Addressing the Current Challenges of Quantum Machine Learning through Multi-Chip Ensembles

TL;DR

This work proposes a multi-chip ensemble VQC framework that systematically overcomes noise, limited scalability, and poor trainability in Variational Quantum Circuits on current hardware, and uniquely reduces both quantum error bias and variance simultaneously without additional mitigation overhead.

Abstract

Practical Quantum Machine Learning (QML) is challenged by noise, limited scalability, and poor trainability in Variational Quantum Circuits (VQCs) on current hardware. We propose a multi-chip ensemble VQC framework that systematically overcomes these hurdles. By partitioning high-dimensional computations across ensembles of smaller, independently operating quantum chips and leveraging controlled inter-chip entanglement boundaries, our approach demonstrably mitigates barren plateaus, enhances generalization, and uniquely reduces both quantum error bias and variance simultaneously without additional mitigation overhead. This allows for robust processing of large-scale data, as validated on standard benchmarks (MNIST, FashionMNIST, CIFAR-10) and a real-world PhysioNet EEG dataset, aligning with emerging modular quantum hardware and paving the way for more scalable QML.

Figures (6)

• Figure 1: Comparison between Single-chip vs Multi-chip Ensemble VQCs. (a) Conventional single-chip approach processes entire input $\boldsymbol{X}$ through a single large VQC. (b) Multi-chip ensemble partitions input into subvectors ($\boldsymbol{x}_1,...\boldsymbol{x}_k$), each processed by independent smaller VQCs on separate chips with outputs classically combined to produce $\boldsymbol{Y}$. This distributed architecture enhances scalability, trainability, and noise resilience.
• Figure 2: Experimental Results on MNIST. (a) Training and validation loss across epochs, showing multi-chip ensembles outperform single-chip VQCs and classical baselines. (b) Generalization error, with lower values indicating better generalization. (c) Quantum error under simulated noise, demonstrating multi-chip models' superior noise resilience compared to both standard and ZNE-mitigated single-chip VQCs. Ensemble 98-Chip processes full-dimensional data without classical reduction, while DimReduc models use multi-chip ensembles with dimension reduction.
• Figure 3: Conceptual comparison of data processing pipelines for high-dimensional inputs. (a) Single-Chip VQC: High-dimensional data typically requires a classical encoder for dimension reduction before being processed by a single VQC, followed by a classical decoder. This can lead to information loss. (b) Multi-Chip Ensemble VQC (Reduced): Demonstrates a multi-chip ensemble approach where the data, after classical dimension reduction by an encoder, is partitioned and processed by multiple smaller VQCs, with outputs combined by a classical decoder. (c) Multi-Chip Ensemble VQC (Full-Dimensional): Our proposed approach, where high-dimensional input data is directly partitioned (e.g., feature-wise) across multiple independent VQCs without prior classical dimension reduction. Outputs are combined by a classical decoder. This architecture aims to leverage the full dimensionality of the data while distributing the quantum computational load.
• Figure 4: Experimental Results on FashionMNIST. (a) Model Performance: Training and validation loss (MSE) over epochs. (b) Generalizability: Generalization error. (c) Noise Resilience: Quantum error over epochs, including comparison with ZNE. Model naming conventions ('Ensemble 98-Chip', 'DimReduc 2/4-Chip', 'Classical', 'Single-Chip', 'ZNE Single-Chip') are consistent with Figure \ref{['Fig_Results_MNIST']}. The results corroborate trends observed on MNIST, showing superior performance and robustness of the multi-chip ensemble approaches.
• Figure 5: Experimental Results on CIFAR-10. (a) Model Performance: Training and validation loss (MSE) over epochs. (b) Generalizability: Generalization error. (c) Noise Resilience: Quantum error over epochs, including comparison with ZNE. The Ensemble 256-Chip model processes full-dimensional CIFAR-10 data. 'DimReduc X-Chip' models use X chips with prior classical dimension reduction. The results further validate the benefits of the multi-chip ensemble framework on a more complex image dataset.