A Model for Circuit Execution Runtime And Its Implications for Quantum Kernels At Practical Data Set Sizes

TL;DR

This paper presents a predictive model for quantum circuit execution time in quantum kernel estimation, validated with real IBM Quantum data, highlighting current speed limitations for large datasets in quantum machine learning.

Contribution

Introduces a heuristic model for quantum circuit runtime based on quantum volume layers, validated with empirical data, and discusses implications for quantum kernel methods at practical data sizes.

Findings

Model accurately predicts runtime for hundreds of feature vectors

Current quantum speeds limit processing to hours for large datasets

Improvements in quantum speed are needed for scalable quantum machine learning

Abstract

Quantum machine learning (QML) is a fast-growing discipline within quantum computing. One popular QML algorithm, quantum kernel estimation, uses quantum circuits to estimate a similarity measure (kernel) between two classical feature vectors. Given a set of such circuits, we give a heuristic, predictive model for the total circuit execution time required, based on a recently-introduced measure of the speed of quantum computers. In doing so, we also introduce the notion of an "effective number of quantum volume layers of a circuit", which may be of independent interest. We validate the performance of this model using synthetic and real data by comparing the model's predictions to empirical runtime data collected from IBM Quantum computers through the use of the Qiskit Runtime service. At current speeds of today's quantum computers, our model predicts data sets consisting of on the order of hundreds of feature vectors can be processed in order a few hours. For a large-data workflow, our model's predictions for runtime imply further improvements in the speed of circuit execution -- as well as the algorithm itself -- are necessary.