of quantum algorithms, with promising results for path-like graphs up to 100 qubits.

Contribution

The paper presents a scalable, noise-aware heuristic qubit-assignment algorithm and analyzes its performance relative to graph properties and size of quantum algorithms.

Findings

Heuristic algorithm performs between brute-force and trivial assignments for small algorithms.

Topological graph properties influence heuristic performance on NISQ devices.

Algorithm scales well for quantum algorithms with path-like graph structures up to 100 qubits.

Abstract

The qubit-mapping problem aims to assign and route qubits of a quantum circuit onto a NISQ device in an optimized fashion, with respect to some cost function. Finding an optimal solution to this problem is known to scale exponentially in computational complexity; as such, it is imperative to investigate scalable qubit-mapping solutions for NISQ computation. In this work, a noise-aware heuristic qubit-assignment algorithm (which assigns initial placements for qubits in a quantum algorithm to qubits on a NISQ device, but does not route qubits during the quantum algorithm's execution) is presented and compared against the optimal \textit{brute-force} solution, as well as a trivial qubit assignment, with the aim to quantify the performance of our heuristic qubit-assignment algorithm. We find that for small, connected-graph algorithms, our heuristic-assignment algorithm faithfully lies in between the effective upper and lower bounds given by the brute-force and trivial qubit-assignment algorithms. Additionally, we find that the topological-graph properties of quantum algorithms with over six qubits play an important role in our heuristic qubit-assignment algorithm's performance on NISQ devices. Finally, we investigate the scaling properties of our heuristic algorithm for quantum processors with up to 100 qubits; here, the algorithm was found to be scalable for quantum-algorithms which admit path-like graphs. Our findings show that as the size of the quantum processor in our simulation grows, so do the benefits from utilizing the heuristic qubit-assignment algorithm, under particular constraints for our heuristic algorithm. This work thus characterizes the performance of a heuristic qubit-assignment algorithm with respect to the topological-graph and scaling properties of a quantum algorithm which one may wish to run on a given NISQ device.