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Russian Microelectronics

Quantum Random Forest Model Prediction Circuit Gate Complexity

Kamil Ravilevich Khadiev, L. I. Safina, I. Zinnatullin

Published Dec 1, 2025• 2 citations
Publisher

Abstract

Abstract In this work, we present quantum random forest prediction circuits for binary and multiclass classification problems and their gate complexities. Gate complexity is defined as the number of elementary one- and two-qubit gates. The presented prediction algorithm requires fewer elementary gates than the general upper bound.
DOI
10.1134/s106373972560205x

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This study investigates the application of machine learning techniques for predicting gate depth in quantum computational systems, focusing on the relationship between quantum circuit parameters and computational performance. Using a dataset of 50 observations encompassing qubit count, gate depth, entanglement rate, and logical error rate, we developed and compared Linear Regression (LR) and Random Forest Regression (RFR) models for gate depth prediction. The research addresses critical challenges in quantum fault tolerance and circuit optimization, which are essential for achieving scalable quantum computation. Our analysis revealed strong negative correlation (-0.65) between qubit count and logical error rate, while gate depth showed moderate positive correlation (0.62) with error rates. The Random Forest model demonstrated superior performance with R² values of 0.96068 on training data and 0.87262 on testing data, significantly outperforming Linear Regression (R²: 0.87552 training, 0.60257 testing). Error metrics further confirmed RFR's superiority, achieving RMSE of 2.33 (training) and 2.97 (testing) compared to LR's 4.15 and 5.25 respectively. The study highlights the importance of quantum error correction mechanisms and the inherent trade-offs between circuit complexity and computational reliability. Both models showed expected performance degradation from training to testing, with RFR maintaining better generalization capabilities. These findings contribute to the development of typed models for quantum mechanics in computational applications, offering insights into quantum circuit optimization and fault-tolerant design. The research demonstrates that ensemble methods like Random Forest provide more robust predictions for quantum system parameters, supporting the advancement of practical quantum computing implementations and algorithm development. KeyWords: Quantum Computation, Gate Depth Prediction, Random Forest Regression, Quantum Error Correction, Machine Learning, Fault Tolerance.
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