A weighted quantum ensemble of homogeneous quantum classifiers

TL;DR

The paper addresses improving predictive accuracy with quantum classifiers by forming a weighted homogeneous ensemble that leverages an indexing register to subsample training points and features in superposition, enabling quantum-parallel execution of $2^d$ internal classifiers. The approach relies on a hybrid training pipeline where weights are learned classically from internal-classifier outputs and then encoded in circuit amplitudes for test-time deployment. Empirical evaluation over 11 real-world UCI binary datasets shows the weighted ensemble generally surpasses single quantum classifiers and can be competitive with XGBoost under certain conditions, with performance influenced by data normalization and classifier type. Overall, the work presents a non-variational, NISQ-friendly ensemble framework that exploits data-subset diversity to enhance quantum learning and offers avenues for further diversification strategies.

Abstract

Ensemble methods in machine learning aim to improve prediction accuracy by combining multiple models. This is achieved by ensuring diversity among predictors to capture different data aspects. Homogeneous ensembles use identical models, achieving diversity through different data subsets, and weighted-average ensembles assign higher influence to more accurate models through a weight learning procedure. We propose a method to achieve a weighted homogeneous quantum ensemble using quantum classifiers with indexing registers for data encoding. This approach leverages instance-based quantum classifiers, enabling feature and training point subsampling through superposition and controlled unitaries, and allowing for a quantum-parallel execution of diverse internal classifiers with different data compositions in superposition. The method integrates a learning process involving circuit execution and classical weight optimization, for a trained ensemble execution with weights encoded in the circuit at test-time. Empirical evaluation demonstrate the effectiveness of the proposed method, offering insights into its performance.

Figures (7)

• Figure 1: Circuit diagram of the ensemble at test time. The control register is prepared with the weights encoded in the amplitudes. Then, the controlled permutation unitary is executed, acting on the data register of the classifier. The data register then partially controls ($a$ qubits out of $n$ and $b$ qubits out of $m$) a NOT gate acting on the ancilla qubit, which is subsequently measured for data selection. The classifier is executed, and the related output qubit is measured. Specifically, the displayed circuit is designed to execute a quantum classifier of type cdc.
• Figure 2: Circuit diagram of the ensemble at training time. The control register is prepared in a balanced superposition using Hadamard gates. Then, the controlled permutation unitary is executed, acting on the data register of the classifier. The data register then partially controls a NOT gate acting on the ancilla qubit, which is subsequently measured for data selection. The classifier is executed, and finally, the control register is measured to get an internal classifier with the related output. Specifically, the displayed circuit is designed to execute a quantum classifier of type cdc.
• Figure 3: Accuracy performance with statevector simulation of single classifiers (full), ensemble's internal classifiers (internal), weighted ensemble and XGBoost in terms of aggregated results over 10 Monte Carlo runs for 11 real-world datasets. The considered internal models are the quantum cosine, quantum distance and SWAP test classifiers. Multiple control register sizes (d) and normalization techniques are taken into account.
• Figure 4: Accuracy performance of local simulation with 8192 shots, considering the quantum distance classifier on 11 datasets over 10 Monte Carlo runs. The left panel shows the accuracy comparison between local simulation and statevector simulation, where points above the bisector indicate accuracy degradation. The right panel presents the accuracy comparison of single and ensemble classifier ($d=5$) with local simulation for the different normalization techniques.
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